Showing 1–50 of 234 results for author: Fujii, K

Quantum machine learning interatomic potential: Application of variational quantum algorithm

Authors: Kohei Numata, Wataru Mizukami, Kosuke Mitarai, Keisuke Fujii, Yutaka Imamura

Abstract: This study applied quantum circuit learning, a commonly used hybrid quantum-classical machine learning algorithm, to a machine learning interatomic potential (MLIP) for predicting the energies of molecules in molecular datasets. We retrained the ANI model using the quantum transfer learning architecture [Mari et al., Quantum, 4:340, 2020] and evaluated numerical accuracy with a quantum circuit sim… ▽ More This study applied quantum circuit learning, a commonly used hybrid quantum-classical machine learning algorithm, to a machine learning interatomic potential (MLIP) for predicting the energies of molecules in molecular datasets. We retrained the ANI model using the quantum transfer learning architecture [Mari et al., Quantum, 4:340, 2020] and evaluated numerical accuracy with a quantum circuit simulator. The evaluation confirmed that inserting a quantum circuit into the classical neural network of the MLIP yielded slightly higher accuracy than the fully classical neural network under certain conditions. In particular, the model incorporating a quantum circuit was more effective when the pretraining model had room for improvement in accuracy. These findings may contribute to advancing the application of quantum machine learning for MLIPs. △ Less

Submitted 30 July, 2026; originally announced July 2026.

Comments: 15 pages, 7 figures

Scalable Variational Quantum Optimization via Pauli Correlation Encoding: Application to Large-Scale Power Demand Portfolio Optimization

Authors: Takuya Yoshioka, Keita Sasada, Riku Usuki, Yuichiro Nakano, Keisuke Fujii

Abstract: Variational quantum algorithms offer a promising route to combinatorial optimization, but their applicability is limited by the challenge of encoding large-scale problems within restricted qubit resources. In this work, we introduce a scalable variational framework based on Pauli correlation encoding (PCE) and apply it to electric power demand portfolio optimization. Binary variables are represent… ▽ More Variational quantum algorithms offer a promising route to combinatorial optimization, but their applicability is limited by the challenge of encoding large-scale problems within restricted qubit resources. In this work, we introduce a scalable variational framework based on Pauli correlation encoding (PCE) and apply it to electric power demand portfolio optimization. Binary variables are represented through expectation values of Pauli correlation operators, which encode multi-body correlations of the quantum state and provide a continuous relaxation enabling compact representations with few qubits. We further propose a two-stage hybrid formulation, in which a time-averaged problem provides initialization for a time-resolved optimization. Numerical simulations demonstrate near-optimal performance across problem sizes ranging from $m$=18 to 10,296, with normalized cost gaps on the order of $10^{-4}$ relative to solutions with certified optimality. We show that the performance is governed by the interplay between continuous relaxation and discretization: the effective resolution of the correlator representation determines how reliably improvements in the continuous loss translate into better discrete solutions, with larger systems exhibiting more consistent behavior. Finally, we demonstrate robustness on a trapped-ion quantum processor, where high-quality solutions are obtained despite noise and finite sampling. These results establish PCE as a physically motivated and qubit-efficient framework for large-scale combinatorial optimization. △ Less

Submitted 27 July, 2026; originally announced July 2026.

Comments: 17 pages, 10 figures

Zero-level $CCZ$ Distillation

Authors: Tomohiro Itogawa, Yutaka Hirano, Yutaro Akahoshi, Keisuke Fujii

Abstract: Magic state distillation is a key component of fault-tolerant quantum computation, as it enables the implementation of non-Clifford gates such as the $T$ gate and the $CCZ$ gate via gate teleportation. However, conventional distillation protocols require a large number of logical qubits and introduce substantial spatial and temporal overhead, posing a significant bottleneck for scalable fault-tole… ▽ More Magic state distillation is a key component of fault-tolerant quantum computation, as it enables the implementation of non-Clifford gates such as the $T$ gate and the $CCZ$ gate via gate teleportation. However, conventional distillation protocols require a large number of logical qubits and introduce substantial spatial and temporal overhead, posing a significant bottleneck for scalable fault-tolerant quantum computation. In this work, we propose a zero-level distillation protocol that efficiently generates a high-fidelity logical $CCZ$ magic state using only physical qubits on a two-dimensional square lattice with nearest-neighbor interactions. Our method leverages the transversal $T/T^\dagger$ operation of the $[[ 8,3,2 ]]$ code to fault-tolerantly encode the state $\overline{CCZ}|+++\rangle$, which is subsequently teleported to three surface-code logical qubits via lattice surgery. To enable teleportation between codes with different distances, we introduce adaptively initialized teleportation (AIT), a tailored initialization procedure for the surface code. Numerical simulations demonstrate that the logical error rate scales as $p_L \simeq 300 \times p^2$ with respect to the physical error rate $p$. For example, the proposed method improves the logical error rate by approximately one and two orders of magnitude at $p = 10^{-3}$ and $p = 10^{-4}$, respectively, compared to conventional seven-$T$-gate approaches. The distillation circuit requires only 22 physical qubits, 3 logical qubits, and a circuit depth of 24, reducing the space-time overhead by a factor of approximately 5-10 compared to previous methods. This result highlights the practicality of $CCZ$-state distillation in early fault-tolerant quantum computation and offers a new direction toward resource-efficient physical-level magic state distillation beyond conventional $T$-state generation. △ Less

Submitted 20 May, 2026; originally announced May 2026.

Comments: 12 pages and 13 figures

Efficient Fault-Tolerant Ancilla Preparation for Quantum BCH codes via Cyclic Symmetry

Authors: Kohei Yamamoto, Keisuke Fujii

Abstract: One of the major challenges in realizing fault-tolerant quantum computers (FTQCs) is the requirement for a large number of physical qubits. To address this issue, high-rate quantum error correcting codes, which efficiently embed logical qubits into physical qubits, have recently attracted considerable attention. Among such codes, quantum BCH codes, which offer both high rates and large code distan… ▽ More One of the major challenges in realizing fault-tolerant quantum computers (FTQCs) is the requirement for a large number of physical qubits. To address this issue, high-rate quantum error correcting codes, which efficiently embed logical qubits into physical qubits, have recently attracted considerable attention. Among such codes, quantum BCH codes, which offer both high rates and large code distances, are promising yet underexplored candidates. However, no fault-tolerant ancilla preparation method specialized for this class had been established. We employ a two-stage approach (non-fault-tolerant preparation + entanglement distillation) for ancilla preparation. We then propose a framework for designing low-overhead distillation method that strategically leverages the cyclic symmetry of quantum BCH codes to determine which non-fault-tolerant circuits can successfully produce a fault-tolerant state. Numerical simulations on several high-performance quantum BCH codes up to 127 qubits demonstrate that our method achieves lower spatial overhead and logical error rates than conventional distillation circuits. Furthermore, we evaluated the logical error rates under a circuit-level noise model, and obtained performance benchmarks in realistic settings. This efficient state preparation technique is expected to contribute to the early realization of practical FTQCs, particularly on highly connected quantum platforms such as neutral atom systems. △ Less

Submitted 19 May, 2026; originally announced May 2026.

Comments: 19 pages, 15 figures

Adaptive Window Decoding based on Spatiotemporal Complementary Gap

Authors: Moeto Mishima, Riki Toshio, Kaito Kishi, Jun Fujisaki, Hirotaka Oshima, Shintaro Sato, Keisuke Fujii

Abstract: Real-time decoding plays a crucial role in practical fault-tolerant quantum computing. Window decoding, in which the decoding problem is divided into windows, is a promising approach. While reducing the window size is desirable for faster decoding, each window contains a buffer region whose size must typically be at least the code distance to avoid degrading the logical error rate, which limits ho… ▽ More Real-time decoding plays a crucial role in practical fault-tolerant quantum computing. Window decoding, in which the decoding problem is divided into windows, is a promising approach. While reducing the window size is desirable for faster decoding, each window contains a buffer region whose size must typically be at least the code distance to avoid degrading the logical error rate, which limits how much the window can shrink. In this paper, we propose an adaptive decoding scheme in which window decoding is first performed with a small buffer size and a decoding confidence (soft information) is computed; if the confidence is low, the buffer size is enlarged and decoding is redone. This approach reduces the average decoding time, since most shots are decoded with a small buffer. A central challenge in realizing this scheme is that existing forms of soft information are not directly applicable to window decoding, especially with a small buffer. We address this challenge by introducing a new form of soft information, the spatiotemporal complementary gap, specifically designed for this setting. Numerical simulations demonstrate that the proposed scheme reduces the average buffer size by approximately 40% while maintaining the logical error rate. △ Less

Submitted 14 May, 2026; originally announced May 2026.

Divide-and-Conquer Neural Network Surrogates for Quantum Sampling: Accelerating Markov Chain Monte Carlo in Large-Scale Constrained Optimization Problems

Authors: Yuya Kawamata, Yuichiro Nakano, Keisuke Fujii

Abstract: Sampling problems are promising candidates for demonstrating quantum advantage, and one approach known as quantum-enhanced Markov chain Monte Carlo [Layden, D. et al., Nature 619, 282-287 (2023)] uses quantum samples as a proposal distribution to accelerate convergence to a target distribution. On the other hand, many practical problems are large-scale and constrained, making it difficult to const… ▽ More Sampling problems are promising candidates for demonstrating quantum advantage, and one approach known as quantum-enhanced Markov chain Monte Carlo [Layden, D. et al., Nature 619, 282-287 (2023)] uses quantum samples as a proposal distribution to accelerate convergence to a target distribution. On the other hand, many practical problems are large-scale and constrained, making it difficult to construct efficient proposal distributions in classical methods and slowing down MCMC mixing. In this work, we propose a divide-and-conquer neural network surrogate framework for quantum sampling to accelerate MCMC under fixed Hamming weight constraints. Our method divides the interaction graph for an Ising problem into subgraphs, generates samples using QAOA for those subproblems with an XY mixer, and trains neural network surrogates conditioned on the Hamming weight to provide proposal distributions for each subset while preserving the constraint. In numerical experiments of Boltzmann sampling on 3-regular graphs, our method consistently accelerated mixing as the system size $N$ increased, with average improvements in the autocorrelation decay rate constant by speedup factors of about $20.3$ and $7.6$ over classical pair-flip methods based on nearest-neighbor and non-nearest-neighbor exchanges, respectively. We also applied the method to an MNIST feature mask optimization problem with $N=784$, obtaining faster energy convergence and a $2.03\%$ higher classification accuracy. These results show that our method enables efficient and scalable MCMC and can outperform classical methods for practical applications on NISQ devices. △ Less

Submitted 22 April, 2026; originally announced April 2026.

