Showing 1–50 of 149 results for author: Kwek, L C

Quantum-enhanced sensing in a driven-dissipative system via chiral waveguide

Authors: Yan Xi Foo, Saubhik Sarkar, Leong Chuan Kwek, Abolfazl Bayat, Davit Aghamalyan

Abstract: Quantum sensors can achieve precision unattainable by classical sensors. However, dissipation coming from interaction with the environment can greatly degrade the performance of quantum sensors. Therefore, it is crucial to attempt harnessing dissipation to our advantage and investigate the sensing performance of driven-dissipative systems to gain practical quantum advantages. In this paper, we stu… ▽ More Quantum sensors can achieve precision unattainable by classical sensors. However, dissipation coming from interaction with the environment can greatly degrade the performance of quantum sensors. Therefore, it is crucial to attempt harnessing dissipation to our advantage and investigate the sensing performance of driven-dissipative systems to gain practical quantum advantages. In this paper, we study a system of two-level systems driven coherently at a detuned frequency, and importantly, connected to a chiral waveguide that serves both as an interaction mediator and a bath. We show analytically that the steady state of such a system shows enhanced sensitivity to estimate weak detuning strength while the probe preparation time only grows linearly with system size. Therefore, the enhanced sensitivity is sustained even when the preparation time is incorporated. We further establish measurement protocols to achieve such sensitivity that are experimentally implementable. The chirality of the waveguide helps us to control both precision and range of enhanced sensitivity. △ Less

Submitted 24 August, 2026; originally announced August 2026.

Comments: 5+16 pages, 5 figures

Stabilizer Statistical Mechanics: A Framework for Efficient Quantification and Classification of Magic States

Authors: William E. Salazar, Gaurav Saxena, Jack S. Baker, Leong Chuan Kwek, Thi Ha Kyaw

Abstract: The partition function is statistical mechanics' answer to an exponentially large spectrum, distilling it into a single analytic object whose temperature dependence resolves the full structure of the underlying ensemble. We show that magic, the resource separating universal quantum computation from classically simulable stabilizer dynamics, admits precisely such a description. Mapping the Pauli sp… ▽ More The partition function is statistical mechanics' answer to an exponentially large spectrum, distilling it into a single analytic object whose temperature dependence resolves the full structure of the underlying ensemble. We show that magic, the resource separating universal quantum computation from classically simulable stabilizer dynamics, admits precisely such a description. Mapping the Pauli spectrum of a quantum state onto the energy levels of a fictitious many-body system, the Pauli gas, we construct its canonical partition function, the stabilizer partition function, and from its associated free energy a magic monotone that we call the stabilizer work. Both these objects are analytic functions of an inverse-temperature-like parameter and are efficiently estimable via Bell sampling. The framework is analytically tractable. We derive exact ensemble-averaged partition functions for Haar-random, $ν$-compressible, and pseudomagic states, together with concentration guarantees. We show that for every value of its parameter, the stabilizer work is a faithful, Subadditive magic monotone, while remaining efficiently accessible on quantum hardware and admitting an operational interpretation. Unlike measures that probe a single moment of the Pauli distribution, the stabilizer work is intrinsically moment-generating. As the temperature is tuned from high to low, it interpolates continuously between the stabilizer 2-Rényi entropy and the stabilizer nullity, revealing two previously disconnected monotones as limiting cases of a single object. We demonstrate the framework on low-rank stabilizer simulation, resource interconversion, molecular ground states, and quantum many-body systems. A thermodynamics of magic is therefore not merely an analogy but a working toolkit, opening a statistical-mechanical route to magic properties of quantum systems that no single measure can access. △ Less

Submitted 14 August, 2026; originally announced August 2026.

