Showing 1–50 of 95 results for author: Liang, J

Nonadiabatic Holonomic Single-Qubit Gates in Non-Hermitian Systems

Authors: Wei Li, Yue Zhang, Yu Kun Chen, Jia Yao Liang

Abstract: Holonomic quantum computation offers a promising route to robust quantum gates, but decoherence remains a central obstacle in realistic implementations. Here we develop a nonadiabatic holonomic scheme for a driven three-level system in the no-jump regime described by an effective non-Hermitian Hamiltonian. Within a biorthogonal framework, tailored complex pulses enforce exact closure of the comput… ▽ More Holonomic quantum computation offers a promising route to robust quantum gates, but decoherence remains a central obstacle in realistic implementations. Here we develop a nonadiabatic holonomic scheme for a driven three-level system in the no-jump regime described by an effective non-Hermitian Hamiltonian. Within a biorthogonal framework, tailored complex pulses enforce exact closure of the computational-subspace evolution at the final time despite the underlying nonunitary dynamics, enabling arbitrary single-qubit holonomic gates without requiring cyclic evolution in its orthogonal complement. In contrast to existing non-Hermitian treatments, which either neglect the overall exponential prefactor or, in adiabatic settings, include dissipation only on the auxiliary excited level, our scheme incorporates decay and dephasing of all bare eigenstates directly into the pulse design, so that dissipation does not reduce the no-jump gate fidelity. △ Less

Submitted 25 June, 2026; originally announced June 2026.

Optomechanical system with tunable dissipative and dispersive couplings

Authors: Quansen Wang, Yuefan Wu, Doudou Wang, Genyuan Xu, Jiawei Liang, Qiang Zhang, Yongmin Li

Abstract: We demonstrate an optomechanical system with tunable dissipative and dispersive couplings using a Fabry-Perot cavity and a string mechanical resonator. By varying the diameter and material of the mechanical resonator, and the relative location between the mechanical resonator and the cavity, the relative strengths of dissipative and dispersive coupling could be tuned continuously from dissipation-… ▽ More We demonstrate an optomechanical system with tunable dissipative and dispersive couplings using a Fabry-Perot cavity and a string mechanical resonator. By varying the diameter and material of the mechanical resonator, and the relative location between the mechanical resonator and the cavity, the relative strengths of dissipative and dispersive coupling could be tuned continuously from dissipation-dominated regime to dispersion-dominated regime. In our experiments, the dissipative-to-dispersive coupling ratios of 1.3 and 0.6 are achieved by using two different mechanical resonators, corresponding to a transition from dissipation-dominated to dispersion-dominated optomechanical system. Theoretically, the coupling ratio could be tuned from 25 to 0.02 by optimizing the mechanical resonator, spanning over three orders of magnitude. These two distinct coupling regimes are achieved with the same experimental platform. The capability to freely adjust the coupling ratio provides a versatile platform for exploring quantum effects of massive mechanical resonators and quantum-limited measurements. △ Less

Submitted 8 June, 2026; originally announced June 2026.

Comments: 24 pages, 11 figures

Universal Speed Limit in a Far-from-Equilibrium Bose Gas: Symmetry and Dynamical Decoherence

Authors: Jun-Cheng Liang, Bo Chen

Abstract: Predicting universal transport coefficients in far-from-equilibrium quantum systems remains a fundamental challenge. A paradigmatic example is the non-thermal fixed point (NTFP) of isolated Bose gases, where coherence spreads as $\ell^2(t) = C\hbar t/m$ with a universal constant $C$. While the scaling exponent $z=2$ is well established, the amplitude $C$ has remained elusive because the underlying… ▽ More Predicting universal transport coefficients in far-from-equilibrium quantum systems remains a fundamental challenge. A paradigmatic example is the non-thermal fixed point (NTFP) of isolated Bose gases, where coherence spreads as $\ell^2(t) = C\hbar t/m$ with a universal constant $C$. While the scaling exponent $z=2$ is well established, the amplitude $C$ has remained elusive because the underlying particle cascade $n(k)\sim k^{-4}$ leads to a divergent kinetic energy, threatening the very existence of a constant speed limit. Here we resolve this paradox and present the first analytical, parameter-free prediction of a universal amplitude $C$. A deep interplay between symmetry and dissipation is uncovered. The emergent weak U(1) symmetry at the NTFP enforces a conserved total current, forcing the low-energy phase dynamics to obey a diffusive Langevin equation with noise entering as the divergence of a stochastic current. This structure, combined with dynamical decoherence of high-momentum modes, yields a universal power-law momentum distribution $\tilde{f}(v)\sim(1+v^2)^{-3}$ (with $v=k\ell$) that naturally regularizes the ultraviolet divergence. From this, a parameter-free geometric baseline $C=3$ is obtained, independent of microscopic details. The experimental value $C=3.4(3)$ [Martirosyan et al., Nature 647, 608 (2025)] is then shown to be quantitatively consistent with universal logarithmic corrections arising from a marginally irrelevant coupling at the fixed point. A new paradigm is thus established for predicting transport coefficients in strongly correlated non-equilibrium systems: symmetry constraints determine the low-energy effective theory, dynamical decoherence provides a natural ultraviolet completion, and scaling analysis delivers testable predictions moving beyond scaling exponents to quantitative amplitude prediction. △ Less

Submitted 3 August, 2026; v1 submitted 12 May, 2026; originally announced May 2026.

Comments: We withdraw this manuscript as the theoretical framework uses a weak-coupling approximation, but the non-thermal fixed point is strongly correlated. Hence, the derived diffusive response, Ward identity, and the predicted $C$ are not justified

Reaching for the performance limit of hybrid density functional theory for molecular chemistry

Authors: Jiashu Liang, Martin Head-Gordon

Abstract: Density functional theory (DFT) offers an exceptional balance between accuracy and efficiency, but practical density functional approximations face an unavoidable trade-off among simplicity, accuracy, and transferability. A systematic protocol is therefore needed to develop functionals that are reliably most accurate within a chosen application domain. Here we present such a protocol by combining… ▽ More Density functional theory (DFT) offers an exceptional balance between accuracy and efficiency, but practical density functional approximations face an unavoidable trade-off among simplicity, accuracy, and transferability. A systematic protocol is therefore needed to develop functionals that are reliably most accurate within a chosen application domain. Here we present such a protocol by combining constraint enforcement, flexible functional forms, and modern optimization. Applying this strategy to the range-separated hybrid (RSH) meta-GGA framework, we obtain the carefully optimized and appropriately constrained hybrid (COACH) functional. Across broad molecular benchmarks, COACH improves both accuracy and transferability relative to leading RSH meta-GGAs, including \omegaB97M-V, while retaining the computational practicality of its rung. Finally, our analysis of the remaining trade-offs and saturation behavior suggests that further systematic progress will likely require the incorporation of genuinely nonlocal information. △ Less

Submitted 24 March, 2026; originally announced March 2026.

Ising Blockade of Resonant Energy Transport in Dense Spin Ensembles

Authors: Hong-Ze Ding, Jiu-Qing Liang

Abstract: Resonant energy transport in dense, disordered dipolar spin ensembles relaxes far more slowly than predicted by exchange-only theories. We identify the missing mechanism as an Ising blockade: configuration-dependent diagonal interactions dynamically detune neighboring spins, so that the transport bottleneck is set by the correlated pair-detuning $ε_{ij}$ rather than by the single-spin linewidth. T… ▽ More Resonant energy transport in dense, disordered dipolar spin ensembles relaxes far more slowly than predicted by exchange-only theories. We identify the missing mechanism as an Ising blockade: configuration-dependent diagonal interactions dynamically detune neighboring spins, so that the transport bottleneck is set by the correlated pair-detuning $ε_{ij}$ rather than by the single-spin linewidth. The resonant fraction is suppressed linearly with the Ising broadening $Γ_{\mathrm{Ising}}$ -- in contrast to the quadratic suppression of conventional relaxation-time approximations. This single emergent scale yields a fit-free renormalization, $T_r^{\mathrm{corr}} \simeq T_r^{\mathrm{orig}}\,Γ_{\mathrm{Ising}}/σ_{\mathrm{exp}}$, which quantitatively accounts for the anomalous scaling $T_r \propto r^{4.5}$ in three-dimensional superradiant masers. The framework extends naturally across dimensions: geometry-dependent accumulation of Ising fields unifies the 3D exponent with the $T_r\propto r^{3}$ scaling observed in two-dimensional surface spin ensembles. △ Less

Submitted 24 May, 2026; v1 submitted 4 February, 2026; originally announced February 2026.

Comments: 5 pages main text, 2 figures; 9 pages Supplemental Material

Three-body scattering area of identical bosons in two dimensions

Authors: Junjie Liang, Hongye Yu, Shina Tan

Abstract: We study the wave function $φ^{(3)}$ of three identical bosons scattering at zero energy, zero total momentum, and zero orbital angular momentum in two dimensions, interacting via short-range potentials with a finite two-body scattering length $a$. We derive asymptotic expansions of $φ^{(3)}$ in two regimes: the 111-expansion, where all three pairwise distances are large, and the 21-expansion, whe… ▽ More We study the wave function $φ^{(3)}$ of three identical bosons scattering at zero energy, zero total momentum, and zero orbital angular momentum in two dimensions, interacting via short-range potentials with a finite two-body scattering length $a$. We derive asymptotic expansions of $φ^{(3)}$ in two regimes: the 111-expansion, where all three pairwise distances are large, and the 21-expansion, where one particle is far from the other two. In the 111-expansion, the leading term grows as $\ln^3(B/a)$ at large hyperradius $B=\sqrt{(s_1^2+s_2^2+s_3^2)/2}$. At order $B^{-2}\ln^{-3}(B/a)$, we identify a three-body parameter $D$ with dimension of length squared, which we term the three-body scattering area. This quantity should be contrasted with the three-body scattering area previously studied for infinite or vanishing two-body scattering length. If the two-body interaction is attractive and supports bound states, $D$ acquires a negative imaginary part, and we derive its relation to the probability amplitudes for the production of two-body bound states in three-body collisions. Under weak modifications of the interaction potentials, we derive the corresponding shift of $D$ in terms of $φ^{(3)}$ and the changes of the two-body and three-body potentials. We also study the effects of $D$ and $φ^{(3)}$ on three-body and many-body physics, including the three-body ground-state energy in a large periodic volume, the many-body energy and the three-body correlation function of the dilute two-dimensional Bose gas, and the three-body recombination rates of two-dimensional ultracold atomic Bose gases. △ Less

Submitted 28 January, 2026; originally announced January 2026.