Comments: 12 pages, 9 figures

The Impact of Qubit Connectivity on Quantum Advantage in Noisy IQP Circuits

Authors: Leonardo Placidi, Enrico Rinaldi, Keisuke Fujii, Chen-Yu Liu

Abstract: Instantaneous Quantum Polynomial-time (IQP) circuits are a candidate for demonstrating near-term quantum advantage, as their sampling task is believed to be classically hard in the ideal theoretical setting under standard complexity-theoretic assumptions. In noisy implementations, however, this hardness can disappear once circuit depth exceeds a noise-dependent critical threshold. We show that qub… ▽ More Instantaneous Quantum Polynomial-time (IQP) circuits are a candidate for demonstrating near-term quantum advantage, as their sampling task is believed to be classically hard in the ideal theoretical setting under standard complexity-theoretic assumptions. In noisy implementations, however, this hardness can disappear once circuit depth exceeds a noise-dependent critical threshold. We show that qubit connectivity is a key parameter in this transition, since sparse architectures require additional routing to implement long-range interactions, thereby increasing compiled circuit depth. To make this explicit, we present a connectivity-aware analysis of compiled IQP circuits. For a fixed abstract IQP instance, different hardware connectivity graphs yield different compiled depths and thus different effective positions relative to the noisy-IQP simulatability boundary. We quantify this architecture-dependent shift using the compiled depth overhead and the corresponding simulatability margin. We combine analytic depth estimates for sparse geometries, including the two-dimensional grid, with native-gateset-aware compilation experiments across seven hardware-grounded experimental device models derived from publicly available topologies. To compare these device models under a unified empirical framework, we approximate the effective noise level primarily through reported two-qubit gate error rates. This lets us compare how much effective noise sparse and fully connected architectures can tolerate for the same position relative to the noisy-IQP simulatability boundary. Our results show that sparse connectivity requires a lower effective noise level to sustain the same margin relative to the noisy-IQP simulatability boundary, and they provide a quantitative framework for determining when compiled IQP experiments are likely to remain outside, or instead enter, the classically simulatable regime. △ Less

Submitted 24 July, 2026; v1 submitted 14 April, 2026; originally announced April 2026.

Comments: Accepted at IEEE QCE 2026 as a Technical Paper

STAR-Magic Mutation: Even More Efficient Analog Rotation Gates for Early Fault-Tolerant Quantum Computer

Authors: Riki Toshio, Shota Kanasugi, Jun Fujisaki, Hirotaka Oshima, Shintaro Sato, Keisuke Fujii

Abstract: We introduce STAR-magic mutation, an efficient protocol for implementing logical rotation gates on early fault-tolerant quantum computers. This protocol judiciously combines two of the latest state preparation protocols: transversal multi-rotation protocol and magic state cultivation. It achieves a logical rotation gate with a favorable error scaling of… ▽ More We introduce STAR-magic mutation, an efficient protocol for implementing logical rotation gates on early fault-tolerant quantum computers. This protocol judiciously combines two of the latest state preparation protocols: transversal multi-rotation protocol and magic state cultivation. It achieves a logical rotation gate with a favorable error scaling of $\mathcal{O}(θ_L^{2(1-Θ(1/d))}p_{\text{ph}})$, while requiring only the ancillary space of a single surface code patch. Here, $θ_L$ is the logical rotation angle, $p_{\text{ph}}$ is the physical error rate, and $d$ is the code distance. This scaling marks a significant improvement over the previous state-of-the-art, $\mathcal{O}(θ_L p_{\text{ph}})$, making our protocol particularly powerful for implementing a sequence of small-angle rotation gates, like Trotter-based circuits. Notably, for $θ_L \lesssim 10^{-5}$, our protocol achieves a two-order-of-magnitude reduction in both the execution time and the error rate of analog rotation gates compared to the standard $T$-gate synthesis using cultivated magic states. Building upon this protocol, we also propose a novel quantum computing architecture designed for early fault-tolerant quantum computers, dubbed ``STAR ver.~3". It employs a refined circuit compilation strategy based on Clifford+$T$+$φ$ gate set, rather than the conventional Clifford+$T$ or Clifford+$φ$ gate sets. We establish a theoretical bound on the feasible circuit size on this architecture and illustrate its capabilities by analyzing the spacetime costs for simulating the dynamics of quantum many-body systems. Specifically, we demonstrate that our architecture can simulate biologically-relevant molecules or lattice models at scales beyond the reach of exact classical simulation, with only a few hundred thousand physical qubits, even assuming a realistic error rate of $p_{\text{ph}}=10^{-3}$. △ Less

Submitted 24 March, 2026; originally announced March 2026.

Efficient Quantum Algorithm for Solving Linear Distributed Delay Differential Equations

Authors: Wataru Setoyama, Keisuke Fujii

Abstract: Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay differential equations and identify the condition under which it applies. Using the linear chain trick, the distributed delay differential equations can be embe… ▽ More Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay differential equations and identify the condition under which it applies. Using the linear chain trick, the distributed delay differential equations can be embedded into ordinary differential equations augmented with auxiliary variables, when the kernel function is characterized by a phase-type distribution. Employing the Schrödingerization method, the resulting equations can be embedded into the Schrödinger equation and efficiently solved by Hamiltonian simulation. Although this embedding requires the augmented differential equation to be semi-stable, we show that it is satisfied if and only if the original distributed-delay differential equations are semi-stable. The query complexity to obtain the normalized solution state of the $N$-dimensional delay system $|\mathbf{x}(t)\rangle\equiv\mathbf{x(t)}/\vert\vert\mathbf{x}(t)\vert\vert$ is $\mathcal{O}((st\vert\vert H\vert\vert_{\max}+\logε^{-1}/\log\logε^{-1})\vert\vert\mathbf{x}(0)\vert\vert/\vert\vert\mathbf{x}(t)\vert\vert)$ with $ε$, $g$, $H$, and $s$ being the allowable error, the dimension of the auxiliary variables associated with each kernel function, the Hamiltonian operator, and its sparsity, respectively. The gate complexity is given by this quantity multiplied by $\mathcal{O}(m+\log(N(1+gs)))$, where $m$ is the number of precision bits. To demonstrate the efficacy of our method, we present its applications to the generalized master equation and to the Redfield equation of the dephasing model. △ Less

Submitted 18 March, 2026; originally announced March 2026.

Comments: 10 pages

Partially Fault-Tolerant Quantum Computation for Megaquop Applications

Authors: Ming-Zhi Chung, Ali H. Z. Kavaki, Artur Scherer, Abdullah Khalid, Xiangzhou Kong, Toru Kawakubo, Namit Anand, Gebremedhin A Dagnew, Zachary Webb, Allyson Silva, Gaurav Gyawali, Tennin Yan, Keisuke Fujii, Alan Ho, Masoud Mohseni, Pooya Ronagh, John Martinis

Abstract: Partially fault-tolerant quantum computing (FTQC) has recently emerged as a promising approach for the execution of megaquop-scale circuits with millions of logical operations. In this work, we demonstrate the strengths and the limitations of this approach by conducting quantum resource estimation (QRE) of the space--time-efficient analog rotation (STAR) architecture using realistic hardware speci… ▽ More Partially fault-tolerant quantum computing (FTQC) has recently emerged as a promising approach for the execution of megaquop-scale circuits with millions of logical operations. In this work, we demonstrate the strengths and the limitations of this approach by conducting quantum resource estimation (QRE) of the space--time-efficient analog rotation (STAR) architecture using realistic hardware specifications for superconducting processors, and compare it against the QRE of the full FTQC architecture. We show how the performance of the STAR architecture's protocols is affected by hardware improvements. We also reduce the space requirements for partial FTQC by developing a procedure leveraging code growth to decrease the size of a factory producing analog rotation states. Our results reveal a non-trivial dependence of the optimal pre-growth code distance on the rotation angle with respect to post-growth infidelity. Further, we analyze space--time trade-offs between the factory size and the error-mitigation overhead, and observe that in an application-agnostic setting, there is a Goldilocks zone for circuits in the regime of roughly $10^5$--$10^6$ small-angle rotation gates. We show that quantum simulation of 2D Fermi--Hubbard model systems is a particularly well-suited application for the STAR architecture, requiring only hundreds of thousands of physical qubits and runtimes on the order of minutes for modest system sizes. Due to its favourable algorithmic scaling to larger system sizes, utility-scale simulation of the 2D Fermi--Hubbard model could potentially be attained using partial FTQC. △ Less

Submitted 13 March, 2026; originally announced March 2026.

Comments: 30 pages, 20 figures

Variational Quantum Operator Simulation

Authors: Satoru Shoji, Kosuke Ito, Yukihiro Shimizu, Keisuke Fujii

Abstract: Implementing time-evolution operators in shallow quantum circuits is important for quantum simulations. The standard method of Trotterization requires a large number of gates to achieve practical accuracy. Variational Quantum Simulation (VQS) is an algorithm that calculates the time evolution of a quantum state and can be executed with shallower circuits than Trotterization. However, the operator… ▽ More Implementing time-evolution operators in shallow quantum circuits is important for quantum simulations. The standard method of Trotterization requires a large number of gates to achieve practical accuracy. Variational Quantum Simulation (VQS) is an algorithm that calculates the time evolution of a quantum state and can be executed with shallower circuits than Trotterization. However, the operator obtained by VQS evolves only a fixed initial state and is not the time evolution operator itself. In this paper, we propose Variational Quantum Operator Simulation (VQOS), a method to realize time evolution operators in shallow quantum circuits. This method is based on the variational principle for operators and does not require the implementation of the desired Trotter decomposition of the time evolution operator. We performed numerical simulations of the VQOS algorithm and successfully implemented the time evolution operator for closed systems in a quantum circuit that is up to 5 times shallower than the Trotterization. By providing a more practical way to implement time evolution operators, VQOS increases the applicability of near-term quantum computers. △ Less

Submitted 15 August, 2026; v1 submitted 6 March, 2026; originally announced March 2026.

Comments: 12pages, 10 figures

Journal ref: Phys. Rev. A 114, 022414 (2026)

Even More Efficient Soft-Output Decoding with Extra-Cluster Growth and Early Stopping

Authors: Kaito Kishi, Riki Toshio, Jun Fujisaki, Hirotaka Oshima, Shintaro Sato, Keisuke Fujii

Abstract: In fault-tolerant quantum computing, soft outputs from real-time decoders play a crucial role in improving decoding accuracy, post-selecting magic states, and accelerating lattice surgery. A recent paper by Meister et al. [arXiv:2405.07433 (2024)] proposed an efficient method to evaluate soft outputs for cluster-based decoders, including the Union-Find (UF) decoder. However, in parallel computing… ▽ More In fault-tolerant quantum computing, soft outputs from real-time decoders play a crucial role in improving decoding accuracy, post-selecting magic states, and accelerating lattice surgery. A recent paper by Meister et al. [arXiv:2405.07433 (2024)] proposed an efficient method to evaluate soft outputs for cluster-based decoders, including the Union-Find (UF) decoder. However, in parallel computing environments, its computational complexity is comparable to or even surpasses that of the UF decoder itself, resulting in a substantial overhead. Furthermore, this method requires global information about the decoding graph, making it poorly suited for existing hardware implementations of the UF decoder on Field-Programmable Gate Arrays (FPGAs). In this paper, to alleviate these issues, we develop more efficient methods for evaluating high-quality soft outputs in cluster-based decoders by introducing several early-stopping techniques. Our central idea is that the precise value of a large soft output is often unnecessary in practice. Based on this insight, we introduce two types of novel soft-outputs: the bounded cluster gap and the extra-cluster gap. The former reduces the computational complexity of Meister's method by terminating the calculation at an early stage. Our numerical simulations show that this method achieves improved scaling with code distance $d$ compared to the original proposal. The latter, the extra-cluster gap, quantifies decoder reliability by performing a small, additional growth of the clusters obtained by the decoder. This approach offers the significant advantage of enabling soft-output computation without modifying the existing architecture of FPGA-implemented UF decoders. These techniques offer lower computational complexity and higher hardware compatibility, laying a crucial foundation for future real-time decoders with soft outputs. △ Less

Submitted 3 February, 2026; originally announced February 2026.