Comments: 42 pages, 11 figures. Comments are welcome. William E. Salazar and Gaurav Saxena contributed equally to this work

Photonic-Implemented Efficient Deep Quantum Neural Network via Virtual-Driven Hilbert Space Expansion

Authors: Haoran Ma, Huihui Zhu, Zichao Zhao, Qishen Liang, Liao Ye, Baojie Hou, Jia Guo, Leong Chuan Kwek, Mile Gu, Jayne Thompson, Wei Luo, Yuehai Wang, Jianyi Yang

Abstract: The growing computational demands of classical neural networks have intensified the search for energy-efficient and powerful computational alternatives. Quantum neural networks (QNNs) implemented on integrated photonic platforms offer a compelling avenue, offering exceptional computational power enhancements, with inherent programmability and scalability of integrated architectures. A critical cha… ▽ More The growing computational demands of classical neural networks have intensified the search for energy-efficient and powerful computational alternatives. Quantum neural networks (QNNs) implemented on integrated photonic platforms offer a compelling avenue, offering exceptional computational power enhancements, with inherent programmability and scalability of integrated architectures. A critical challenge, however, is implementing the fundamental non-unitary and nonlinear activation function of QNNs within a linear quantum photonic system. Existing strategies, such as the adding ancillary qubits and measurement-based feedback or forward are constrained by high qubit resource costs, overhead devices, and poor cascadability. Here, we propose a novel deep photonic QNN with an expanded computational Hilbert space via input replication and mode expansion, which enables the realization of effective non-unitary and nonlinear activation on a linear programmable quantum photonic chip. This approach eliminates the need for physical ancillary qubits, measurement-induced qubit consumption and the measurement device burden, thereby significantly reduce resource costs. The fabricated chip integrates four high-quality entanglement sources and a programmable high-dimensional interferometric network, enabling a two-hidden-layer QNN that exhibits dimension-enhanced expressivity over the existing QNN architectures. We demonstrate its capabilities across diverse tasks, including nonlinear classification, image generation, and quantum Gibbs state preparation. This work establishes a scalable and efficient architecture toward practical quantum deep learning systems capable of tackling problems beyond the reach of classical computation. △ Less

Submitted 7 May, 2026; originally announced May 2026.

Comments: 14 pages, 5 figures

Transient entanglement generation in driven chiral networks beyond the secular approximation

Authors: Yan Xi Foo, Kian Hwee Lim, Jia-Bin You, Leong Chuan Kwek, Davit Aghamalyan

Abstract: We study transient entanglement generation between two quantum nodes coupled through a chiral one-dimensional channel. In an emitter-only Born-Markov description, we show that continuous driving and an initial ground state can raise the maximum transient concurrence above the undriven $2/e$ benchmark associated with the effectively single-excitation model. We then consider a more microscopic XX sp… ▽ More We study transient entanglement generation between two quantum nodes coupled through a chiral one-dimensional channel. In an emitter-only Born-Markov description, we show that continuous driving and an initial ground state can raise the maximum transient concurrence above the undriven $2/e$ benchmark associated with the effectively single-excitation model. We then consider a more microscopic XX spin-chain channel with triangular plaquette couplings and compare a nonsecular time-convolutionless master equation (TCL-ME) with matrix-product-state (MPS) simulations. In the optimal driven regime, the nonsecular TCL-2 treatment reproduces the concurrence envelope and first transient peak qualitatively, while the remaining discrepancy is mainly attributable to beyond-Born system-bath correlations. The enhancement is traced to the failure of the secular approximation under strong driving, where nearby dressed transitions are not well separated on the dissipative timescale and nonsecular terms mix dressed-state coherences. Finally, we examine within TCL-2 the sensitivity of the protocol to positional disorder, imperfect chirality, and loss into nonguided modes. These results clarify when the familiar $2/e$ limitation ceases to apply and separate the roles of secular breakdown, Born-factorization error, and reduced-state memory in driven chiral entanglement generation; we believe that our study contributes to one of the first studies where the breakdown of the secular approximation is useful rather than detrimental. △ Less

Submitted 15 April, 2026; originally announced April 2026.

Comments: 34 pages, 14 figures

Integrated Photonic Quantum Computing: From Silicon to Lithium Niobate

Authors: Hui Zhang, Yiming Ma, Yuancheng Zhan, Yuzhi Shi, Zhanshan Wang, Leong Chuan Kwek, Anthony Laing, Ai Qun Liu, Xinbin Cheng