Comments: 18 pages, 2 figures

QDK/Chemistry: A Modular Toolkit for Quantum Chemistry Applications

Authors: Nathan A. Baker, Brian Bilodeau, Chi Chen, Yingrong Chen, Marco Eckhoff, Alexandra Efimovskaya, Piero Gasparotto, Puck van Gerwen, Rushi Gong, Kevin Hoang, Zahra Hooshmand, Andrew J. Jenkins, Conrad S. N. Johnston, Run R. Li, Jiashu Liang, Hongbin Liu, Alexis Mills, Maximilian Mörchen, George Nishibuchi, Chong Sun, Bill Ticehurst, Matthias Troyer, Jan P. Unsleber, Stefan Wernli, David B. Williams-Young , et al. (1 additional authors not shown)

Abstract: We present QDK/Chemistry, a software toolkit for quantum chemistry workflows targeting quantum computers. The toolkit addresses a key challenge in the field: while quantum algorithms for chemistry have matured considerably, the infrastructure connecting classical electronic structure calculations to quantum circuit execution remains fragmented. QDK/Chemistry provides this infrastructure through a… ▽ More We present QDK/Chemistry, a software toolkit for quantum chemistry workflows targeting quantum computers. The toolkit addresses a key challenge in the field: while quantum algorithms for chemistry have matured considerably, the infrastructure connecting classical electronic structure calculations to quantum circuit execution remains fragmented. QDK/Chemistry provides this infrastructure through a modular architecture that separates data representations from computational methods, enabling researchers to compose workflows from interchangeable components. In addition to providing native implementations of targeted algorithms in the quantum-classical pipeline, the toolkit builds upon and integrates with widely used open-source quantum chemistry packages and quantum computing frameworks through a plugin system, allowing users to combine methods from different sources without modifying workflow logic. This paper describes the design philosophy, current capabilities, and role of QDK/Chemistry as a foundation for reproducible quantum chemistry experiments. △ Less

Submitted 21 January, 2026; originally announced January 2026.

Comments: 32 pages, 3 figures

Macroscopic quantum states, quantum phase transition for $N$ three-level atoms in an optical cavity -- Gauge principle and non-Hermitian Hamiltonian

Authors: Ni Liu, Xinyu Jia, J. -Q. Liang

Abstract: We study in this paper the quantum phase transition (QPT) from normal phase (NP) to superradiant phase (SP) for $N$ three-level atoms in a single-mode optical cavity for both Hermitian and non Hermitian Hamiltonians, where the $Ξ$-type three-level atom is described by spin-$1$ pseudo-spin operators. The long standing gauge-choice ambiguity of $\mathbf{A\cdot p}$ and $\mathbf{d\cdot E}$ called resp… ▽ More We study in this paper the quantum phase transition (QPT) from normal phase (NP) to superradiant phase (SP) for $N$ three-level atoms in a single-mode optical cavity for both Hermitian and non Hermitian Hamiltonians, where the $Ξ$-type three-level atom is described by spin-$1$ pseudo-spin operators. The long standing gauge-choice ambiguity of $\mathbf{A\cdot p}$ and $\mathbf{d\cdot E}$ called respectively the Coulomb and dipole gauges is resolved by the time-dependent gauge transformation on the Schrödinger equation. Both $\mathbf{A\cdot p}$ and $\mathbf{d\cdot E}$ interactions are included in the unified gauge, which is truly gauge equivalent to the minimum coupling principle. The Coulomb and dipole interactions are just the special cases of unified gauge. Remarkably three interactions lead to the same results under the resonant condition of field-atom frequencies, while significant difference appears in red and blue detunings. The QPT is analyzed in terms of spin coherent-state variational method, which indicates the abrupt changes of energy spectrum, average photon number as well as the atomic population at the critical point of interaction constant. Crucially, we reveal the sensitive dependence on the initial optical-phase, which is particularly useful to test the validity of three gauges experimentally. The non-Hermitian atom-field interaction results in the exceptional point (EP), beyond which the semiclassical energy function becomes complex. However the energy spectrum of variational ground state is real in the absence of EP, and does not become complex. The superradiant state is unstable due to the non-Hermitian interaction induced photon-number loss. Thus only the NP exists in the non-Hermitian Dicke Model Hamiltonian. △ Less

Submitted 23 December, 2025; originally announced December 2025.

Decoding Quantum Search Advantage: The Critical Role of State Properties in Random Walks

Authors: Si-Qi Zhou, Jin-Min Liang, Ziheng Ding, Zhihua Chen, Shao-Ming Fei, Zhihao Ma

Abstract: Quantum algorithms have demonstrated provable speedups over classical counterparts, yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge. In this work, we decode the quantum search advantage by investigating the critical role of quantum state properties in random-walk-based algorithms. We propose three distinct variants of quantum rand… ▽ More Quantum algorithms have demonstrated provable speedups over classical counterparts, yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge. In this work, we decode the quantum search advantage by investigating the critical role of quantum state properties in random-walk-based algorithms. We propose three distinct variants of quantum random-walk search algorithms and derive exact analytical expressions for their success probabilities. These probabilities are fundamentally determined by specific initial state properties: the coherence fraction governs the first algorithm's performance, while entanglement and coherence dominate the outcomes of the second and third algorithms, respectively. We show that increased coherence fraction enhances success probability, but greater entanglement and coherence reduce it in the latter two cases. These findings reveal fundamental insights into harnessing quantum properties for advantage and guide algorithm design. Our searches achieve Grover-like speedups and show significant potential for quantum-enhanced machine learning. △ Less

Submitted 10 November, 2025; originally announced November 2025.

Comments: 7+7 pages, 5 figures

Journal ref: Chinese Physics Letters, 42(9): 090602 (2025)

Static and dynamic coherence fraction in the Bernstein-Vazirani algorithm

Authors: Si-Qi Zhou, Jin-Min Liang, Jiayin Peng, Zhihua Chen, Shao-Ming Fei, Zhihao Ma

Abstract: Quantum entanglement and coherence are crucial resources in quantum information theory. In some scenarios, however, it is not necessary to directly estimate entanglement or coherence measures to quantify the capabilities of a state in quantum information processing. Instead, fully entangled fraction and coherence fraction are two alternatives for entanglement and coherence in specific quantum task… ▽ More Quantum entanglement and coherence are crucial resources in quantum information theory. In some scenarios, however, it is not necessary to directly estimate entanglement or coherence measures to quantify the capabilities of a state in quantum information processing. Instead, fully entangled fraction and coherence fraction are two alternatives for entanglement and coherence in specific quantum tasks. Here, we establish a link between the coherence fraction and the Bernstein-Vazirani algorithm, which has several potential applications including cryptography and database search. We show that the success probability of the generalized Bernstein-Vazirani algorithm depends only on the coherence fraction of the initial state rather than its entanglement or coherence. Moreover, we discuss the coherence fraction dynamics and establish a relation between the operator's coherence fraction and the algorithm's success probability. Our findings highlight how quantum coherence fraction influences the efficiency of quantum algorithms. △ Less

Submitted 10 November, 2025; originally announced November 2025.

Comments: 9 pages, 3 figures

Journal ref: Advanced Quantum Technologies, 8(10), 2400709 (2025)

Coherence Fraction in Grover Search Algorithm

Authors: Si-Qi Zhou, Hai Jin, Jin-Min Liang, Shao-Ming Fei, Yunlong Xiao, Zhihao Ma

Abstract: The question of which resources drive the advantages in quantum algorithms has long been a fundamental challenge. While entanglement and coherence are critical to many quantum algorithms, our results indicate that they do not fully explain the quantum advantage achieved by the Grover search algorithm. By introducing a generalized Grover search algorithm, we demonstrate that the success probability… ▽ More The question of which resources drive the advantages in quantum algorithms has long been a fundamental challenge. While entanglement and coherence are critical to many quantum algorithms, our results indicate that they do not fully explain the quantum advantage achieved by the Grover search algorithm. By introducing a generalized Grover search algorithm, we demonstrate that the success probability depends not only on the querying number of oracles but also on the coherence fraction, which quantifies the fidelity between an arbitrary initial quantum state and the equal superposition state. Additionally, we explore the role of the coherence fraction in the quantum minimization algorithm, which offers a framework for solving complex problems in quantum machine learning. These findings offer insights into the origins of quantum advantage and open pathways for the development of new quantum algorithms. △ Less

Submitted 10 November, 2025; originally announced November 2025.