Fair sampling of ground-state configurations using hybrid quantum-classical MCMC algorithms

Authors: Yuichiro Nakano, Keisuke Fujii

Abstract: We study the fair sampling properties of hybrid quantum-classical Markov chain Monte Carlo (MCMC) algorithms for combinatorial optimization problems with degenerate ground states. While quantum optimization heuristics such as quantum annealing and the quantum approximate optimization algorithm (QAOA) are known to induce biased sampling, hybrid quantum-classical MCMC incorporates quantum dynamics o… ▽ More We study the fair sampling properties of hybrid quantum-classical Markov chain Monte Carlo (MCMC) algorithms for combinatorial optimization problems with degenerate ground states. While quantum optimization heuristics such as quantum annealing and the quantum approximate optimization algorithm (QAOA) are known to induce biased sampling, hybrid quantum-classical MCMC incorporates quantum dynamics only as a proposal transition and enforces detailed balance through classical acceptance steps. Using small Ising models, we show that MCMC post-processing corrects the sampling bias of quantum dynamics and restores near-uniform sampling over degenerate ground states. We then apply the method to random $k$-SAT problems near the satisfiability threshold. For random 2-SAT, a hybrid MCMC combining QAOA-assisted neural proposals with single spin-flip updates achieves fairness comparable to that of PT-ICM. For random 3-SAT, where such classical methods are no longer applicable, the hybrid MCMC still attains approximately uniform sampling. We also examine solution counting and find that the required number of transitions is comparable to that of WalkSAT. These results indicate that hybrid quantum-classical MCMC provides a viable framework for fair sampling and solution enumeration. △ Less

Submitted 16 December, 2025; originally announced December 2025.

Comments: 12 pages, 7 figures

Tensor Network Formulation of Dequantized Algorithms for Ground State Energy Estimation

Authors: Hidetaka Manabe, Takanori Sugimoto, Keisuke Fujii

Abstract: Verifying quantum advantage for practical problems, particularly the ground state energy estimation (GSEE) problem, is one of the central challenges in quantum computing theory. For that purpose, dequantization algorithms play a central role in providing a clear theoretical framework to separate the complexity of quantum and classical algorithms. However, existing dequantized algorithms typically… ▽ More Verifying quantum advantage for practical problems, particularly the ground state energy estimation (GSEE) problem, is one of the central challenges in quantum computing theory. For that purpose, dequantization algorithms play a central role in providing a clear theoretical framework to separate the complexity of quantum and classical algorithms. However, existing dequantized algorithms typically rely on sampling procedures, leading to prohibitively large computational overheads and hindering their practical implementation on classical computers. In this work, we propose a tensor network-based dequantization framework for GSEE that eliminates the sampling process while preserving the asymptotic complexity of prior dequantized algorithms. In our formulation, the overhead arising from sampling is replaced by the growth of the bond dimension required to represent Chebyshev vectors as tensor network states. Consequently, physical structure, such as entanglement and locality, is naturally reflected in the computational cost. By combining this approach with tensor network approximations, such as Matrix Product States (MPS), we construct a practical dequantization algorithm that is executable within realistic computational resources. Numerical simulations demonstrate that our method can efficiently construct high-degree polynomials up to $d=10^4$ for Hamiltonians with up to $100$ qubits, explicitly revealing the crossover between classically tractable and quantum advantaged regimes. These results indicate that tensor network-based dequantization provides a crucial tool toward the rigorous, quantitative verification of quantum advantage in realistic many-body systems. △ Less

Submitted 15 December, 2025; originally announced December 2025.

Comments: 21 pages, 12 figures

Out-of-Time-Order Correlator Spectroscopy

Authors: Keisuke Fujii

Abstract: Out-of-time-order correlators (OTOCs) are central probes of quantum scrambling, and their generalizations have recently become key primitives for both benchmarking quantum advantage and learning the structure of Hamiltonians. Yet their behavior has lacked a unified algorithmic interpretation. We show that higher-order OTOCs naturally fit within the framework of quantum signal processing (QSP): eac… ▽ More Out-of-time-order correlators (OTOCs) are central probes of quantum scrambling, and their generalizations have recently become key primitives for both benchmarking quantum advantage and learning the structure of Hamiltonians. Yet their behavior has lacked a unified algorithmic interpretation. We show that higher-order OTOCs naturally fit within the framework of quantum signal processing (QSP): each $\mathrm{OTOC}^{(k)}$ measures the $2k$-th Fourier component of the phase distribution associated with the singular values of a spatially resolved truncated propagator. This explains the contrasting sensitivities of time-ordered correlators (TOCs) and higher-order OTOCs to causal-cone structure and to chaotic, integrable, or localized dynamics. Based on this understanding, we further generalize higher-order OTOCs by polynomial transformation of the singular values of the spatially resolved truncated propagator. The resultant signal allows us to construct frequency-selective filters, which we call \emph{OTOC spectroscopy}. This extends conventional OTOCs into a mode-resolved tool for probing scrambling and spectral structure of quantum many-body dynamics. △ Less

Submitted 27 November, 2025; originally announced November 2025.

Comments: 10 pages, 2 figures

Decoder Switching: Breaking the Speed-Accuracy Tradeoff in Real-Time Quantum Error Correction

Authors: Riki Toshio, Kaito Kishi, Jun Fujisaki, Hirotaka Oshima, Shintaro Sato, Keisuke Fujii

Abstract: The realization of fault-tolerant quantum computers hinges on the construction of high-speed, high-accuracy, real-time decoding systems. The persistent challenge lies in the fundamental trade-off between speed and accuracy: efforts to improve the decoder's accuracy often lead to unacceptable increases in decoding time and hardware complexity, while attempts to accelerate decoding result in a signi… ▽ More The realization of fault-tolerant quantum computers hinges on the construction of high-speed, high-accuracy, real-time decoding systems. The persistent challenge lies in the fundamental trade-off between speed and accuracy: efforts to improve the decoder's accuracy often lead to unacceptable increases in decoding time and hardware complexity, while attempts to accelerate decoding result in a significant degradation in logical error rate. To overcome this challenge, we propose a novel framework, decoder switching, which balances these competing demands by combining a faster, soft-output decoder ("weak decoder") with a slower, high-accuracy decoder ("strong decoder"). In usual rounds, the weak decoder processes error syndromes and simultaneously evaluates its reliability via soft information. Only when encountering a decoding window with low reliability do we switch to the strong decoder to achieve more accurate decoding. Numerical simulations suggest that this framework can achieve accuracy comparable to, or even surpassing, that of the strong decoder, while maintaining an average decoding time on par with the weak decoder. We also develop an online decoding scheme tailored to our framework, named double window decoding, and elucidate the criteria for preventing an exponential slowdown of quantum computation. These findings break the long-standing speed-accuracy trade-off, paving the way for scalable real-time decoding devices. △ Less

Submitted 29 October, 2025; originally announced October 2025.

Efficient magic state cultivation with lattice surgery

Authors: Yutaka Hirano, Riki Toshio, Tomohiro Itogawa, Keisuke Fujii

Abstract: Magic state distillation plays a crucial role in fault-tolerant quantum computation and represents a major bottleneck. In contrast to traditional logical-level distillation, physical-level distillation offers significant overhead reduction by enabling direct implementation with physical gates. Magic state cultivation is a state-of-the-art physical-level distillation protocol that is compatible wit… ▽ More Magic state distillation plays a crucial role in fault-tolerant quantum computation and represents a major bottleneck. In contrast to traditional logical-level distillation, physical-level distillation offers significant overhead reduction by enabling direct implementation with physical gates. Magic state cultivation is a state-of-the-art physical-level distillation protocol that is compatible with the square-grid connectivity and yields high-fidelity magic states. However, it relies on the complex grafted code, which incurs substantial spacetime overhead and complicates practical implementation. In this work, we propose an efficient cultivation-based protocol compatible with the square-grid connectivity. We reduce the spatial overhead by avoiding the grafted code and further reduce the average spacetime overhead by utilizing code expansion and enabling early rejection. Numerical simulations show that, with a color code distance of 3 and a physical error probability of $10^{-3}$, our protocol achieves a logical error probability for the resulting magic state comparable to that of magic state cultivation ($\approx 3 \times 10^{-6}$), while requiring about half the spacetime overhead. Our work provides an efficient and simple distillation protocol suitable for megaquop use cases and early fault-tolerant devices. △ Less

Submitted 18 August, 2026; v1 submitted 28 October, 2025; originally announced October 2025.

Comments: 16 pages, 19 figures

Runtime reduction in lattice surgery utilizing time-like soft information

Authors: Yutaro Akahoshi, Riki Toshio, Jun Fujisaki, Hirotaka Oshima, Shintaro Sato, Keisuke Fujii

Abstract: Runtime optimization of the quantum computing within a given computational resource is important to achieve practical quantum advantage. In this paper, we propose a runtime reduction protocol for the lattice surgery, which utilizes the soft information corresponding to the logical measurement error. Our proposal is a simple two-step protocol: operating the lattice surgery with the small number of… ▽ More Runtime optimization of the quantum computing within a given computational resource is important to achieve practical quantum advantage. In this paper, we propose a runtime reduction protocol for the lattice surgery, which utilizes the soft information corresponding to the logical measurement error. Our proposal is a simple two-step protocol: operating the lattice surgery with the small number of syndrome measurement cycles, and reexecuting it with full syndrome measurement cycles in cases where the time-like soft information catches logical error symptoms. We firstly discuss basic features of the time-like complementary gap as the concrete example of the time-like soft information based on numerical results. Then, we show that our protocol surpasses the existing runtime reduction protocol called temporally encoded lattice surgery (TELS) for the most cases. In addition, we confirm that the combination of our protocol and the TELS protocol can reduce the runtime further, over 50% in comparison to the naive serial execution of the lattice surgery. The proposed protocol in this paper can be applied to any quantum computing architecture based on the lattice surgery, and we expect that this will be one of the fundamental building blocks of runtime optimization to achieve practical scale quantum computing. △ Less

Submitted 24 October, 2025; originally announced October 2025.