Abstract: Quantum technologies have surpassed classical systems by leveraging the unique properties of superposition and entanglement in photons and matter. Recent advancements in integrated quantum photonics, especially in silicon-based and lithium niobate platforms, are pushing the technology toward greater scalability and functionality. Silicon circuits have progressed from centimeter-scale, dual-photon… ▽ More Quantum technologies have surpassed classical systems by leveraging the unique properties of superposition and entanglement in photons and matter. Recent advancements in integrated quantum photonics, especially in silicon-based and lithium niobate platforms, are pushing the technology toward greater scalability and functionality. Silicon circuits have progressed from centimeter-scale, dual-photon systems to millimeter-scale, high-density devices that integrate thousands of components, enabling sophisticated programmable manipulation of multi-photon states. Meanwhile, lithium niobate, thanks to its wide optical transmission window, outstanding nonlinear and electro-optic coefficients, and chemical stability, has emerged as an optimal substrate for fully integrated photonic quantum chips. Devices made from this material exhibit high efficiency in in generating, manipulating, converting, storing, and detecting photon states, thereby establishing a basis for deterministic multi-photon generation and single-photon quantum interactions, as well as comprehensive frequency-state control. This review explores the development of integrated photonic quantum technologies based on both silicon and lithium niobate, highlighting invaluable insights gained from silicon-based systems that can assist the scaling of lithium niobate technologies. It examines the functional integration mechanisms of lithium niobate in electro-optic tuning and nonlinear energy conversion, showcasing its transformative impact throughout the photonic quantum computing process. Looking ahead, we speculate on the developmental pathways for lithium niobate platforms and their potential to revolutionize areas such as quantum communication, complex system simulation, quantum sampling, and optical quantum computing paradigms. △ Less

Submitted 2 February, 2026; v1 submitted 23 January, 2026; originally announced January 2026.

Timing quantum emission: coherence, superradiance, and entanglement in order

Authors: Nur Fadhillah Binti Rahimi, Norman Koo Tze Wei, Daniel Schumayer, Christopher Gies, Leong Chuan Kwek, David. A. W. Hutchinson

Abstract: We investigate the short-term temporal dynamics of superradiance in closely spaced quantum emitters. Building on Dicke's 1954 framework, we analyze the sequential emergence of coherence, superradiance, and entanglement, revealing a distinct temporal hierarchy in their extremal values: relative coherence develops first, followed by the peak of correlated emission, then minimal entanglement, and fin… ▽ More We investigate the short-term temporal dynamics of superradiance in closely spaced quantum emitters. Building on Dicke's 1954 framework, we analyze the sequential emergence of coherence, superradiance, and entanglement, revealing a distinct temporal hierarchy in their extremal values: relative coherence develops first, followed by the peak of correlated emission, then minimal entanglement, and finally correlated dephasing. These findings suggest that enhanced relative coherence initiates correlated emission and when correlated dephasing is negligible, entanglement and correlated emission become tightly linked in time. △ Less

Submitted 7 December, 2025; originally announced December 2025.

Comments: 5 pages, 5 figures

Variational quantum classifiers via a programmable photonic microprocessor

Authors: Hexiang Lin, Huihui Zhu, Zan Tang, Wei Luo, Wei Wang, Man-Wai Mak, Xudong Jiang, Lip Ket Chin, Leong Chuan Kwek, Ai Qun Liu

Abstract: Quantum computing holds promise across various fields, particularly with the advent of Noisy Intermediate-Scale Quantum (NISQ) devices, which can outperform classical supercomputers in specific tasks. However, challenges such as noise and limited qubit capabilities hinder its practical applications. Variational Quantum Algorithms (VQAs) offer a viable strategy to achieve quantum advantage by combi… ▽ More Quantum computing holds promise across various fields, particularly with the advent of Noisy Intermediate-Scale Quantum (NISQ) devices, which can outperform classical supercomputers in specific tasks. However, challenges such as noise and limited qubit capabilities hinder its practical applications. Variational Quantum Algorithms (VQAs) offer a viable strategy to achieve quantum advantage by combining quantum and classical computing. Leveraging on VQAs, the performance of Variational Quantum Classifiers (VQCs) is competitive with many classical classifiers. This work implements a VQC using a silicon-based quantum photonic microprocessor and a classical computer, demonstrating its effectiveness in nonlinear binary and multi-classification tasks. An efficient gradient free genetic algorithm is employed for training. The VQC's performance was evaluated on three synthetic binary classification tasks with square-, circular-, and sine-shape decision boundaries and a real-world multiclass Iris dataset. The accuracies on the three binary classification tasks were 87.5%, 92.5%, and 85.0%, respectively, and 98.8% on the real world Iris dataset, highlighting the platform's potential to handle complex data patterns. △ Less

Submitted 6 December, 2024; v1 submitted 3 December, 2024; originally announced December 2024.