Comments: 9 pages, 6 figures. Published in Physical Review A 110, 062429 (2024)

Detecting gravitational waves with spin systems

Authors: Jiamin Liang, Mingqiu Li, Yu Gao, Wei Ji, Sichun Sun, Qi-Shu Yan

Abstract: The observation of gravitational waves has opened a new window into the Universe through gravitational-wave astronomy. However, high-frequency gravitational waves remain undetected. In this work, we propose that spin systems can be employed to detect gravitational waves in this unexplored frequency regime. We derive the spin's response to gravitational waves and identify three distinct effects: th… ▽ More The observation of gravitational waves has opened a new window into the Universe through gravitational-wave astronomy. However, high-frequency gravitational waves remain undetected. In this work, we propose that spin systems can be employed to detect gravitational waves in this unexplored frequency regime. We derive the spin's response to gravitational waves and identify three distinct effects: the well-known Gertsenshtein effect, a metric-induced interaction, and the gravitational spin Hall effect. We focus on nuclear spins and utilize nuclear magnetic resonance to enhance the gravitational response, leveraging the advantages of long coherence time, high polarization, and a small gyromagnetic ratio. The proposed experimental scheme is capable of probing gravitational waves in the kilohertz to gigahertz range, with projected sensitivities reaching $\sqrt{S_h}\approx10^{-20}~\mathrm{Hz}^{-1/2}$. △ Less

Submitted 13 October, 2025; originally announced October 2025.

Comments: 8 pages, 3 figures

High-fidelity realisation of CNOT gate in Majorana-based optical platform

Authors: Jia-Kun Li, Kai Sun, Ze-Yan Hao, Jia-He Liang, Jiannis K. Pachos, Lucy Byles, Jin-Shi Xu, Yong-Jian Han, Chuan-Feng Li, Guang-Can Guo

Abstract: We present the experimental realisation of a robust CNOT quantum gate using Majorana zero modes simulated on a photonic platform. Three Kitaev chains supporting Majorana zero modes at their endpoints are used to encode two logical qubits, and both intra-chain and inter-chain braiding operations are performed to implement the CNOT gate. While the topological encoding of quantum information in Major… ▽ More We present the experimental realisation of a robust CNOT quantum gate using Majorana zero modes simulated on a photonic platform. Three Kitaev chains supporting Majorana zero modes at their endpoints are used to encode two logical qubits, and both intra-chain and inter-chain braiding operations are performed to implement the CNOT gate. While the topological encoding of quantum information in Majorana fermions does not offer full topological protection in our non-interacting photonic setting, it nevertheless exhibits a natural resilience to the dominant noise and decoherence effects present in the experiment. Consequently, the fidelity of the CNOT gate is significantly enhanced, surpassing 0.992 and addressing a key limitation in the path toward scalable quantum computation. These results represent a major advancement in topological quantum computing with Majorana fermions and underscore the potential of photonic platforms for realising high-fidelity quantum gates. △ Less

Submitted 23 December, 2025; v1 submitted 20 August, 2025; originally announced August 2025.

Comments: 8 pages, 6 figures

Gold-Standard Chemical Database 137 (GSCDB137): A diverse set of accurate energy differences for assessing and developing density functionals

Authors: Jiashu Liang, Martin Head-Gordon

Abstract: We present GSCDB137, a rigorously curated benchmark library of 137 data sets (8377 entries) covering main-group and transition-metal reaction energies and barrier heights, (intramolecular) non-covalent interactions, dipole moments, polarizabilities, electric-field response energies, and vibrational frequencies. Legacy data from GMTKN55 and MGCDB84 have been updated to today's best reference values… ▽ More We present GSCDB137, a rigorously curated benchmark library of 137 data sets (8377 entries) covering main-group and transition-metal reaction energies and barrier heights, (intramolecular) non-covalent interactions, dipole moments, polarizabilities, electric-field response energies, and vibrational frequencies. Legacy data from GMTKN55 and MGCDB84 have been updated to today's best reference values; redundant, spin-contaminated, or low-quality points were removed, and many new, property-focused sets were added. Testing 29 popular density functional approximations (DFAs) confirms the expected Jacob's-ladder hierarchy overall but also reveals notable exceptions: functional performance for frequencies and electric-field properties correlates poorly with that for other ground-state energetics. ωB97M-V and ωB97X-V are the most balanced hybrid meta-GGA and hybrid GGA, respectively; B97M-V and revPBE-D4 lead the meta-GGA and GGA classes. Double hybrids lower mean errors by about 25 % versus the best hybrids but demand careful frozen-core, basis-set, and multi-reference treatment. GSCDB137 offers a comprehensive, openly documented platform for stringent DFA validation and for training the next generation of non-empirical and machine-learned functionals. △ Less

Submitted 4 November, 2025; v1 submitted 18 August, 2025; originally announced August 2025.

Variational-toolbox-based separability detection of multiqubit states

Authors: Jin-Min Liang, Shao-Ming Fei, Qiongyi He

Abstract: Parametrized quantum circuits (PQCs) are crucial in variational quantum algorithms. While it is commonly believed that the optimal PQC is solely used to reproduce the target state, we here reveal that the optimal PQC can also provide valuable insights into the state's properties. We propose variational toolboxes to identify the $k$-separability of pure states, with or without preparation noise, by… ▽ More Parametrized quantum circuits (PQCs) are crucial in variational quantum algorithms. While it is commonly believed that the optimal PQC is solely used to reproduce the target state, we here reveal that the optimal PQC can also provide valuable insights into the state's properties. We propose variational toolboxes to identify the $k$-separability of pure states, with or without preparation noise, by checking the structure within the optimal PQCs. Additionally, we introduce adaptive optimization strategies to detect the $k$-separability of mixed states. Compared to fixed PQCs, our approach controls fewer parameters for low-rank states. Finally, we validate our methods through numerical demonstrations for various states. △ Less

Submitted 8 August, 2025; v1 submitted 5 June, 2025; originally announced June 2025.

Comments: v2: close to the published version

Journal ref: Phys. Rev. A 112, 022404 (2025)

Quantum mechanics of inverted potential well -- Hermitian Hamiltonian with imaginary eigenvalues, quantum-classical correspondence

Authors: Ni Liu, J. -Q. Liang

Abstract: We in this paper study the quantization of a particle in an inverted potential well. The Hamiltonian is Hermitian, while the potential is unbounded below. Classically the particle moves away acceleratingly from the center of potential top. The existing eigenstates must be unstable with imaginary eigenvalues, which characterize the decay rate of states. We solve the Hamiltonian problem of inverted… ▽ More We in this paper study the quantization of a particle in an inverted potential well. The Hamiltonian is Hermitian, while the potential is unbounded below. Classically the particle moves away acceleratingly from the center of potential top. The existing eigenstates must be unstable with imaginary eigenvalues, which characterize the decay rate of states. We solve the Hamiltonian problem of inverted potential well by the algebraic method with imaginary-frequency raising and lowering boson operators similar to the normal oscillator case. The boson number operator is non-Hermitian, while the integer-number eigenvalues are, of course, real. Dual sets of eigenstates, denoted by "bra" and "ket", are requested corresponding respectively to the complex conjugate number-operators. Orthonormal condition exists between the "bra" and "ket" states. We derive a spatially non-localized generating function, from which $n$-th eigenfunctions can be generated by the raising operators in coordinate representation. The "bra" and "ket" generating functions are mutually normalized with the imaginary integration measure. The probability density operators defined between the "bra" and "ket" states are non-Hermitian invariants, which lead to the Schrődinger equations respectively for the "bra" and "ket" states. While probabilities of "bra" and "ket" states themselves are not conserved quantities because of the decay. The imaginary-frequency boson coherent states are defined as eigenstates of lowering operators. The minimum uncertainty relation is proved explicitly in the coherent states. Finally the probability average of Heisenberg equation in the coherent states is shown precisely in agreement with the classical equation of motion. The quantum-classical correspondence exists in the imaginary eigenvalue system. △ Less

Submitted 5 May, 2025; v1 submitted 1 May, 2025; originally announced May 2025.

Experimental Certification of Quantum Measurements with Maximally Mixed States

Authors: Jia-He Liang, Ze-Yan Hao, Jia-Kun Li, Kai Sun, Zhen-Peng Xu, Jin-Shi Xu, Chuan-Feng Li, Guang-Can Guo, Adán Cabello

Abstract: So far, certifying quantum devices from their input-output statistics, under minimal assumptions, required the preparation of specific pure quantum states. Recently, Xu et al. [Phys. Rev. Lett. 132, 140201 (2024)] have demonstrated that certain sets of quantum observables can be certified using any state of full rank. However, their method is restricted to ideal conditions. Here, we address this p… ▽ More So far, certifying quantum devices from their input-output statistics, under minimal assumptions, required the preparation of specific pure quantum states. Recently, Xu et al. [Phys. Rev. Lett. 132, 140201 (2024)] have demonstrated that certain sets of quantum observables can be certified using any state of full rank. However, their method is restricted to ideal conditions. Here, we address this problem and present an experimentally robust method that eliminates the need of preparing states with high fidelity with respect to specific pure states. We demonstrate the feasibility of the method by experimentally certifying photonic devices implementing Peres' set of 24 ququart observables [J. Phys. A 24, L175 (1991)] and Yu and Oh's set of 13 qutrit observables [Phys. Rev. Lett. 108, 030402 (2012)], using maximally mixed states as input. This approach offers a crucial advantage for certifying high-dimensional quantum systems, since it works with maximally mixed and thermal states. △ Less

Submitted 11 January, 2026; v1 submitted 23 April, 2025; originally announced April 2025.