Comments: 15 pages, 19 figures

Measurement-Based Fault-Tolerant Quantum Computation on High-Connectivity Devices: A Resource-Efficient Approach toward Early FTQC

Authors: Yohei Ibe, Yutaka Hirano, Yasuo Ozu, Toru Kawakubo, Keisuke Fujii

Abstract: We propose a measurement-based FTQC (MB-FTQC) architecture for high-connectivity platforms such as trapped ions and neutral atoms. The key idea is to use verified logical ancillas combined with Knill's error-correcting teleportation, eliminating repeated syndrome measurements and simplifying decoding to logical Pauli corrections, thus keeping classical overhead low. To align with near-term device… ▽ More We propose a measurement-based FTQC (MB-FTQC) architecture for high-connectivity platforms such as trapped ions and neutral atoms. The key idea is to use verified logical ancillas combined with Knill's error-correcting teleportation, eliminating repeated syndrome measurements and simplifying decoding to logical Pauli corrections, thus keeping classical overhead low. To align with near-term device scales, we present two implementations benchmarked under circuit-level depolarizing noise: (i) a Steane-code version that uses analog $R_Z(θ)$ rotations, akin to the STAR architecture [Akahoshi et al., PRX Quantum 5, 010337], aiming for the megaquop regime ($\sim 10^6$ $T$ gates) on devices with thousands of qubits; and (ii) a Golay-code version with higher-order zero-level magic-state distillation, targeting the gigaquop regime ($\sim 10^9$ $T$ gates) on devices with tens of thousands of qubits. At a physical error rate $p=10^{-4}$, the Steane path supports $5\times 10^{4}$ logical $R_Z(θ)$ rotations, corresponding to $\sim 2.4\times 10^{6}$ $T$ gates and enabling megaquop-scale computation. With about $2{,}240$ physical qubits, it achieves $\log_{2}\mathrm{QV}=64$. The Golay path supports more than $2\times 10^{9}$ $T$ gates, enabling gigaquop-scale computation. These results suggest that our architecture can deliver practical large-scale quantum computation on near-term high-connectivity hardware without relying on resource-intensive surface codes or complex code concatenation. △ Less

Submitted 9 December, 2025; v1 submitted 21 October, 2025; originally announced October 2025.

Comments: 19 pages, 22 figures

A Quantum Algorithm for Nonlinear Electromagnetic Fluid Dynamics via Koopman-von Neumann Linearization

Authors: Hayato Higuchi, Yuki Ito, Kazuki Sakamoto, Keisuke Fujii, Akimasa Yoshikawa

Abstract: To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational resources that scale polynomially with the number of spatial grids, which poses a significant challenge for large-scale modeling. To address this issue, this stud… ▽ More To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational resources that scale polynomially with the number of spatial grids, which poses a significant challenge for large-scale modeling. To address this issue, this study presents a quantum algorithm for simulating the nonlinear electromagnetic fluid dynamics that govern space plasmas. We map it, by applying Koopman-von Neumann linearization, to the Schrödinger equation and evolve the system using Hamiltonian simulation via quantum singular value transformation. Our algorithm scales $O \left(s N_x \, \mathrm{polylog} \left( N_x \right) T \right)$ in time complexity with $s$, $N_x$, and $T$ being the spatial dimension, the number of spatial grid points per dimension, and the evolution time, respectively. Comparing the scaling $O \left( s N_x^s \left(T^{5/4}+T N_x\right) \right)$ for the classical method with the finite volume scheme, this algorithm achieves polynomial speedup in $N_x$. The space complexity of this algorithm is exponentially reduced from $O\left( s N_x^s \right)$ to $O\left( s \, \mathrm{polylog} \left( N_x \right) \right)$. Numerical experiments validate that accurate solutions are attainable with smaller $m$ than theoretically anticipated and with practical values of $m$ and $R$, underscoring the feasibility of the approach. As a practical demonstration, the method accurately reproduces the Kelvin-Helmholtz instability, underscoring its capability to tackle more intricate nonlinear dynamics. These results suggest that quantum computing can offer a viable pathway to overcome the computational barriers of multiscale plasma modeling. △ Less

Submitted 14 November, 2025; v1 submitted 26 September, 2025; originally announced September 2025.

Comments: 16 pages, 6 figures

Nontrivial multi-product commutation relation toward reducing T-count in sequential Pauli-based computation

Authors: Yusei Mori, Hideaki Hakoshima, Keisuke Fujii

Abstract: Quantum compilers that reduce the number of T gates are essential for minimizing the overhead of fault-tolerant quantum computation. Achieving further T-count reduction calls for identifying equivalent circuit transformation rules beyond those utilized in existing tools. In this paper, we rewrite any given Clifford+T circuit using a Clifford block followed by a sequential Pauli-based computation,… ▽ More Quantum compilers that reduce the number of T gates are essential for minimizing the overhead of fault-tolerant quantum computation. Achieving further T-count reduction calls for identifying equivalent circuit transformation rules beyond those utilized in existing tools. In this paper, we rewrite any given Clifford+T circuit using a Clifford block followed by a sequential Pauli-based computation, and introduce a nontrivial, ancilla-free transformation rule, the multi-product commutation relation (MCR). MCR constructs gate sequences based on specific commutation properties among multi-Pauli operators, yielding seemingly non-commutative instances that can be commuted, thereby enabling gate orderings that cannot be derived from pairwise commutation alone. We also propose the MCR Compiler, which incorporates MCR-based transformations as an optimization pass. To evaluate its effect, we use a benchmark circuit dataset generated through quantum circuit unoptimization. This approach intentionally adds redundancy to the circuit while keeping its equivalence, allowing a quantitative evaluation of compiler performance by comparison with the original circuit. Our numerical experiments reveal that the MCR Compiler achieves further T-count reduction beyond current compilers, establishing MCR-based transformations as a practical optimization primitive. These results highlight an untapped opportunity to enhance the optimization capabilities of quantum compilers. △ Less

Submitted 1 June, 2026; v1 submitted 24 September, 2025; originally announced September 2025.

Comments: 17 pages, 16 figures

Journal ref: PRX Quantum 7, 020345 (2026)

Quasi-Monte Carlo Method for Linear Combination Unitaries via Classical Post-Processing

Authors: Yuya Kawamata, Kosuke Mitarai, Keisuke Fujii

Abstract: We propose the quasi-Monte Carlo method for linear combination of unitaries via classical post-processing (LCU-CPP) on quantum applications. The LCU-CPP framework has been proposed as an approach to reduce hardware resources, expressing a general target operator $F(A)$ as $F(A) = \int_V f(t) G(A, t)dt$, where each $G(A, t)$ is proportional to a unitary operator. On a quantum device,… ▽ More We propose the quasi-Monte Carlo method for linear combination of unitaries via classical post-processing (LCU-CPP) on quantum applications. The LCU-CPP framework has been proposed as an approach to reduce hardware resources, expressing a general target operator $F(A)$ as $F(A) = \int_V f(t) G(A, t)dt$, where each $G(A, t)$ is proportional to a unitary operator. On a quantum device, $Re[Tr(G(A, t)ρ)]$ can be estimated using the Hadamard test and then combined through classical integration, allowing for the realization of nonunitary functions with reduced circuit depth. While previous studies have employed the Monte Carlo method or the trapezoid rule to evaluate the integral in LCU-CPP, we show that the quasi-Monte Carlo method can achieve even lower errors. In two numerical experiments, ground state property estimation and Green's function estimation, the quasi-Monte Carlo method achieves the lowest errors with a number of Hadamard test shots per unitary that is practical for real hardware implementations. These results indicate that quasi-Monte Carlo is an effective integration strategy within the LCU-CPP framework. △ Less

Submitted 20 April, 2026; v1 submitted 17 September, 2025; originally announced September 2025.

Comments: 14 pages,6 figures

Few is different: deciphering many-body dynamics in mesoscopic quantum gases

Authors: Juergen Berges, Sandra Brandstetter, Jasmine Brewer, Georg Bruun, Tilman Enss, Stefan Floerchinger, Keisuke Fujii, Maciej Galka, Giuliano Giacalone, Qingze Guan, Carl Heintze, Lars H. Heyen, Ilya Selyuzhenkov, Selim Jochim, Jesper Levinsen, Philipp Lunt, Silvia Masciocchi, Aleksas Mazeliauskas, Nir Navon, Alice Ohlson, Meera Parish, Stephanie M. Reimann, Francesco Scazza, Thomas Schaefer, Derek Teaney , et al. (5 additional authors not shown)

Abstract: Emergent macroscopic descriptions of matter, such as hydrodynamics, are central to our description of complex physical systems across a wide spectrum of energy scales. The conventional understanding of these many-body phenomena has recently been shaken by a number of experimental findings. Collective behavior of matter has been observed in \emph{mesoscopic} systems, such as high-energy hadron-hadr… ▽ More Emergent macroscopic descriptions of matter, such as hydrodynamics, are central to our description of complex physical systems across a wide spectrum of energy scales. The conventional understanding of these many-body phenomena has recently been shaken by a number of experimental findings. Collective behavior of matter has been observed in \emph{mesoscopic} systems, such as high-energy hadron-hadron collisions, or ultra-cold gases with only few strongly interacting fermions. In such systems, the separation of scales between macroscopic and microscopic dynamics (at the heart of any effective theory) is inapplicable. To address the conceptual challenges that arise from these observations and explore the universality of emergent descriptions of matter, the EMMI Rapid Reaction Task Force was assembled. This document summarizes the RRTF discussions on recent theoretical and experimental advances in this rapidly developing field. Leveraging technological breakthroughs in the control of quantum systems, we can now quantitatively explore what it means for a system to exhibit behavior beyond the sum of its individual parts. In particular, the report highlights how the (in)applicability of hydrodynamics and other effective theories can be probed across three principal frontiers: the size frontier, the equilibrium frontier, and the interaction frontier. △ Less

Submitted 22 June, 2026; v1 submitted 5 September, 2025; originally announced September 2025.

Comments: 67 pages, 12 figures, summary report of EMMI Rapid Reaction Task Force Workshop, March 18-21,2024, see https://indico.gsi.de/event/19234/, published version

Journal ref: Eur. Phys. J. A 62, 115 (2026)

Neural-network-assisted Monte Carlo sampling trained by Quantum Approximate Optimization Algorithm

Authors: Yuichiro Nakano, Ken N. Okada, Keisuke Fujii

Abstract: Sampling problems are widely regarded as the task for which quantum computers can most readily provide a quantum advantage. Leveraging this feature, the quantum-enhanced Markov chain Monte Carlo [Layden, D. et al., Nature 619, 282-287 (2023)] has been proposed recently, where sampling from a quantum computer is used as a proposal distribution and convergence to a target distribution is accelerated… ▽ More Sampling problems are widely regarded as the task for which quantum computers can most readily provide a quantum advantage. Leveraging this feature, the quantum-enhanced Markov chain Monte Carlo [Layden, D. et al., Nature 619, 282-287 (2023)] has been proposed recently, where sampling from a quantum computer is used as a proposal distribution and convergence to a target distribution is accelerated. However, guaranteeing convergence to the target distribution typically forces one to impose restrictive symmetry constraints on the quantum circuit, which makes it hard to design good proposal distributions and prevents making full use of the advantage of a quantum computer. We explore a hybrid quantum-classical MCMC framework that combines a quantum circuit with a generative neural sampler (GNS). The GNS is trained on quantum samples and acts as a classical surrogate to efficiently emulate quantum outputs, thereby lifting circuit constraints. We apply this method to Boltzmann sampling of spin glasses using proposals trained with a QAOA circuit. This approach outperforms conventional methods, showing a $\sim$100$\times$ improvement in spectral gap over uniform proposals. Notably, it maintains similar acceleration even without parameter optimization. These results establish the method as a viable sampling-based quantum algorithm for NISQ devices and highlight its potential for solving practical problems with quantum computation. △ Less

Submitted 2 June, 2025; originally announced June 2025.

Comments: 12 pages, 8 figures

Journal ref: PRX Quantum 7, 010338 (2026)

Hierarchical Quantum Error Correction with Hypergraph Product Code and Rotated Surface Code

Authors: Junichi Haruna, Keisuke Fujii

Abstract: We propose and analyze a hierarchical quantum error correction (QEC) scheme that concatenates hypergraph product (HGP) codes with rotated surface codes, which is compatible with quantum computers with only nearest-neighbor interactions. The upper layer employs (3,4)-random HGP codes, known for their constant encoding rate and favorable distance scaling, while the lower layer consists of a rotated… ▽ More We propose and analyze a hierarchical quantum error correction (QEC) scheme that concatenates hypergraph product (HGP) codes with rotated surface codes, which is compatible with quantum computers with only nearest-neighbor interactions. The upper layer employs (3,4)-random HGP codes, known for their constant encoding rate and favorable distance scaling, while the lower layer consists of a rotated surface code with distance 5, allowing hardware compatibility through lattice surgery. To address the decoding bottleneck, we utilize a soft-decision decoding strategy that combines belief propagation with ordered statistics (BP-OS) decoding, enhanced by a syndrome-conditioned logical error probability computed via a tailored lookup table for the lower layer. Numerical simulations under a code capacity noise model demonstrate that our hierarchical codes achieve logical error suppression below the threshold. Furthermore, we derive explicit conditions under which the proposed codes surpass surface codes in both qubit efficiency and error rate. In particular, for the size parameter $s \geq 4$ (which corresponds to 16 logical qubits) and the distance $d\geq 25$, our construction outperforms the rotated surface code in practical regimes with physical error rates around or less than $10^{-2}$. These results suggest that concatenated qLDPC-surface architectures offer a scalable and resource-efficient path toward near-term fault-tolerant quantum computation. △ Less

Submitted 24 June, 2025; v1 submitted 24 May, 2025; originally announced May 2025.

Comments: 12 pages and 10 figures (v1), added data availability and modified abstract (v2)

Large-Scale Quantum Device Benchmarking via LXEB with Particle-Number-Conserving Random Quantum Circuits

Authors: Takumi Kaneda, Keisuke Fujii, Hiroshi Ueda

Abstract: Linear cross-entropy benchmarking (LXEB) with random quantum circuits is a standard method for evaluating quantum computers. However, LXEB requires classically simulating the ideal output distribution of a given quantum circuit with high numerical precision, which becomes infeasible beyond approximately 50 qubits, even on state-of-the-art supercomputers. As a result, LXEB cannot be directly applie… ▽ More Linear cross-entropy benchmarking (LXEB) with random quantum circuits is a standard method for evaluating quantum computers. However, LXEB requires classically simulating the ideal output distribution of a given quantum circuit with high numerical precision, which becomes infeasible beyond approximately 50 qubits, even on state-of-the-art supercomputers. As a result, LXEB cannot be directly applied to evaluate large-scale quantum devices, which now exceed 100 qubits and continue to grow rapidly in size. To address this limitation, we introduce a constraint known as particle-number conservation into the random quantum circuits used for benchmarking. This restriction significantly reduces the size of the Hilbert space for a fixed particle number, enabling classical simulations of circuits with over 100 qubits when the particle number is $O(1)$. Furthermore, we propose a modified version of LXEB, called MLXEB, which enables fidelity estimation under particle-number-conserving dynamics. Through numerical simulations, we investigate the conditions under which MLXEB provides accurate fidelity estimates. △ Less

Submitted 23 July, 2025; v1 submitted 15 May, 2025; originally announced May 2025.

Comments: 11 pages, 8 figures

On the quantum computational complexity of classical linear dynamics with geometrically local interactions: Dequantization and universality

Authors: Kazuki Sakamoto, Keisuke Fujii

Abstract: The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in simulating classical dynamics with long-range interactions. However, many real-world classical systems, such as those arising from partial differential equations, ex… ▽ More The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in simulating classical dynamics with long-range interactions. However, many real-world classical systems, such as those arising from partial differential equations, exhibit only local interactions. The question remains whether quantum algorithms can still provide exponential speedup under this condition. In this work, we thoroughly characterize the computational complexity of simulating such geometrically local systems on quantum computers. First, we dequantize the quantum algorithm for simulating short-time (polynomial-time) dynamics of such systems. This implies that the problem of simulating this dynamics does not yield any exponential quantum advantage. Second, we show that simulating short-time dynamics is at least as hard as polynomial-time and linear-space probabilistic classical computation. Third, we show that the computational complexity of simulating long-time (exponential-time) dynamics is captured by exponential-time and polynomial-space quantum computation. This suggests a super-polynomial time advantage when restricting the computation to polynomial-space, or an exponential space advantage otherwise. This work offers new insights into the complexity of classical dynamics governed by partial differential equations, providing a pathway for achieving quantum advantage in practical problems. △ Less

Submitted 25 July, 2026; v1 submitted 15 May, 2025; originally announced May 2025.

Comments: 37 pages, 5 figures

Journal ref: Quantum 10, 2182 (2026)

Electric Power Demand Portfolio Optimization by Fermionic QAOA with Self-Consistent Local Field Modulation

Authors: Takuya Yoshioka, Keita Sasada, Yuichiro Nakano, Keisuke Fujii

Abstract: Quantum Approximation Optimization Algorithms (QAOA) have been actively developed, among which Fermionic QAOA (FQAOA) has been successfully applied to financial portfolio optimization problems. We improve FQAOA and apply it to the optimization of electricity demand portfolios aiming to procure a target amount of electricity with minimum risk. Our new algorithm, FQAOA-SCLFM, allows approximate inte… ▽ More Quantum Approximation Optimization Algorithms (QAOA) have been actively developed, among which Fermionic QAOA (FQAOA) has been successfully applied to financial portfolio optimization problems. We improve FQAOA and apply it to the optimization of electricity demand portfolios aiming to procure a target amount of electricity with minimum risk. Our new algorithm, FQAOA-SCLFM, allows approximate integration of constraints on the target amount of power by utilizing self-consistent local field modulation (SCLFM) in a driver Hamiltonian. We demonstrate that this approach performs better than the currently widely used $XY$-QAOA and the previous FQAOA in all instances subjected to this study. △ Less

Submitted 4 May, 2025; originally announced May 2025.

Comments: published in 2024 IEEE International Conference on Quantum Computing and Engineering (QCE)

Journal ref: 2024 IEEE International Conference on Quantum Computing and Engineering (QCE), Montreal, QC, Canada, 2024, pp. 469-475

Locality-aware Pauli-based computation for local magic state preparation

Authors: Yutaka Hirano, Keisuke Fujii

Abstract: Magic state distillation, a process for preparing magic states needed to implement non-Clifford gates fault-tolerantly, plays a crucial role in fault-tolerant quantum computation. Historically, it has been a major bottleneck, leading to the pursuit of computation schemes optimized for slow magic state preparation. Recent advances in magic state distillation have significantly reduced the overhead,… ▽ More Magic state distillation, a process for preparing magic states needed to implement non-Clifford gates fault-tolerantly, plays a crucial role in fault-tolerant quantum computation. Historically, it has been a major bottleneck, leading to the pursuit of computation schemes optimized for slow magic state preparation. Recent advances in magic state distillation have significantly reduced the overhead, enabling the simultaneous preparation of many magic states. However, the magic state transfer cost prevents the conventional layout from efficiently utilizing them, highlighting the need for an alternative scheme optimized for highly parallel quantum algorithms. In this study, we propose locality-aware Pauli-based computation, a novel compilation scheme that distills magic states in the computation area, aiming to reduce execution time by minimizing magic state transfer costs and improving locality. Numerical experiments on random circuit sampling and 2D Ising Hamiltonian simulation demonstrate that our scheme significantly reduces execution time, while incurring little or no additional spatial overhead, compared to sequential Pauli-based computation, a conventional computation scheme, and scales favorably with increasing qubit count. △ Less

Submitted 21 August, 2025; v1 submitted 16 April, 2025; originally announced April 2025.

Comments: 11 pages, 26 figures

Automating quantum feature map design via large language models

Authors: Kenya Sakka, Kosuke Mitarai, Keisuke Fujii

Abstract: Quantum feature maps are a key component of quantum machine learning, encoding classical data into quantum states to exploit the expressive power of high-dimensional Hilbert spaces. Despite their theoretical promise, designing quantum feature maps that offer practical advantages over classical methods remains an open challenge. In this work, we propose an agentic system that autonomously generates… ▽ More Quantum feature maps are a key component of quantum machine learning, encoding classical data into quantum states to exploit the expressive power of high-dimensional Hilbert spaces. Despite their theoretical promise, designing quantum feature maps that offer practical advantages over classical methods remains an open challenge. In this work, we propose an agentic system that autonomously generates, evaluates, and refines quantum feature maps using large language models. The system consists of five components: Generation, Storage, Validation, Evaluation, and Review. Using these components, it iteratively improves quantum feature maps. Through numerical evaluations on widely used benchmark datasets, the system discovers and improves quantum feature maps without human intervention. On MNIST, the best generated feature map achieves 97.3% classification accuracy, outperforming existing quantum feature maps and achieving competitive performance with classical kernels, remaining within 0.3 percentage points of the radial basis function kernel. Similar improvements are observed on Fashion-MNIST and CIFAR-10. These results demonstrate that LLM-driven closed-loop discovery can autonomously explore dataset-adaptive quantum features. More broadly, our approach provides a practical methodology for automated discovery in quantum circuit design, helping bridge the gap between theoretical QML models and their empirical performance on real-world machine learning tasks. △ Less

Submitted 24 March, 2026; v1 submitted 9 April, 2025; originally announced April 2025.

Comments: 39 pages, 9 figures

Clifford gates with logical transversality for self-dual CSS codes

Authors: Theerapat Tansuwannont, Yugo Takada, Keisuke Fujii

Abstract: Quantum error-correcting codes with high encoding rate are good candidates for large-scale quantum computers as they use physical qubits more efficiently than codes of the same distance that encode only a few logical qubits. Some logical gate of a high-rate code can be fault-tolerantly implemented using transversal physical gates, but its logical operation may depend on the choice of a symplectic… ▽ More Quantum error-correcting codes with high encoding rate are good candidates for large-scale quantum computers as they use physical qubits more efficiently than codes of the same distance that encode only a few logical qubits. Some logical gate of a high-rate code can be fault-tolerantly implemented using transversal physical gates, but its logical operation may depend on the choice of a symplectic basis that defines logical Pauli operators of the code. In this work, we focus on $[\![n,k,d]\!]$ self-dual Calderbank-Shor-Steane (CSS) codes with $k \geq 1$ and prove necessary and sufficient conditions for the code to have a symplectic basis such that (1) transversal logical Hadamard gates $\bigotimes_{j=1}^{k} \bar{H}_j$ can be implemented by transversal physical Hadamard gates $\bigotimes_{i=1}^{n} H_i$, and (2) for any $(a_1,\dots,a_k)\in\{-1,1\}^k$, transversal logical phase gates $\bigotimes_{j=1}^{k} \bar{S}_j^{a_j}$ can be implemented by transversal physical phase gates $\bigotimes_{i=1}^{n} S_i^{b_i}$ for some $(b_1,\dots,b_n)\in\{-1,1\}^n$. Self-dual CSS codes satisfying the conditions include any codes with odd $n$. We also generalize the idea to concatenated self-dual CSS codes and show that certain logical Clifford gates have multiple transversal implementations, each by logical gates at a different level of concatenation. Several applications of our results for fault-tolerant quantum computation with low overhead are also provided. △ Less

Submitted 25 March, 2025; originally announced March 2025.