Detecting high-dimensional entanglement by randomized product projections

Authors: Jin-Min Liang, Shuheng Liu, Shao-Ming Fei, Qiongyi He

Abstract: The characterization of high-dimensional entanglement plays a crucial role in the field of quantum information science. Conventional entanglement criteria measuring coherent superpositions of multiple basis states face experimental bottlenecks on most physical platforms due to limited multi-channel control. Here, we introduce a practically efficient detection strategy based on randomized product p… ▽ More The characterization of high-dimensional entanglement plays a crucial role in the field of quantum information science. Conventional entanglement criteria measuring coherent superpositions of multiple basis states face experimental bottlenecks on most physical platforms due to limited multi-channel control. Here, we introduce a practically efficient detection strategy based on randomized product projections. We show that the first-order moments of such projections can be used to estimate entanglement fidelity, thereby enabling practical and efficient certification of the Schmidt number in high-dimensional bipartite systems. By constructing optimal observables, it is sufficient to merely measure a single basis state, substantially reducing experimental overhead. Moreover, we present an algorithm to obtain a lower bound of the Schmidt number with a high confidence level from a limited number of experimental data. Our results open up resource-efficient experimental avenues to detect high-dimensional entanglement and test its implementations in modern information technologies. △ Less

Submitted 10 February, 2026; v1 submitted 2 January, 2025; originally announced January 2025.

Comments: 21 pages

Journal ref: Quantum Sci. Technol. 11 01LT03 (2026)

Real randomized measurements for analyzing properties of quantum states

Authors: Jin-Min Liang, Satoya Imai, Shuheng Liu, Shao-Ming Fei, Otfried Gühne, Qiongyi He

Abstract: Randomized measurements are useful for analyzing quantum systems especially when quantum control is not fully perfect. However, their practical realization typically requires multiple rotations in the complex space due to the adoption of random unitaries. Here, we introduce two simplified randomized measurements that limit rotations in a subspace of the complex space. The first is \textit{real ran… ▽ More Randomized measurements are useful for analyzing quantum systems especially when quantum control is not fully perfect. However, their practical realization typically requires multiple rotations in the complex space due to the adoption of random unitaries. Here, we introduce two simplified randomized measurements that limit rotations in a subspace of the complex space. The first is \textit{real randomized measurements} (RRMs) with orthogonal evolution and real local observables. The second is \textit{partial real randomized measurements} (PRRMs) with orthogonal evolution and imaginary local observables. We show that these measurement protocols exhibit different abilities in capturing correlations of bipartite systems. We explore various applications of RRMs and PRRMs in different quantum information tasks such as characterizing high-dimensional entanglement, quantum imaginarity, and predicting properties of quantum states with classical shadow. △ Less

Submitted 27 August, 2025; v1 submitted 8 November, 2024; originally announced November 2024.

Comments: 25 pages, 5 figures, v2: close to the published version

Journal ref: Phys. Rev. A 112, 022434 (2025)

A High-Performance List Decoding Algorithm for Surface Codes with Erroneous Syndrome

Authors: Jifan Liang, Qianfan Wang, Lvzhou Li, Xiao Ma

Abstract: Quantum error-correcting codes (QECCs) are necessary for fault-tolerant quantum computation. Surface codes are a class of topological QECCs that have attracted significant attention due to their exceptional error-correcting capabilities and easy implementation. In the decoding process of surface codes, the syndromes are crucial for error correction, however, they are not always correctly measured.… ▽ More Quantum error-correcting codes (QECCs) are necessary for fault-tolerant quantum computation. Surface codes are a class of topological QECCs that have attracted significant attention due to their exceptional error-correcting capabilities and easy implementation. In the decoding process of surface codes, the syndromes are crucial for error correction, however, they are not always correctly measured. Most of the existing decoding algorithms for surface codes need extra measurements to correct syndromes with errors, which implies a potential increase in inference complexity and decoding latency. In this paper, we propose a high-performance list decoding algorithm for surface codes with erroneous syndromes, where syndrome soft information is incorporated in the decoding, allowing qubits and syndrome to be recovered without needing extra measurements. Precisely, we first use belief propagation (BP) decoding for pre-processing with syndrome soft information, followed by ordered statistics decoding (OSD) for post-processing to list and recover both qubits and syndromes. Numerical results demonstrate that our proposed algorithm efficiently recovers erroneous syndromes and significantly improves the decoding performance of surface codes with erroneous syndromes compared to minimum-weight perfect matching (MWPM), BP and original BP-OSD algorithms. △ Less

Submitted 8 November, 2024; v1 submitted 10 September, 2024; originally announced September 2024.

Comments: 9 pages, 10 figures

Photonic simulation of Majorana-based Jones polynomials

Authors: Jia-Kun Li, Kai Sun, Ze-Yan Hao, Jia-He Liang, Si-Jing Tao, Jiannis K. Pachos, Jin-Shi Xu, Yong-Jian Han, Chuan-Feng Li, Guang-Can Guo

Abstract: Jones polynomials were introduced as a tool to distinguish between topologically different links. Recently, they emerged as the central building block of topological quantum computation: by braiding non-Abelian anyons it is possible to realise quantum algorithms through the computation of Jones polynomials. So far, it has been a formidable task to evaluate Jones polynomials through the control and… ▽ More Jones polynomials were introduced as a tool to distinguish between topologically different links. Recently, they emerged as the central building block of topological quantum computation: by braiding non-Abelian anyons it is possible to realise quantum algorithms through the computation of Jones polynomials. So far, it has been a formidable task to evaluate Jones polynomials through the control and manipulation of non-Abelian anyons. In this study, a photonic quantum system employing two-photon correlations and non-dissipative imaginary-time evolution is utilized to simulate two inequivalent braiding operations of Majorana zero modes. The resulting amplitudes are shown to be mathematically equivalent to Jones polynomials at a particular value of their parameter. The high-fidelity of our optical platform allows us to distinguish between a wide range of links, such as Hopf links, Solomon links, Trefoil knots, Figure Eight knots and Borromean rings, through determining their corresponding Jones polynomials. Our photonic quantum simulator represents a significant step towards executing fault-tolerant quantum algorithms based on topological quantum encoding and manipulation. △ Less

Submitted 31 May, 2024; v1 submitted 7 March, 2024; originally announced March 2024.

Imaginary eigenvalues of Hermitian Hamiltonian with an inverted potential well and transition to the real spectrum at exceptional point by a non-Hermitian interaction

Authors: Ni Liu, Meng Luo, J. -Q. Liang

Abstract: We in this paper study the hermiticity of Hamiltonian and energy spectrum for the SU(1; 1) systems. The Hermitian Hamiltonian can possess imaginary eigenvalues in contrast with the common belief that hermiticity is a suffcient condition for real spectrum. The imaginary eigenvalues are derived in algebraic method with imaginary-frequency boson operators for the Hamiltonian of inverted potential wel… ▽ More We in this paper study the hermiticity of Hamiltonian and energy spectrum for the SU(1; 1) systems. The Hermitian Hamiltonian can possess imaginary eigenvalues in contrast with the common belief that hermiticity is a suffcient condition for real spectrum. The imaginary eigenvalues are derived in algebraic method with imaginary-frequency boson operators for the Hamiltonian of inverted potential well. Dual sets of mutually orthogonal eigenstates are required corresponding respectively to the complex conjugate eigenvalues. Arbitrary order eigenfunctions seen to be the polynomials of imaginary frequency are generated from the normalized ground-state wave functions, which are spatially non localized. The Hamiltonian including a non-Hermitian interaction term can be converted by similarity transformation to the Hermitian one with an effective potential of reduced slope, which is turnable by the interaction constant. The transformation operator should not be unitary but Hermitian different from the unitary transformation in ordinary quantum mechanics. The effective potential vanishes at a critical value of coupling strength called the exceptional point, where all eigenstates are degenerate with zero eigenvalue and transition from imaginary to real spectra appears. The SU(1; 1) generator $\widehat{S}_{z}$ with real eigenvalues determined by the commutation relation of operators, however, is non-Hermitian in the realization of imaginay-frequency boson operators. The classical counterpart of the quantum Hamiltonian with non-Hermitian interaction is a complex function of the canonical variables. It becomes by the canonical transformation of variables a real function indicating exactly the one to one quantum-classical correspondence of Hamiltonians. △ Less

Submitted 3 April, 2025; v1 submitted 8 February, 2024; originally announced February 2024.

Three-body scattering area for particles with infinite or zero scattering length in two dimensions

Authors: Junjie Liang, Shina Tan

Abstract: We derive the asymptotic expansions of the wave function of three particles having equal mass with finite-range interactions and infinite or zero two-dimensional scattering length colliding at zero energy and zero orbital angular momentum, from which a three-body parameter $D$ is defined. The dimension of $D$ is length squared, and we call $D$ three-body scattering area. We find that the ground st… ▽ More We derive the asymptotic expansions of the wave function of three particles having equal mass with finite-range interactions and infinite or zero two-dimensional scattering length colliding at zero energy and zero orbital angular momentum, from which a three-body parameter $D$ is defined. The dimension of $D$ is length squared, and we call $D$ three-body scattering area. We find that the ground state energy per particle of a zero-temperature dilute Bose gas with these interactions is approximately $\frac{\hbar^2 D }{6m}ρ^2$, where $ρ$ is the number density of the bosons, $m$ is the mass of each boson, and $\hbar$ is Planck's constant over $2π$. Such a Bose gas is stable at $D\geq 0$ in the thermodynamic limit, and metastable at $D<0$ in the harmonic trap if the number of bosons is less than $N_{cr}\approx 3.6413 \sqrt{\frac{\hbar}{mω|D|}}$, where $ω$ is the angular frequency of the harmonic trap. If the two-body interaction supports bound states, $D$ typically acquires a negative imaginary part, and we find the relation between this imaginary part and the amplitudes of the pair-boson production processes. We derive a formula for the three-body recombination rate constant of the many-boson system in terms of the imaginary part of $D$. △ Less

Submitted 28 April, 2024; v1 submitted 3 February, 2024; originally announced February 2024.