Comments: 34 pages, 8 figures

Logical entanglement distribution between distant 2D array qubits

Authors: Yuya Maeda, Yasunari Suzuki, Toshiki Kobayashi, Takashi Yamamoto, Yuuki Tokunaga, Keisuke Fujii

Abstract: Sharing logical entangled pairs between distant quantum nodes is a key process to achieve fault tolerant quantum computation and communication. However, there is a gap between current experimental specifications and theoretical requirements for sharing logical entangled states while improving experimental techniques. Here, we propose an efficient logical entanglement distribution protocol based on… ▽ More Sharing logical entangled pairs between distant quantum nodes is a key process to achieve fault tolerant quantum computation and communication. However, there is a gap between current experimental specifications and theoretical requirements for sharing logical entangled states while improving experimental techniques. Here, we propose an efficient logical entanglement distribution protocol based on surface codes for two distant 2D qubit array with nearest-neighbor interaction. A notable feature of our protocol is that it allows post-selection according to error estimations, which provides the tunability between the infidelity of logical entanglements and the success probability of the protocol. With this feature, the fidelity of encoded logical entangled states can be improved by sacrificing success rates. We numerically evaluated the performance of our protocol and the trade-off relationship, and found that our protocol enables us to prepare logical entangled states while improving fidelity in feasible experimental parameters. We also discuss a possible physical implementation using neutral atom arrays to show the feasibility of our protocol. △ Less

Submitted 30 March, 2026; v1 submitted 19 March, 2025; originally announced March 2025.

Comments: 10 pages, 6 figures

Journal ref: Phys. Rev. Research 8, 013282, 2026

Optimal elemental configuration search in crystal using quantum approximate optimization algorithm

Authors: Kazuhide Ichikawa, Genta Hayashi, Satoru Ohuchi, Tomoyasu Yokoyama, Ken N. Okada, Keisuke Fujii

Abstract: Optimal elemental configuration search in crystal is a crucial task to discovering industrially important materials such as lithium-ion battery cathodes. In this paper we present application of quantum approximate optimization algorithm, the representative near-term quantum algorithm for combinatorial optimization, to finding the most stable elemental configuration in a crystal, using Au-Cu alloys… ▽ More Optimal elemental configuration search in crystal is a crucial task to discovering industrially important materials such as lithium-ion battery cathodes. In this paper we present application of quantum approximate optimization algorithm, the representative near-term quantum algorithm for combinatorial optimization, to finding the most stable elemental configuration in a crystal, using Au-Cu alloys as an example. After expressing the energy of the crystal in the form of the Ising model through the cluster expansion method combined with first-principles calculations, we numerically perform QAOA with three types of parameter optimization. As a result, we have demonstrated that the optimal solution can be sampled with a high probability for crystals containing up to 32 atoms. Our results could pave the way for optimal elemental configuration search in a crystal using a near-term quantum computer. △ Less

Submitted 12 March, 2025; originally announced March 2025.

Comments: 10 pages, 3 figures

Explicit error bounds with commutator scaling for time-dependent product and multi-product formulas

Authors: Kaoru Mizuta, Tatsuhiko N. Ikeda, Keisuke Fujii

Abstract: Product formula (PF), which approximates the time evolution under a many-body Hamiltonian by the product of local time evolution operators, is one of the central approaches for simulating quantum dynamics by quantum computers. It has been of great interest whether PFs have a bound of the error from the exact time evolution, which is expressed by commutators among local terms (called commutator sca… ▽ More Product formula (PF), which approximates the time evolution under a many-body Hamiltonian by the product of local time evolution operators, is one of the central approaches for simulating quantum dynamics by quantum computers. It has been of great interest whether PFs have a bound of the error from the exact time evolution, which is expressed by commutators among local terms (called commutator scaling), since it brings the substantial suppression of the computational cost in the system size. Although recent studies have revealed the presence and the explicit formulas of the PF error bounds for time-independent systems, those for time-dependent Hamiltonians remain to be a difficult problem except for low-order PFs. In this paper, we derive an explicit error bound of generic PFs for smooth time-dependent Hamiltonians, which is expressed by commutators among local terms and their time derivatives. This error bound can also host the substantial suppression in the system size for generic local Hamiltonians with finite-, short-, and long-ranged interactions, thereby giving a much better estimate of gate counts. Our derivation employs Floquet theory; Embedding generic smooth time-dependent Hamiltonians into time-periodic ones, we map the time-dependent PF error to the time-independent one defined on an infinite-dimensional space. This approach allows to obtain the error bounds not only for the ordinary time-dependent PF but also for its various family. In particular, we also clarify the explicit error bound of a time-dependent multi-product formula, with which we can achieve much smaller error by a linear combination of time-dependent PFs. Our results will shed light on various applications of quantum computers, ranging from quantum simulation of nonequilibrium materials to faster algorithms exploiting time-dependent Hamiltonians like adiabatic state preparation. △ Less

Submitted 2 December, 2025; v1 submitted 18 October, 2024; originally announced October 2024.

Comments: 57 pages, 2 figures, 1 table

Polynomial time constructive decision algorithm for multivariable quantum signal processing

Authors: Yuki Ito, Hitomi Mori, Kazuki Sakamoto, Keisuke Fujii

Abstract: Quantum signal processing (QSP) and quantum singular value transformation (QSVT) have provided a unified framework for understanding many quantum algorithms, including factorization, matrix inversion, and Hamiltonian simulation. As a multivariable version of QSP, multivariable quantum signal processing (M-QSP) is proposed. M-QSP interleaves signal operators corresponding to each variable with sign… ▽ More Quantum signal processing (QSP) and quantum singular value transformation (QSVT) have provided a unified framework for understanding many quantum algorithms, including factorization, matrix inversion, and Hamiltonian simulation. As a multivariable version of QSP, multivariable quantum signal processing (M-QSP) is proposed. M-QSP interleaves signal operators corresponding to each variable with signal processing operators, which provides an efficient means to perform multivariable polynomial transformations. However, the necessary and sufficient condition for what types of polynomials can be constructed by M-QSP is unknown. In this paper, we propose a classical algorithm to determine whether a given pair of multivariable Laurent polynomials can be implemented by M-QSP, which returns True or False. As one of the most important properties of this algorithm, its returning True is the necessary and sufficient condition. The proposed classical algorithm runs in polynomial time in the number of variables and signal operators. Our algorithm also provides a constructive method to select the necessary parameters for implementing M-QSP. These findings offer valuable insights for identifying practical applications of M-QSP. △ Less

Submitted 7 May, 2026; v1 submitted 3 October, 2024; originally announced October 2024.

Comments: 21 pages, 2 figures

Journal ref: Quantum 10, 2102 (2026)

Efficient state preparation for multivariate Monte Carlo simulation

Authors: Hitomi Mori, Kosuke Mitarai, Keisuke Fujii

Abstract: Quantum state preparation is a task to prepare a state with a specific function encoded in the amplitude, which is an essential subroutine in many quantum algorithms. In this paper, we focus on multivariate state preparation, as it is an important extension for many application areas. Specifically in finance, multivariate state preparation is required for multivariate Monte Carlo simulation, which… ▽ More Quantum state preparation is a task to prepare a state with a specific function encoded in the amplitude, which is an essential subroutine in many quantum algorithms. In this paper, we focus on multivariate state preparation, as it is an important extension for many application areas. Specifically in finance, multivariate state preparation is required for multivariate Monte Carlo simulation, which is used for important numerical tasks such as risk aggregation and multi-asset derivative pricing. Using existing methods, multivariate quantum state preparation requires the number of gates exponential in the number of variables $D$. For this task, we propose a quantum algorithm that only requires the number of gates linear in $D$. Our algorithm utilizes multivariable quantum signal processing (M-QSP), a technique to perform the multivariate polynomial transformation of matrix elements. Using easily prepared block-encodings corresponding to each variable, we apply the M-QSP to construct the target function. In this way, our algorithm prepares the target state efficiently for functions achievable with M-QSP. △ Less

Submitted 11 September, 2024; originally announced September 2024.

Compilation of Trotter-Based Time Evolution for Partially Fault-Tolerant Quantum Computing Architecture

Authors: Yutaro Akahoshi, Riki Toshio, Jun Fujisaki, Hirotaka Oshima, Shintaro Sato, Keisuke Fujii

Abstract: Achieving practical quantum speedup with limited resources is a crucial challenge in both academic and industrial communities. To address this, a partially fault-tolerant quantum computing architecture called ``space-time efficient analog rotation quantum computing architecture (STAR architecture)'' has been recently proposed. This architecture focuses on minimizing resource requirements while max… ▽ More Achieving practical quantum speedup with limited resources is a crucial challenge in both academic and industrial communities. To address this, a partially fault-tolerant quantum computing architecture called ``space-time efficient analog rotation quantum computing architecture (STAR architecture)'' has been recently proposed. This architecture focuses on minimizing resource requirements while maximizing the precision of non-Clifford gates, essential for universal quantum computation. However, non-deterministic processes such as the repeat-until-success (RUS) protocol and state injection can introduce significant computational overhead. Therefore, optimizing the logical circuit to minimize this overhead by using efficient fault-tolerant operations is essential. This paper presents an efficient method for simulating the time evolution of the 2D Hubbard model Hamiltonian, a promising application of the STAR architecture. We present two techniques, parallel injection protocol and adaptive injection region updating, to reduce unnecessary time overhead specific to our architecture. By integrating these with the existing fSWAP technique, we develop an efficient Trotter-based time evolution operation for the 2D Hubbard model. Our analysis reveals an acceleration of over 10 times compared to naive serial compilation. This optimized compilation enables us to estimate the computational resources required for quantum phase estimation of the 2D Hubbard model. For devices with a physical error rate of $p_{\rm phys} = 10^{-4}$, we estimate that approximately $6.5 \times 10^4$ physical qubits are required to achieve faster ground state energy estimation of the $8\times8$ Hubbard model compared to classical computation. △ Less

Submitted 23 October, 2024; v1 submitted 27 August, 2024; originally announced August 2024.

Comments: Added a note to the main text. Some references were updated. 22 pages, 33 figures

Practical quantum advantage on partially fault-tolerant quantum computer

Authors: Riki Toshio, Yutaro Akahoshi, Jun Fujisaki, Hirotaka Oshima, Shintaro Sato, Keisuke Fujii

Abstract: Achieving quantum speedups in practical tasks remains challenging for current noisy intermediate-scale quantum (NISQ) devices. These devices always encounter significant obstacles such as inevitable physical errors and the limited scalability of current near-term algorithms. Meanwhile, assuming a typical architecture for fault-tolerant quantum computing (FTQC), realistic applications inevitably re… ▽ More Achieving quantum speedups in practical tasks remains challenging for current noisy intermediate-scale quantum (NISQ) devices. These devices always encounter significant obstacles such as inevitable physical errors and the limited scalability of current near-term algorithms. Meanwhile, assuming a typical architecture for fault-tolerant quantum computing (FTQC), realistic applications inevitably require a vast number of qubits, typically exceeding $10^6$, which seems far beyond near-term realization. In this work, to bridge the gap between the NISQ and FTQC eras, we propose an alternative approach to achieve practical quantum advantages on early-FTQC devices. Our framework is based on partially fault-tolerant logical operations to minimize spatial overhead and avoids the costly distillation techniques typically required for executing non-Clifford gates. To this end, we develop a space-time efficient state preparation protocol to generate an ancillary non-Clifford state consumed for implementing an analog rotation gate with an arbitrary small angle $θ$ and a remarkably low worst-case error rate below $\mathcal{O}(|θ| p_{\text{ph}})$, where $p_{\text{ph}}$ is the physical error rate. Furthermore, we propose several error suppression schemes tailored to our preparation protocol, which are essential to minimize the overhead for mitigating errors. Based on this framework, we present several promising applications that leverage the potential of our framework, including the Trotter simulation and quantum phase estimation (QPE). Notably, we demonstrate that our framework allows us to perform the QPE for $(8\times 8)$-site Hubbard model with fewer than $4.9\times 10^4$ qubits and an execution time of 9 days (or 12 minutes with full parallelization) under $p_{\text{ph}}=10^{-4}$, which is significantly faster than recent classical estimation with tensor network techniques (DMRG and PEPS). △ Less

Submitted 27 August, 2024; originally announced August 2024.

Explicit quantum surrogates for quantum kernel models

Authors: Akimoto Nakayama, Hayata Morisaki, Kosuke Mitarai, Hiroshi Ueda, Keisuke Fujii

Abstract: Quantum machine learning (QML) leverages quantum states for data encoding, with key approaches being explicit models that use parameterized quantum circuits and implicit models that use quantum kernels. Implicit models often have lower training errors but face issues such as overfitting and high prediction costs, while explicit models can struggle with complex training and barren plateaus. We prop… ▽ More Quantum machine learning (QML) leverages quantum states for data encoding, with key approaches being explicit models that use parameterized quantum circuits and implicit models that use quantum kernels. Implicit models often have lower training errors but face issues such as overfitting and high prediction costs, while explicit models can struggle with complex training and barren plateaus. We propose a quantum-classical hybrid algorithm to create an explicit quantum surrogate (EQS) for trained implicit models. This involves diagonalizing an observable from the implicit model and constructing a corresponding quantum circuit using an extended automatic quantum circuit encoding algorithm. The EQS framework reduces prediction costs, provides a powerful strategy to mitigate barren plateau issues, and combines the strengths of both QML approaches. △ Less

Submitted 5 December, 2025; v1 submitted 6 August, 2024; originally announced August 2024.

Comments: 27 pages, 10 figures

Scalable circuit depth reduction in feedback-based quantum optimization with a quadratic approximation

Authors: Don Arai, Ken N. Okada, Yuichiro Nakano, Kosuke Mitarai, Keisuke Fujii

Abstract: Combinatorial optimization problems are one of the areas where near-term noisy quantum computers may have practical advantage against classical computers. Recently a novel feedback-based quantum optimization algorithm has been proposed by Magann \textit{et al}. The method explicitly determines quantum circuit parameters by feeding back measurement results thus avoids classical parameter optimizati… ▽ More Combinatorial optimization problems are one of the areas where near-term noisy quantum computers may have practical advantage against classical computers. Recently a novel feedback-based quantum optimization algorithm has been proposed by Magann \textit{et al}. The method explicitly determines quantum circuit parameters by feeding back measurement results thus avoids classical parameter optimization that is known to cause significant trouble in quantum approximate optimization algorithm, the well-studied near-term algorithm. Meanwhile, a significant drawback of the feedback-based quantum optimization is that it requires deep circuits, rendering the method unsuitable to noisy quantum devices. In this study we propose a new feedback law for parameter determination by introducing the second-order approximation with respect to time interval, a hyperparameter in the feedback-based quantum optimization. This allows one to take larger time interval, leading to acceleration of convergence to solutions. In numerical simulations on the maximum cut problem we demonstrate that our proposal significantly reduces circuit depth, with its linear scaling with the problem size smaller by more than an order of magnitude. We expect that the new feedback law proposed in this work may pave the way for feedback-based quantum optimization with near-term noisy quantum computers. △ Less

Submitted 25 July, 2024; originally announced July 2024.

Comments: 7 pages, 6 figures

Journal ref: Phys. Rev. Research 7, 013035 (2025)

MagicPool: Dealing with Magic State Distillation Failures on Large-Scale Fault-Tolerant Quantum Computer

Authors: Yutaka Hirano, Yasunari Suzuki, Keisuke Fujii

Abstract: Magic state distillation, which is a probabilistic process used to generate magic states, plays an important role in universal fault-tolerant quantum computers. On the other hand, to solve interesting problems, we need to run complex programs on fault-tolerant quantum computers, and hence, the system needs to use hardware resources efficiently. Taking advantage of parallelism is a major optimizati… ▽ More Magic state distillation, which is a probabilistic process used to generate magic states, plays an important role in universal fault-tolerant quantum computers. On the other hand, to solve interesting problems, we need to run complex programs on fault-tolerant quantum computers, and hence, the system needs to use hardware resources efficiently. Taking advantage of parallelism is a major optimization strategy and compilers are responsible for performing optimizations to allow parallel processing. However, the probabilistic nature of magic state distillation is not compatible with compile-time optimizations and results in an additional run-time delay. To reduce the additional run-time delay, we propose introducing a pool of magic states. We run simulations of quantum circuits to verify the magnitude of the run-time delay and the usefulness of the mitigation approach. The experimental results show that the run-time delay is amplified by parallel processing, and pooling effectively reduces the run-time delay with a small spatial cost. △ Less

Submitted 10 July, 2024; originally announced July 2024.

Comments: 13 pages, 17 figures

Feedback-driven quantum reservoir computing for time-series analysis

Authors: Kaito Kobayashi, Keisuke Fujii, Naoki Yamamoto

Abstract: Quantum reservoir computing (QRC) is a highly promising computational paradigm that leverages quantum systems as a computational resource for nonlinear information processing. While its application to time-series analysis is eagerly anticipated, prevailing approaches suffer from the collapse of the quantum state upon measurement, resulting in the erasure of temporal input memories. Neither repeate… ▽ More Quantum reservoir computing (QRC) is a highly promising computational paradigm that leverages quantum systems as a computational resource for nonlinear information processing. While its application to time-series analysis is eagerly anticipated, prevailing approaches suffer from the collapse of the quantum state upon measurement, resulting in the erasure of temporal input memories. Neither repeated initializations nor weak measurements offer a fundamental solution, as the former escalates the time complexity while the latter restricts the information extraction from the Hilbert space. To address this issue, we propose the feedback-driven QRC framework. This methodology employs projective measurements on all qubits for unrestricted access to the quantum state, with the measurement outcomes subsequently fed back into the reservoir to restore the memory of prior inputs. We demonstrate that our QRC successfully acquires the fading-memory property through the feedback connections, a critical element in time-series processing. Notably, analysis of measurement trajectories reveal three distinct phases depending on the feedback strength, with the memory performance maximized at the edge of chaos. We also evaluate the predictive capabilities of our QRC, demonstrating its suitability for forecasting signals originating from quantum spin systems. △ Less

Submitted 13 September, 2024; v1 submitted 22 June, 2024; originally announced June 2024.

Comments: 15 pages, 10 figures

Journal ref: PRX Quantum 5, 040325 (2024)

Variational quantum Hamiltonian engineering

Authors: Benchi Zhao, Keisuke Fujii

Abstract: The Hamiltonian of a quantum system is represented in terms of operators corresponding to the kinetic and potential energies of the system. The expectation value of a Hamiltonian and Hamiltonian simulation are two of the most fundamental tasks in quantum computation. The overheads for realizing the two tasks are determined by the Pauli norm of Hamiltonian, which sums over all the absolute values o… ▽ More The Hamiltonian of a quantum system is represented in terms of operators corresponding to the kinetic and potential energies of the system. The expectation value of a Hamiltonian and Hamiltonian simulation are two of the most fundamental tasks in quantum computation. The overheads for realizing the two tasks are determined by the Pauli norm of Hamiltonian, which sums over all the absolute values of Pauli coefficients. In this work, we propose a variational quantum algorithm (VQA) called variational quantum Hamiltonian engineering (VQHE) to minimize the Pauli norm of Hamiltonian, such that the overhead for executing expectation value estimation and Hamiltonian simulation can be reduced. First, we develop a theory to encode the Pauli norm optimization problem into the vector L1-norm minimization problem. Then we devise an appropriate cost function and utilize the parameterized quantum circuits (PQC) to minimize the cost function. We also conduct numerical experiments to reduce the Pauli norm of the Ising Hamiltonian and molecules' Hamiltonian to show the efficiency of the proposed VQHE. △ Less

Submitted 13 June, 2024; originally announced June 2024.

Comments: 13 pages, 6 figures

Linearly simplified QAOA parameters and transferability

Authors: Ryo Sakai, Hiromichi Matsuyama, Wai-Hong Tam, Yu Yamashiro, Keisuke Fujii

Abstract: Quantum Approximate Optimization Algorithm (QAOA) provides a way to solve combinatorial optimization problems using quantum computers. QAOA circuits consist of time evolution operators by the cost Hamiltonian and of state mixing operators, and embedded variational parameter for each operator is tuned so that the expectation value of the cost function is minimized. The optimization of the variation… ▽ More Quantum Approximate Optimization Algorithm (QAOA) provides a way to solve combinatorial optimization problems using quantum computers. QAOA circuits consist of time evolution operators by the cost Hamiltonian and of state mixing operators, and embedded variational parameter for each operator is tuned so that the expectation value of the cost function is minimized. The optimization of the variational parameters is taken place on classical devices while the cost function is measured in the sense of quantum. To facilitate the classical optimization, there are several previous works on making decision strategies for optimal/initial parameters and on extracting similarities among instances. In our current work, we consider simplified QAOA parameters that take linear forms along with the depth in the circuit. Such a simplification, which would be suggested from an analogy to quantum annealing, leads to a drastic reduction of the parameter space from 2p to 4 dimensions with the any number of QAOA layers p. In addition, cost landscapes in the reduced parameter space have some stability on differing instances. This fact suggests that an optimal parameter set for a given instance can be transferred to other instances. In this paper we present some numerical results that are obtained for instances of the random Ising model and of the max-cut problem. The transferability of linearized parameters is demonstrated for randomly generated source and destination instances, and its dependence on features of the instances are investigated. △ Less

Submitted 1 May, 2024; originally announced May 2024.