Single-modulated-pulse two-qubit gates for Rydberg atoms with noncyclic geometric control

Authors: Zi-Yuan Chen, Jia-Hao Liang, Zhao-Xin Fu, Hong-Zhi Liu, Ze-Rui He, 1 Meng Wang, Zhi-Wei Han, Jia-Yi Huang, Qing-Xian Lv, Yan-Xiong Du

Abstract: Arrays of neutral atoms have emerged as promising platforms for quantum computing. Realization of high-fidelity two-qubit gates with robustness is currently a significant important task for large-scale operations. In this paper, we present a convenient approach for implementing a two-qubit controlled-phase gate using Rydberg blockade. We achieve the noncyclic geometric control with a single modula… ▽ More Arrays of neutral atoms have emerged as promising platforms for quantum computing. Realization of high-fidelity two-qubit gates with robustness is currently a significant important task for large-scale operations. In this paper, we present a convenient approach for implementing a two-qubit controlled-phase gate using Rydberg blockade. We achieve the noncyclic geometric control with a single modulated pulse. As compared with the control scheme by cyclic evolution that determined by dynamical parameters, the robustness of the proposal against systematic errors will be remarkably improved due to the geometric characteristic. Importantly, the noncyclic geometric control reduces the gate time for small rotation angles and will be more insensitive to the decoherence effect. We accelerate the adiabatic control with the aid of shortcuts to adiabaticity to further shorten the operation time. We apply our protocol to the algorithm of quantum Fourier transformation to show the actual acceleration. Therefore, the proposed scheme will provide an analytical waveforms for arbitrary two-qubit gates and may have important use in the experiments of atomic arrays. △ Less

Submitted 1 February, 2024; originally announced February 2024.

Comments: 8 pages, 5 figures

Effects of Different Q-swaps Modes on Percolation Threshold in Small-world Quantum Networks

Authors: JianXiong Liang, Xiaoguang Chen, Yaoyao Wang

Abstract: Quantum networks are interconnected by nodes, between singlets which are formed to ensure the successful transmission of information with a probability of 1. However, in real quantum networks, nodes often share a partially entangled state instead of a singlet due to factors such as environmental noise. Therefore, it is necessary to convert the partially entangled state into a singlet for efficient… ▽ More Quantum networks are interconnected by nodes, between singlets which are formed to ensure the successful transmission of information with a probability of 1. However, in real quantum networks, nodes often share a partially entangled state instead of a singlet due to factors such as environmental noise. Therefore, it is necessary to convert the partially entangled state into a singlet for efficient communication. Percolation happens during the conversion of connected edges in the whole network. As a result, when the singlet conversion probability (SCP) is greater than the percolation threshold, a giant interconnected cluster that meets the basic requirements of communication will appear in the network. The percolation threshold of the network reveals the minimum resources required to carry out large scale quantum communication. In this paper, we investigate the effect of different q-swaps on the percolation threshold in quantum entanglement percolation of small world networks. We show that Quantum Entanglement Percolation (QEP) has a better percolation performance than Classical Entanglement Percolation (CEP). By using different q swaps in Watts Strogatz (WS) small world networks and Kleinberg networks for simulation, we also show that the percolation threshold is minimized when SCP is equal to the average degree of the network. Furthermore, we introduce quantum walk as a new scheme to have an extra reduction in the percolation threshold. △ Less

Submitted 22 January, 2024; originally announced January 2024.

Proposal of detecting topological transition of quantum braiding in three-fold degenerate eigen subspace

Authors: Zhi-Wei Han, Jia-Hao Liang, Zhao-Xin Fu, Hong-Zhi Liu, Zi-Yuan Chen, Meng Wang, Ze-Rui He, Jia-Yi Huang, Qing-Xian Lv, Kai-Yu Liao, Yan-Xiong Du

Abstract: The braiding operations of quantum states have attracted substantial attention due to their great potential for realizing topological quantum computations. In this paper, we show that a three-fold degenerate eigen subspace can be obtained in a four-level Hamiltonian which is the minimal physical system. Braiding operations are proposed to apply to dressed states in the subspace. The topology of th… ▽ More The braiding operations of quantum states have attracted substantial attention due to their great potential for realizing topological quantum computations. In this paper, we show that a three-fold degenerate eigen subspace can be obtained in a four-level Hamiltonian which is the minimal physical system. Braiding operations are proposed to apply to dressed states in the subspace. The topology of the braiding diagram can be characterized through physical methods once that the sequential braiding pulses are adopted. We establish an equivalent relationship function between the permutation group and the output states where different output states correspond to different values of the function. The topological transition of the braiding happens when two operations overlap, which is detectable through the measurement of the function. Combined with the phase variation method, we can analyze the wringing pattern of the braiding. Therefore, the experimentally-feasible system provides a platform to investigate braiding dynamics, the SU(3) physics and the qutrit gates. △ Less

Submitted 3 January, 2024; originally announced January 2024.

Comments: 10 pages, 6 figures

Probing topological phase transition with non-Hermitian perturbations

Authors: Jingcheng Liang, Chen Fang, Jiangping Hu

Abstract: We demonstrate that non-Hermitian perturbations can probe topological phase transitions and unambiguously detect non-Abelian zero modes. We show that under carefully designed non-Hermitian perturbations, the Loschmidt echo(LE) decays into 1/N where N is the ground state degeneracy in the topological non-trivial phase, while it approaches 1 in the trivial phase. This distinction is robust against s… ▽ More We demonstrate that non-Hermitian perturbations can probe topological phase transitions and unambiguously detect non-Abelian zero modes. We show that under carefully designed non-Hermitian perturbations, the Loschmidt echo(LE) decays into 1/N where N is the ground state degeneracy in the topological non-trivial phase, while it approaches 1 in the trivial phase. This distinction is robust against small parameter deviations in the non-Hermitian perturbations. We further study four well-known models that support Majorana or parafermionic zero modes. By calculating their dynamical responses to specific non-Hermitian perturbations, we prove that the steady-state LE can indeed differentiate between different phases. This method avoids the ambiguity introduced by trivial zero-energy states and thus provides an alternative and promising way to demonstrate the emergence of topologically non-trivial phases. The experimental realizations of non-Hermitian perturbations are discussed. △ Less

Submitted 31 December, 2023; originally announced January 2024.

Comments: 11 pages, 4 figures

Exact solutions of a spin-orbit coupling model in two-dimensional central-potentials and quantum-classical correspondence

Authors: Jun-Li Xin, Jiu-Qing Liang

Abstract: In this paper we present both the classical and quantum periodic-orbits of a neutral spinning particle constrained in two-dimensional central-potentials with a cylindrically symmetric electric-field in addition which leads to an effective non-Abelian gauge field generated by the spin-orbit coupling. Coherent superposition of orbital angular-eigenfunctions obtained explicitly at the condition of ze… ▽ More In this paper we present both the classical and quantum periodic-orbits of a neutral spinning particle constrained in two-dimensional central-potentials with a cylindrically symmetric electric-field in addition which leads to an effective non-Abelian gauge field generated by the spin-orbit coupling. Coherent superposition of orbital angular-eigenfunctions obtained explicitly at the condition of zero-energy exhibits the quantum-classical correspondence in the meaning of exact coincidence between classical orbits and spatial patterns of quantum wave-functions, which as a consequence results in the fractional quantization of orbital angular-momentum by the requirement of the same rotational symmetry of quantum and classical orbits. A non-Abelian anyon-model emerges in a natural way. △ Less

Submitted 20 August, 2023; originally announced August 2023.

Comments: 16 pages, 4 figures

Journal ref: Sci China-Phys Mech Astron August, 2014, 57(8),1504-1510

Sharing EPR steering between sequential pairs of observers

Authors: Qiao-Qiao Lv, Jin-Min Liang, Zhi-Xi Wang, Shao-Ming Fei

Abstract: The recycling of quantum correlations has attracted widespread attention both theoretically and experimentally. Previous works show that bilateral sharing of nonlocality is impossible under mild measurement strategy and 2-qubit entangled state can be used to witness entanglement arbitrary many times by sequential and independent pairs of observers. However, less is known about the bilateral sharin… ▽ More The recycling of quantum correlations has attracted widespread attention both theoretically and experimentally. Previous works show that bilateral sharing of nonlocality is impossible under mild measurement strategy and 2-qubit entangled state can be used to witness entanglement arbitrary many times by sequential and independent pairs of observers. However, less is known about the bilateral sharing of EPR steering yet. Here, we aim at investigating the EPR steering sharing between sequential pairs of observers. We show that an unbounded number of sequential Alice-Bob pairs can share the EPR steering as long as the initially shared state is an entangled two-qubit pure state. The claim is also true for particular class of mixed entangled states. △ Less

Submitted 19 July, 2023; originally announced July 2023.