Comments: 10 pages, 12 figures, submitted to 2024 IEEE International Conference on Quantum Computing and Engineering (QCE24)

Leveraging Zero-Level Distillation to Generate High-Fidelity Magic States

Authors: Yutaka Hirano, Tomohiro Itogawa, Keisuke Fujii

Abstract: Magic state distillation plays an important role in universal fault-tolerant quantum computing, and its overhead is one of the major obstacles to realizing fault-tolerant quantum computers. Hence, many studies have been conducted to reduce this overhead. Among these, Litinski has provided a concrete assessment of resource-efficient distillation protocol implementations on the rotated surface code.… ▽ More Magic state distillation plays an important role in universal fault-tolerant quantum computing, and its overhead is one of the major obstacles to realizing fault-tolerant quantum computers. Hence, many studies have been conducted to reduce this overhead. Among these, Litinski has provided a concrete assessment of resource-efficient distillation protocol implementations on the rotated surface code. On the other hand, recently, Itogawa et al. have proposed zero-level distillation, a distillation protocol offering very small spatial and temporal overhead to generate relatively low-fidelity magic states. While zero-level distillation offers preferable spatial and temporal overhead, it cannot directly generate high-fidelity magic states since it only reduces the logical error rate of the magic state quadratically. In this study, we evaluate the spatial and temporal overhead of two-level distillation implementations generating relatively high-fidelity magic states, including ones incorporating zero-level distillation. To this end, we introduce (0+1)-level distillation, a two-level distillation protocol which combines zero-level distillation and the 15-to-1 distillation protocol. We refine the second-level 15-to-1 implementation in it to capitalize on the small footprint of zero-level distillation. Under conditions of a physical error probability of $p_{\mathrm{phys}} = 10^{-4}$ ($10^{-3}$) and targeting an error rate for the magic state within $[5 \times 10^{-17}, 10^{-11}]$ ($[5 \times 10^{-11}, 10^{-8}]$), (0+1)-level distillation reduces the spatiotemporal overhead by more than 63% (61%) compared to the (15-to-1)$\times$(15-to-1) protocol and more than 43% (44%) compared to the (15-to-1)$\times$(20-to-4) protocol, offering a substantial efficiency gain over the traditional protocols. △ Less

Submitted 15 April, 2024; originally announced April 2024.

Comments: 11 pages, 19 figures. This work has been submitted to the IEEE for possible publication

Probabilistic channel simulation using coherence

Authors: Benchi Zhao, Kosuke Ito, Keisuke Fujii

Abstract: Channel simulation using coherence, which refers to realizing a target channel with coherent states and free operations, is a fundamental problem in the quantum resource theory of coherence. The limitations of the accuracy of deterministic channel simulation motivate us to consider the more general probabilistic framework. In this paper, we develop the framework for probabilistic channel simulatio… ▽ More Channel simulation using coherence, which refers to realizing a target channel with coherent states and free operations, is a fundamental problem in the quantum resource theory of coherence. The limitations of the accuracy of deterministic channel simulation motivate us to consider the more general probabilistic framework. In this paper, we develop the framework for probabilistic channel simulation using coherence with free operations. When the chosen set of free operations is the maximally incoherent operations, we provide an efficiently computable semidefinite program (SDP) to calculate the maximal success probability and derive the analytic expression of success probability for some special cases. When the chosen set of free operations is the dephasing-covariant incoherent operations (DIO), we show that if the target channel is not a resource nonactivating channel, then one cannot simulate it exactly both deterministically and probabilistically. The SDP for maximal success probability of simulating a channel by DIO is also given correspondingly. △ Less

Submitted 17 December, 2024; v1 submitted 10 April, 2024; originally announced April 2024.

Comments: 8+2pages, 3 figures. Accepted by PR Research

Efficient Magic State Distillation by Zero-Level Distillation

Authors: Tomohiro Itogawa, Yugo Takada, Yutaka Hirano, Keisuke Fujii

Abstract: Magic state distillation (MSD) is an essential element for universal fault-tolerant quantum computing, which distills a high-fidelity magic state from noisy magic states using ideal (error-corrected) Clifford operations. For ideal Clifford operations, it needs to be performed on the logical qubits and hence incurs a large spatiotemporal overhead, which is one of the major bottlenecks for the reali… ▽ More Magic state distillation (MSD) is an essential element for universal fault-tolerant quantum computing, which distills a high-fidelity magic state from noisy magic states using ideal (error-corrected) Clifford operations. For ideal Clifford operations, it needs to be performed on the logical qubits and hence incurs a large spatiotemporal overhead, which is one of the major bottlenecks for the realization of fault-tolerant quantum computers (FTQCs). Here we propose zero-level distillation, which prepares a high-fidelity logical magic state at the physical level, namely zero level, using physical qubits and nearest-neighbor two-qubit gates on a square lattice. We develop a zero-level distillation circuit and show that distillation can be made even more efficient than the conventional sophisticated approaches with logical level distillations. The key idea involves the Knill et al.-type distillation using the Steane code and its careful mapping to the square-lattice architecture with error detection. The distilled magic state on the Steane-code state is then teleported or converted to surface codes. We numerically find that the error rate of the logical magic state scales as approximately $100 \times p^{2}$ in terms of the physical error rate $p$. For example, with a physical error rate of $p = 10^{-4}$ ($10^{-3}$), the logical error rate is reduced to $p_{L} = 10^{-6}$ ($10^{-4}$), resulting in an improvement of 2 (1) orders of magnitude. This contributes to reducing both space and time overhead for early FTQC as well as full-fledged FTQC combined with conventional multilevel distillation protocols. △ Less

Submitted 20 June, 2025; v1 submitted 6 March, 2024; originally announced March 2024.

Comments: 13 pages and 17 figures

Journal ref: PRX Quantum 6, 020356 (2025)

Improving threshold for fault-tolerant color code quantum computing by flagged weight optimization

Authors: Yugo Takada, Keisuke Fujii

Abstract: Color codes are promising quantum error correction (QEC) codes because they have an advantage over surface codes in that all Clifford gates can be implemented transversally. However, thresholds of color codes under circuit-level noise are relatively low mainly because measurements of their high-weight stabilizer generators cause an increase in a circuit depth, and thus, substantial errors are intr… ▽ More Color codes are promising quantum error correction (QEC) codes because they have an advantage over surface codes in that all Clifford gates can be implemented transversally. However, thresholds of color codes under circuit-level noise are relatively low mainly because measurements of their high-weight stabilizer generators cause an increase in a circuit depth, and thus, substantial errors are introduced. This makes color codes not the best candidate for fault-tolerant quantum computing. Here, we propose a method to suppress the impact of such errors by optimizing weights of decoders using conditional error probabilities conditioned on the measurement outcomes of flag qubits. In numerical simulations, we improve the threshold of the (4.8.8) color code under circuit-level noise from 0.14% to around 0.27%, which is calculated by using an integer programming decoder. Furthermore, in the (6.6.6) color code, we achieve a circuit-level threshold of around 0.36%, which is almost the same value as the highest value in the previous studies employing the same noise model. In both cases, an effective code distance is also improved compared to a conventional method that uses a single ancilla qubit for each stabilizer measurement. Thereby, the achieved logical error rates at low physical error rates are almost one order of magnitude lower than those of the conventional method with the same code distance. Even when compared to the single ancilla method with higher code distance, considering the increased number of qubits used in our method, we achieve lower logical error rates in most cases. This method can also be applied to other weight-based decoders, making the color codes more promising for the candidate of experimental implementation of QEC. Furthermore, one can utilize this approach to improve a threshold of wider classes of QEC codes, such as high-rate quantum low-density parity check codes. △ Less

Submitted 17 September, 2024; v1 submitted 21 February, 2024; originally announced February 2024.

Comments: 16 pages, 20 figures

Journal ref: PRX Quantum 5, 030352 (2024)

SantaQlaus: A resource-efficient method to leverage quantum shot-noise for optimization of variational quantum algorithms

Authors: Kosuke Ito, Keisuke Fujii

Abstract: We introduce SantaQlaus, a resource-efficient optimization algorithm tailored for variational quantum algorithms (VQAs), including applications in the variational quantum eigensolver (VQE) and quantum machine learning (QML). Classical optimization strategies for VQAs are often hindered by the complex landscapes of local minima and saddle points. Although some existing quantum-aware optimizers adap… ▽ More We introduce SantaQlaus, a resource-efficient optimization algorithm tailored for variational quantum algorithms (VQAs), including applications in the variational quantum eigensolver (VQE) and quantum machine learning (QML). Classical optimization strategies for VQAs are often hindered by the complex landscapes of local minima and saddle points. Although some existing quantum-aware optimizers adaptively adjust the number of measurement shots, their primary focus is on maximizing gain per iteration rather than strategically utilizing quantum shot-noise (QSN) to address these challenges. Inspired by the classical Stochastic AnNealing Thermostats with Adaptive momentum (Santa) algorithm, SantaQlaus explicitly leverages inherent QSN for optimization. The algorithm dynamically adjusts the number of quantum measurement shots in an annealing framework: fewer shots are allocated during the early, high-temperature stages for efficient resource utilization and landscape exploration, while more shots are employed later for enhanced precision. Numerical simulations on VQE and QML demonstrate that SantaQlaus outperforms existing optimizers, particularly in mitigating the risks of converging to poor local optima, all while maintaining shot efficiency. This paves the way for efficient and robust training of quantum variational models. △ Less

Submitted 25 December, 2023; originally announced December 2023.

Comments: 22 pages, 4 figures

Experimental Demonstration of Fermionic QAOA with One-Dimensional Cyclic Driver Hamiltonian

Authors: Takuya Yoshioka, Keita Sasada, Yuichiro Nakano, Keisuke Fujii

Abstract: Quantum approximate optimization algorithm (QAOA) has attracted much attention as an algorithm that has the potential to efficiently solve combinatorial optimization problems. Among them, a fermionic QAOA (FQAOA) for solving constrained optimization problems has been developed [Yoshioka, Sasada, Nakano, and Fujii, Phys. Rev. Research vol. 5, 023071, 2023]. In this algorithm, the constraints are es… ▽ More Quantum approximate optimization algorithm (QAOA) has attracted much attention as an algorithm that has the potential to efficiently solve combinatorial optimization problems. Among them, a fermionic QAOA (FQAOA) for solving constrained optimization problems has been developed [Yoshioka, Sasada, Nakano, and Fujii, Phys. Rev. Research vol. 5, 023071, 2023]. In this algorithm, the constraints are essentially imposed as fermion number conservation at arbitrary approximation level. We take the portfolio optimization problem as an application example and propose a new driver Hamiltonian on an one-dimensional cyclic lattice. Our FQAOA with the new driver Hamiltonian reduce the number of gate operations in quantum circuits. Experiments on a trapped-ion quantum computer using 16 qubits on Amazon Braket demonstrates that the proposed driver Hamiltonian effectively suppresses noise effects compared to the previous FQAOA. △ Less

Submitted 7 December, 2023; originally announced December 2023.

Comments: published in 2023 IEEE International Conference on Quantum Computing and Engineering (QCE)

Journal ref: 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), Bellevue, WA, USA, 2023, pp. 300-306