Comments: 11 pages, 1 figure

Journal ref: J. Phys. A: Math. Theor., 56 (2023) 325301

Ising Hamiltonians for Constrained Combinatorial Optimization Problems and the Metropolis-Hastings Warm-Starting Algorithm

Authors: Hui-Min Li, Jin-Min Liang, Zhi-Xi Wang, Shao-Ming Fei

Abstract: Quantum approximate optimization algorithm (QAOA) is a promising variational quantum algorithm for combinatorial optimization problems. However, the implementation of QAOA is limited due to the requirement that the problems be mapped to Ising Hamiltonians and the nonconvex optimization landscapes. Although the Ising Hamiltonians for many NP hard problems have been obtained, a general method to obt… ▽ More Quantum approximate optimization algorithm (QAOA) is a promising variational quantum algorithm for combinatorial optimization problems. However, the implementation of QAOA is limited due to the requirement that the problems be mapped to Ising Hamiltonians and the nonconvex optimization landscapes. Although the Ising Hamiltonians for many NP hard problems have been obtained, a general method to obtain the Ising Hamiltonians for constrained combinatorial optimization problems (CCOPs) has not yet been investigated. In this paper, a general method is introduced to obtain the Ising Hamiltonians for CCOPs and the Metropolis-Hastings warm-starting algorithm for QAOA is presented which can provably converge to the global optimal solutions. The effectiveness of this method is demonstrated by tackling the minimum weight vertex cover (MWVC) problem, the minimum vertex cover (MVC) problem, and the maximal independent set problem as examples. The Ising Hamiltonian for the MWVC problem is obtained first time by using this method. The advantages of the Metropolis-Hastings warm-starting algorithm presented here is numerically analyzed through solving 30 randomly generated MVC cases with 1-depth QAOA. △ Less

Submitted 18 July, 2023; originally announced July 2023.

Journal ref: Advanced Quantum Technologies 2300101(2023)

Parameterized coherence measure

Authors: Meng-Li Guo, Zhi-Xiang Jin, Jin-Min Liang, Bo Li, Shao-Ming Fei

Abstract: Quantifying coherence is an essential endeavor for both quantum mechanical foundations and quantum technologies. We present a bona fide measure of quantum coherence by utilizing the Tsallis relative operator $(α, β)$-entropy. We first prove that the proposed coherence measure fulfills all the criteria of a well defined coherence measure, including the strong monotonicity in the resource theories o… ▽ More Quantifying coherence is an essential endeavor for both quantum mechanical foundations and quantum technologies. We present a bona fide measure of quantum coherence by utilizing the Tsallis relative operator $(α, β)$-entropy. We first prove that the proposed coherence measure fulfills all the criteria of a well defined coherence measure, including the strong monotonicity in the resource theories of quantum coherence. We then study the ordering of the Tsallis relative operator $(α, β)$-entropy of coherence, Tsallis relative $α$-entropies of coherence, Rényi $α$-entropy of coherence and $l_{1}$ norm of coherence for both pure and mixed qubit states. This provides a new method for defining new coherence measure and entanglement measure, and also provides a new idea for further study of quantum coherence. △ Less

Submitted 20 June, 2023; originally announced June 2023.

Comments: 10 pages, 6 figures

Journal ref: Results in Physics,51,106611 (2023)

Bounds on positive operator-valued measure based coherence of superposition

Authors: Meng-Li Guo, Jin-Min Liang, Bo Li, Shao-Ming Fei, Zhi-Xi Wang

Abstract: Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued measures (POVMs), POVM-based coherence measures have been proposed with respect to the relative entropy of coherence, the $l_1$ norm of coherence, the robustness of co… ▽ More Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued measures (POVMs), POVM-based coherence measures have been proposed with respect to the relative entropy of coherence, the $l_1$ norm of coherence, the robustness of coherence and the Tsallis relative entropy of coherence. We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition. Our results can be used to estimate range of quantum coherence of superposed states. Detailed examples are presented to verify our analytical bounds. △ Less

Submitted 11 May, 2023; originally announced May 2023.

Comments: 15 pages, 2 figures

Journal ref: Chinese Phys. B 32, 050302 (2023)

Measurement of non-Abelian gauge fields using multi-loop amplification

Authors: Qing-Xian Lv, Hong-Zhi Liu, Yan-Xiong Du, Lin-Qing Chen, Meng Wang, Jia-Hao Liang, Zhao-Xin Fu, Zi-Yuan Chen, Hui Yan, Shi-Liang Zhu

Abstract: Non-Abelian gauge field (NAGF) plays a central role in understanding the geometrical and topological phenomena in physics. Here we experimentally induce a NAGF in the degenerate eigen subspace of a double-$Λ$ four-level atomic system. The non-Abelian nature of the gauge field is detected through the measurement of the non-commutativity of two successive evolution loops. Then we theoretically pro… ▽ More Non-Abelian gauge field (NAGF) plays a central role in understanding the geometrical and topological phenomena in physics. Here we experimentally induce a NAGF in the degenerate eigen subspace of a double-$Λ$ four-level atomic system. The non-Abelian nature of the gauge field is detected through the measurement of the non-commutativity of two successive evolution loops. Then we theoretically propose and experimentally demonstrate a novel scheme to measure the NAGF through multi-loop evolution and robust holonomic quantum gates. The demonstrated scheme offers the advantage of detecting the NAGF with amplification through multi-loop evolution. Our results pave the way for an experimentally-feasible approach to achieving high-resolution and high-precision measurements of the gauge fields. △ Less

Submitted 9 May, 2023; originally announced May 2023.

Comments: 11 pages, 8 figures

Assisted quantum simulation of open quantum systems

Authors: Jin-Min Liang, Qiao-Qiao Lv, Zhi-Xi Wang, Shao-Ming Fei

Abstract: Universal quantum algorithms (UQA) implemented on fault-tolerant quantum computers are expected to achieve an exponential speedup over classical counterparts. However, the deep quantum circuits makes the UQA implausible in the current era. With only the noisy intermediate-scale quantum (NISQ) devices in hand, we introduce the quantum-assisted quantum algorithm, which reduces the circuit depth of U… ▽ More Universal quantum algorithms (UQA) implemented on fault-tolerant quantum computers are expected to achieve an exponential speedup over classical counterparts. However, the deep quantum circuits makes the UQA implausible in the current era. With only the noisy intermediate-scale quantum (NISQ) devices in hand, we introduce the quantum-assisted quantum algorithm, which reduces the circuit depth of UQA via NISQ technology. Based on this framework, we present two quantum-assisted quantum algorithms for simulating open quantum systems, which utilize two parameterized quantum circuits to achieve a short-time evolution. We propose a variational quantum state preparation method, as a subroutine to prepare the ancillary state, for loading a classical vector into a quantum state with a shallow quantum circuit and logarithmic number of qubits. We demonstrate numerically our approaches for a two-level system with an amplitude damping channel and an open version of the dissipative transverse field Ising model on two sites. △ Less

Submitted 16 April, 2023; v1 submitted 26 February, 2023; originally announced February 2023.

Comments: 19 pages,5 figures

Journal ref: iScience 26,106306 (2023)

Unified multivariate trace estimation and quantum error mitigation

Authors: Jin-Min Liang, Qiao-Qiao Lv, Zhi-Xi Wang, Shao-Ming Fei

Abstract: Calculating the trace of the product of $m$ $n$-qubit density matrices (multivariate trace) is a crucial subroutine in quantum error mitigation and information measures estimation. We propose an unified multivariate trace estimation (UMT) which conceptually unifies the previous qubit-optimal and depth-optimal approaches with tunable quantum circuit depth and the number of qubits. The constructed c… ▽ More Calculating the trace of the product of $m$ $n$-qubit density matrices (multivariate trace) is a crucial subroutine in quantum error mitigation and information measures estimation. We propose an unified multivariate trace estimation (UMT) which conceptually unifies the previous qubit-optimal and depth-optimal approaches with tunable quantum circuit depth and the number of qubits. The constructed circuits have $\lceil(m-1)/s\rceil$ or $n\lceil(m-1)/s\rceil$ depth corresponding to $(s+m)n$ or $s+mn$ qubits for $s\in\{1,\cdots,\lfloor m/2\rfloor\}$, respectively. Such flexible circuit structures enable people to choose suitable circuits according different hardware devices. We apply UMT to virtual distillation for achieving exponential error suppression and design a family of concrete circuits to calculate the trace of the product of $8$ and $9$ $n$-qubit density matrices. Numerical example shows that the additional circuits still mitigate the noise expectation value under the global depolarizing channel. △ Less

Submitted 28 January, 2023; originally announced January 2023.

Comments: 8 pages, 4 figures

Journal ref: Phys. Rev. A 107, 012606 (2023)

Improved iterative quantum algorithm for ground-state preparation

Authors: Jin-Min Liang, Qiao-Qiao Lv, Shu-Qian Shen, Ming Li, Zhi-Xi Wang, Shao-Ming Fei

Abstract: Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point is to optimize a cost function on the state space via the quantum gradient descent (QGD) implemented on quantum devices. We provide practical guideline on the… ▽ More Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point is to optimize a cost function on the state space via the quantum gradient descent (QGD) implemented on quantum devices. We provide practical guideline on the selection of the learning rate in QGD by finding a fundamental upper bound and establishing a relationship between our algorithm and the first-order approximation of the imaginary time evolution. Furthermore, we adapt a variational quantum state preparation method as a subroutine to generate an ancillary state by utilizing only polylogarithmic quantum resources. The performance of our algorithm is demonstrated by numerical calculations of the deuteron molecule and Heisenberg model without and with noises. Compared with the existing algorithms, our approach has advantages including the higher success probability at each iteration, the measurement precision-independent sampling complexity, the lower gate complexity, and only quantum resources are required when the ancillary state is well prepared. △ Less

Submitted 24 October, 2022; v1 submitted 16 October, 2022; originally announced October 2022.

Comments: 12 pages,7 figures

Journal ref: Adv Quantum Technol. 2022, 2200090

Efficient Calculation of NMR Shielding Constants Using Composite Method Approximations and Locally Dense Basis Sets

Authors: Jiashu Liang, Zhe Wang, Jie Li, Jonathan Wong, Xiao Liu, Brad Ganoe, Teresa Head-Gordon, Martin Head-Gordon

Abstract: This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n $\geq1$ and can slightly reduce compute costs. We identify two different LDBS partition schemes th… ▽ More This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n $\geq1$ and can slightly reduce compute costs. We identify two different LDBS partition schemes that perform very effectively for density functional calculations. We select a large subset of the recent NS372 database containing 290 H, C, N, and O shielding values evaluated by reference methods on 106 molecules to carefully assess methods of the high, medium, and low compute costs to make practical recommendations. Our assessment covers conventional electronic structure methods (DFT and wavefunction) with global basis calculations, as well as their use in one of the satisfactory LDBS approaches, and a range of composite approaches, also with and without LDBS. Altogether 99 methods are evaluated. On this basis, we recommend different methods to reach three different levels of accuracy and time requirements across the four nuclei considered. △ Less

Submitted 11 November, 2022; v1 submitted 9 September, 2022; originally announced September 2022.

Comments: 29 pages, 7 figures, 2 tables

Generalized gauge transformation with $PT$-symmetric non-unitary operator and classical correspondence of non-Hermitian Hamiltonian for a periodically driven system

Authors: Yan Gu, Xiao-Lei Hao, J. -Q. Liang

Abstract: We in this paper demonstrate that the $PT$-symmetric non-Hermitian Hamiltonian for a periodically driven system can be generated from a kernel Hamiltonian by a generalized gauge transformation. The kernel Hamiltonian is Hermitian and static, while the time-dependent transformation operator has to be $PT$ symmetric and non-unitary in general. Biorthogonal sets of eigenstates appear necessarily as a… ▽ More We in this paper demonstrate that the $PT$-symmetric non-Hermitian Hamiltonian for a periodically driven system can be generated from a kernel Hamiltonian by a generalized gauge transformation. The kernel Hamiltonian is Hermitian and static, while the time-dependent transformation operator has to be $PT$ symmetric and non-unitary in general. Biorthogonal sets of eigenstates appear necessarily as a consequence of non-Hermitian Hamiltonian. We obtain analytically the wave functions and associated non-adiabatic Berry phase $γ_{n}$ for the $n$th eigenstate. The classical version of the non-Hermitian Hamiltonian becomes a complex function of canonical variables and time. The corresponding kernel Hamiltonian is derived with $PT$ symmetric canonical-variable transfer in the classical gauge transformation. Moreover, with the change of position-momentum to angle-action variables it is revealed that the non-adiabatic Hannay's angle $Δθ_{H}$ and Berry phase satisfy precisely the quantum-classical correspondence,$γ_{n}=$ $(n+1/2)Δθ_{H}$. △ Less

Submitted 3 September, 2022; originally announced September 2022.

Comments: 8 pages

Journal ref: Ann. Phys. (Berlin) 2022, 534, 2200069

Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments

Authors: Jiashu Liang, Xintian Feng, Martin Head-Gordon

Abstract: VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and eff… ▽ More VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. This study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to grid size and atomic orbital basis set size is studied and recommendations reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V). △ Less

Submitted 2 April, 2023; v1 submitted 31 August, 2022; originally announced August 2022.

Comments: 30 pages, 5 figures, 4 tables

Non-Hermitian Hamiltonian beyond PT-symmetry for time-dependant SU(1,1) and SU(2) systems -- exact solution and geometric phase in pseudo-invariant theory

Authors: Nadjat Amaouche, Maroua Sekhri, Rahma Zerimeche, Maamache Mustapha, J. -Q. Liang

Abstract: We investigate in this paper time-dependent non-Hermitian Hamiltonians, which consist respectively of SU(1,1) and SU(2) generators. The former Hamiltonian is PT symmetric but the latter one is not. A time-dependent non-unitary operator is proposed to construct the non-Hermitian invariant, which is verified as pseudo-Hermitian with real eigenvalues. The exact solutions are obtained in terms of the… ▽ More We investigate in this paper time-dependent non-Hermitian Hamiltonians, which consist respectively of SU(1,1) and SU(2) generators. The former Hamiltonian is PT symmetric but the latter one is not. A time-dependent non-unitary operator is proposed to construct the non-Hermitian invariant, which is verified as pseudo-Hermitian with real eigenvalues. The exact solutions are obtained in terms of the eigenstates of the pseudo-Hermitian invariant operator for both the SU(1,1)and SU(2)systems in a unified manner. Then, we derive the LR phase, which can be separated to the dynamic phase and the geometrical phase. The analytical results are exactly in agreement with those of corresponding Hermitian Hamiltonians in the literature. △ Less

Submitted 10 July, 2022; v1 submitted 6 July, 2022; originally announced July 2022.

Comments: 9 pages

Revealing hidden standard tripartite nonlocality by local filtering

Authors: Qiao-Qiao Lv, Jin-Min Liang, Zhi-Xi Wang, Shao-Ming Fei

Abstract: Quantum nonlocality is a kind of significant quantum correlation that is stronger than quantum entanglement and EPR steering. The standard tripartite nonlocality can be detected by the violation of the Mermin inequality. By using local filtering operations, we give a tight upper bound on the maximal expected value of the Mermin operators. By detailed examples we show that the hidden standard nonlo… ▽ More Quantum nonlocality is a kind of significant quantum correlation that is stronger than quantum entanglement and EPR steering. The standard tripartite nonlocality can be detected by the violation of the Mermin inequality. By using local filtering operations, we give a tight upper bound on the maximal expected value of the Mermin operators. By detailed examples we show that the hidden standard nonlocality can be revealed by local filtering which can enhance the robustness of the noised entangled states. △ Less

Submitted 21 May, 2022; originally announced May 2022.

Comments: 10 pages, 4 figures

Journal ref: Quantum Inf Process 21,183(2022)

Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems

Authors: Jin-Min Liang, Shi-Jie Wei, Shao-Ming Fei

Abstract: The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient descent have been investigated and implemented in calculating molecular ground states and optimizing polynomial functions. Based on the quantum gradient descent alg… ▽ More The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient descent have been investigated and implemented in calculating molecular ground states and optimizing polynomial functions. Based on the quantum gradient descent algorithm and Choi-Jamiolkowski isomorphism, we present approaches to simulate efficiently the nonequilibrium steady states of Markovian open quantum many-body systems. Two strategies are developed to evaluate the expectation values of physical observables on the nonequilibrium steady states. Moreover, we adapt the quantum gradient descent algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications, by converting these algebraic problems into the simulations of closed quantum systems with well-defined Hamiltonians. Detailed examples are given to test numerically the effectiveness of the proposed algorithms for the dissipative quantum transverse Ising models and matrix-vector multiplications. △ Less

Submitted 18 April, 2022; v1 submitted 14 April, 2022; originally announced April 2022.

Comments: 12 pages, 4 figures

Journal ref: Sci. China-Phys. Mech. Astron. 65, 250313 (2022)

Quantum Information Masking in Non-Hermitian Systems and Robustness

Authors: Qiao-Qiao Lv, Jin-Min Liang, Zhi-Xi Wang, Shao-Ming Fei

Abstract: By studying quantum information masking in non-Hermitian quantum systems, we show that mutually orthogonal quantum states can be deterministically masked, while an arbitrary set of quantum states cannot be masked in non-Hermitian quantum systems. We further demonstrate that a set of linearly independent states which are mutually $η$-orthogonal can be deterministically masked by a pseudo-unitary op… ▽ More By studying quantum information masking in non-Hermitian quantum systems, we show that mutually orthogonal quantum states can be deterministically masked, while an arbitrary set of quantum states cannot be masked in non-Hermitian quantum systems. We further demonstrate that a set of linearly independent states which are mutually $η$-orthogonal can be deterministically masked by a pseudo-unitary operator. Moreover, we study robustness of quantum information masking against noisy environments. The robustness of deterministic and probabilistic quantum information masking under different quantum noise channels is analyzed in detail. Accordingly, we propose and discuss the $r$-uniform probabilistic quantum information masking in multipartite systems. △ Less

Submitted 8 March, 2022; originally announced March 2022.

Comments: 7 pages, 1 figure

Journal ref: Laser Phys. Lett. 19 (2022) 045203

Revisiting the performance of time-dependent density functional theory for electronic excitations: Assessment of 43 popular and recently developed functionals from rungs one to four

Authors: Jiashu Liang, Xintian Feng, Diptarka Hait, Martin Head-Gordon

Abstract: In this paper, the performance of more than 40 popular or recently developed density functionals is assessed for the calculation of 463 vertical excitation energies against the large and accurate QuestDB benchmark set. For this purpose, the Tamm-Dancoff approximation offers a good balance between performance and accuracy. The functionals $ω$B97X-D and BMK are found to offer the best performance ov… ▽ More In this paper, the performance of more than 40 popular or recently developed density functionals is assessed for the calculation of 463 vertical excitation energies against the large and accurate QuestDB benchmark set. For this purpose, the Tamm-Dancoff approximation offers a good balance between performance and accuracy. The functionals $ω$B97X-D and BMK are found to offer the best performance overall with a Root-Mean Square Error (RMSE) of 0.28 eV, better than the computationally more demanding CIS(D) wavefunction method with a RMSE of 0.36 eV. The results also suggest that Jacob's ladder still holds for TDDFT excitation energies, though hybrid meta-GGAs are not generally better than hybrid GGAs. Effects of basis set convergence, gauge invariance correction to meta-GGAs, and nonlocal correlation (VV10) are also studied, and practical basis set recommendations are provided. △ Less

Submitted 18 May, 2022; v1 submitted 26 February, 2022; originally announced February 2022.

Comments: 12 pages, 8 figures; 8 pages, 7 figures for supporting info

$PT$-symmetric non-Hermitian Hamiltonian and invariant operator in periodically driven $SU(1,1)$ system

Authors: Yan Gu, Xue-Min Bai, Xiao-Lei Hao, J. -Q. Liang

Abstract: We study in this paper the time evolution of $PT$-symmetric non-Hermitian Hamiltonian consisting of periodically driven $SU(1,1)$ generators. A non-Hermitian invariant operator is adopted to solve the Schrödinger equation, since the time-dependent Hamiltonian is no longer a conserved quantity. We propose a scheme to construct the non-Hermitian invariant with a $PT$-symmetric but non-unitary transf… ▽ More We study in this paper the time evolution of $PT$-symmetric non-Hermitian Hamiltonian consisting of periodically driven $SU(1,1)$ generators. A non-Hermitian invariant operator is adopted to solve the Schrödinger equation, since the time-dependent Hamiltonian is no longer a conserved quantity. We propose a scheme to construct the non-Hermitian invariant with a $PT$-symmetric but non-unitary transformation operator. The eigenstates of invariant and its complex conjugate form a bi-orthogonal basis to formulate the exact solution. We obtain the non-adiabatic Berry phase, which reduces to the adiabatic one in the slow time-variation limit. A non-unitary time-evolution operator is found analytically. As an consequence of the non-unitarity the ket ($|ψ(t)\rangle $) and bra ($\langle ψ(t)|$) states are not normalized each other. While the inner product of two states can be evaluated with the help of a metric operator. It is shown explicitly that the model can be realized by a periodically driven oscillator. △ Less

Submitted 1 January, 2022; originally announced January 2022.

Comments: 5 pages

Generalized Bell-like inequality and maximum violation for multiparticle entangled Schrödinger-cat-states of spin-s

Authors: Yan Gu, Wei-Dong Li, Xiao-Lei Hao, Jiu-Qing Liang, Lian-Fu Wei

Abstract: This paper proposes a generalized Bell-like inequality (GBI) for multiparticle entangled Schrödinger-cat--states of arbitrary spin-$s$. Based on quantum probability statistics the GBI and violation are formulated in an unified manner with the help of state density operator, which can be separated to local and non-local parts. The local part gives rise to the inequality, while the non-local part is… ▽ More This paper proposes a generalized Bell-like inequality (GBI) for multiparticle entangled Schrödinger-cat--states of arbitrary spin-$s$. Based on quantum probability statistics the GBI and violation are formulated in an unified manner with the help of state density operator, which can be separated to local and non-local parts. The local part gives rise to the inequality, while the non-local part is responsible for the violation. The GBI is not violated at all by quantum average except the spin-$1/2$ entangled states. If the measuring outcomes are restricted in the subspace of spin coherent state (SCS), namely, only the maximum spin values $\pm s$, the GBI is still meaningful for the incomplete measurement. With the help of SCS quantum probability statistics, it is proved that the violation of GBI can occur only for half-integer spins but not integer spins. Moreover, the maximum violation bound depends on the number parity of entangled particles, that it is $1/2$ for the odd particle-numbers while $1$ for even numbers. △ Less

Submitted 31 December, 2021; originally announced December 2021.

Comments: 12 pages

Quantum algorithms for the generalized eigenvalue problem

Authors: Jin-Min Liang, Shu-Qian Shen, Ming Li, Shao-Ming Fei

Abstract: The generalized eigenvalue (GE) problems are of particular importance in various areas of science engineering and machine learning. We present a variational quantum algorithm for finding the desired generalized eigenvalue of the GE problem, $\mathcal{A}|ψ\rangle=λ\mathcal{B}|ψ\rangle$, by choosing suitable loss functions. Our approach imposes the superposition of the trial state and the obtained e… ▽ More The generalized eigenvalue (GE) problems are of particular importance in various areas of science engineering and machine learning. We present a variational quantum algorithm for finding the desired generalized eigenvalue of the GE problem, $\mathcal{A}|ψ\rangle=λ\mathcal{B}|ψ\rangle$, by choosing suitable loss functions. Our approach imposes the superposition of the trial state and the obtained eigenvectors with respect to the weighting matrix $\mathcal{B}$ on the Rayleigh-quotient. Furthermore, both the values and derivatives of the loss functions can be calculated on near-term quantum devices with shallow quantum circuit. Finally, we propose a full quantum generalized eigensolver (FQGE) to calculate the minimal generalized eigenvalue with quantum gradient descent algorithm. As a demonstration of the principle, we numerically implement our algorithms to conduct a 2-qubit simulation and successfully find the generalized eigenvalues of the matrix pencil $(\mathcal{A},\,\mathcal{B})$. The numerically experimental result indicates that FQGE is robust under Gaussian noise. △ Less

Submitted 6 March, 2022; v1 submitted 5 December, 2021; originally announced December 2021.

Journal ref: Quantum Inf Process 21, 23 (2022)

Measurement of spin Chern numbers in quantum simulated topological insulators

Authors: Qing-Xian Lv, Yan-Xiong Du, Zhen-Tao Liang, Hong-Zhi Liu, Jia-Hao Liang, Lin-Qing Chen, Li-Ming Zhou, Shan-Chao Zhang, Dan-Wei Zhang, Bao-Quan Ai, Hui Yan, Shi-Liang Zhu

Abstract: The topology of quantum systems has become a topic of great interest since the discovery of topological insulators. However, as a hallmark of the topological insulators, the spin Chern number has not yet been experimentally detected. The challenge to directly measure this topological invariant lies in the fact that this spin Chern number is defined based on artificially constructed wavefunctions.… ▽ More The topology of quantum systems has become a topic of great interest since the discovery of topological insulators. However, as a hallmark of the topological insulators, the spin Chern number has not yet been experimentally detected. The challenge to directly measure this topological invariant lies in the fact that this spin Chern number is defined based on artificially constructed wavefunctions. Here we experimentally mimic the celebrated Bernevig-Hughes-Zhang model with cold atoms, and then measure the spin Chern number with the linear response theory. We observe that, although the Chern number for each spin component is ill defined, the spin Chern number measured by their difference is still well defined when both energy and spin gaps are non-vanished. △ Less

Submitted 27 July, 2021; originally announced July 2021.

Comments: 12 pages, 9 figures

Journal ref: Phys. Rev. Lett. 127, 136802 (2021)

Manipulation and readout of spin states of a single-molecule magnet by a spin-polarized current

Authors: Hai-Bin Xue, Jiu-Qing Liang, Wu-Ming Liu

Abstract: Single-molecule memory device based on a single-molecule magnet (SMM) is one of the ultimate goals of semiconductor nanofabrication technologies. Here, we study how to manipulate and readout the SMM's two spin-state of stored information that characterized by the maximum and minimum average value of the $Z$-component of the total spin of the SMM and the conduction-electron, which are recognized as… ▽ More Single-molecule memory device based on a single-molecule magnet (SMM) is one of the ultimate goals of semiconductor nanofabrication technologies. Here, we study how to manipulate and readout the SMM's two spin-state of stored information that characterized by the maximum and minimum average value of the $Z$-component of the total spin of the SMM and the conduction-electron, which are recognized as the information bits "$1$" and "$0$". We demonstrate that the switching time depends on both the sequential tunneling gap $\varepsilon_{se}$ and the spin-selection-rule allowed transition-energy $\varepsilon_{trans}$, which can be tuned by the gate voltage. In particular, when the external bias voltage is turned off, in the cases of the unoccupied and doubly-occupied ground eigenstates, the time derivative of the transport current can be used to read out the SMM's two spin-state of stored information. Moreover, the tunneling strength of and the asymmetry of the SMM-electrode coupling have a strong influence on the switching time, but that have a slight influence on the readout time that being on the order of nanoseconds. Our results suggest a SMM-based memory device, and provide fundamental insight into the electrical controllable manipulation and readout of the SMM's two spin-state of stored information. △ Less

Submitted 6 September, 2021; v1 submitted 14 April, 2021; originally announced April 2021.

Comments: 15 pages, 10 figures

Journal ref: Physica E 138 (2022) 115086

Microwave electrometry via electromagnetically induced absorption in cold Rydberg atoms

Authors: Kai-Yu Liao, Hai-Tao Tu, Shu-Zhe Yang, Chang-Jun Chen, Xiao-Hong Liu, Jie Liang, Xin-Ding Zhang, Hui Yan, Shi-Liang Zhu

Abstract: The atom-based traceable standard for microwave electrometry shows promising advantages by enabling stable and uniform measurement. Here we theoretically propose and then experimentally realize an alternative direct International System of Units (SI)-traceable and self-calibrated method for measuring a microwave electric field strength based on electromagnetically induced absorption (EIA) in cold… ▽ More The atom-based traceable standard for microwave electrometry shows promising advantages by enabling stable and uniform measurement. Here we theoretically propose and then experimentally realize an alternative direct International System of Units (SI)-traceable and self-calibrated method for measuring a microwave electric field strength based on electromagnetically induced absorption (EIA) in cold Rydberg atoms. Comparing with the method of electromagnetically induced transparency, we show that the equivalence relation between microwave Rabi frequency and Autler-Townes splitting is more valid and is even more robust against the experimental parameters in the EIA's linear region. Furthermore, a narrower linewidth of cold Rydberg EIA enables us to realize a direct SI-traceable microwave-electric-field measurement as small as $\sim$100 $μ\mathrm{\!V} \mathrm{cm}^{\!-\!1}$. △ Less

Submitted 19 May, 2020; v1 submitted 3 February, 2020; originally announced February 2020.

Journal ref: Phys. Rev. A 101, 053432 (2020)