Loop Quantum Photonic Chip for Coherent Multi-Time-Step Evolution

Authors: Yuancheng Zhan, Hui Zhang, Rebecca Erbanni, Andreas Burger, Lingxiao Wan, Xudong Jiang, Sanghoon Chae, Aiqun Liu, Dario Poletti, Leong Chuan Kwek

Abstract: Quantum evolution is crucial for the understanding of complex quantum systems. However, current implementations of time evolution on quantum photonic platforms are limited by both low photon generation efficiency and high propagation loss, making photon detection difficult. Furthermore, the single-layer complexity of most implementations cannot support multi-step quantum simulations. In this work,… ▽ More Quantum evolution is crucial for the understanding of complex quantum systems. However, current implementations of time evolution on quantum photonic platforms are limited by both low photon generation efficiency and high propagation loss, making photon detection difficult. Furthermore, the single-layer complexity of most implementations cannot support multi-step quantum simulations. In this work, we present a loop quantum photonic chip (Loop-QPC) designed to efficiently simulate quantum dynamics over multiple time steps in a single chip. Our approach employs a recirculating loop structure to reuse computational resources and eliminate the need for multiple quantum tomography steps or chip reconfigurations. A cycle-or-measure circuit at the input and output stages allows dynamic routing of photons between evolution and measurement, enabling efficient control over the simulation loop and minimizing loss. We experimentally demonstrate the dynamics of the spin-boson model on a low-loss Silicon Nitride integrated photonic chip. The Loop-QPC achieves a three-step unitary evolution closely matching the theoretical predictions. These results establish the Loop-QPC as a promising method for efficient and scalable quantum simulation, advancing the development of quantum simulation on programmable photonic circuits. △ Less

Submitted 15 April, 2026; v1 submitted 18 November, 2024; originally announced November 2024.

A short tutorial on Wirtinger Calculus with applications in quantum information

Authors: Kelvin Koor, Yixian Qiu, Leong Chuan Kwek, Patrick Rebentrost

Abstract: The optimization of system parameters is a ubiquitous problem in science and engineering. The traditional approach involves setting to zero the partial derivatives of the objective function with respect to each parameter, in order to extract the optimal solution. However, the system parameters often take the form of complex matrices. In such situations, conventional methods become unwieldy. The `W… ▽ More The optimization of system parameters is a ubiquitous problem in science and engineering. The traditional approach involves setting to zero the partial derivatives of the objective function with respect to each parameter, in order to extract the optimal solution. However, the system parameters often take the form of complex matrices. In such situations, conventional methods become unwieldy. The `Wirtinger Calculus' provides a relatively simple methodology for such optimization problems. In this tutorial, we provide a pedagogical introduction to Wirtinger Calculus. To illustrate the utility of this framework in quantum information theory, we also discuss a few example applications. △ Less

Submitted 8 December, 2023; originally announced December 2023.

Comments: Comments are most welcome

Efficient option pricing with unary-based photonic computing chip and generative adversarial learning

Authors: Hui Zhang, Lingxiao Wan, Sergi Ramos-Calderer, Yuancheng Zhan, Wai-Keong Mok, Hong Cai, Feng Gao, Xianshu Luo, Guo-Qiang Lo, Leong Chuan Kwek, José Ignacio Latorre, Ai Qun Liu

Abstract: In the modern financial industry system, the structure of products has become more and more complex, and the bottleneck constraint of classical computing power has already restricted the development of the financial industry. Here, we present a photonic chip that implements the unary approach to European option pricing, in combination with the quantum amplitude estimation algorithm, to achieve a q… ▽ More In the modern financial industry system, the structure of products has become more and more complex, and the bottleneck constraint of classical computing power has already restricted the development of the financial industry. Here, we present a photonic chip that implements the unary approach to European option pricing, in combination with the quantum amplitude estimation algorithm, to achieve a quadratic speedup compared to classical Monte Carlo methods. The circuit consists of three modules: a module loading the distribution of asset prices, a module computing the expected payoff, and a module performing the quantum amplitude estimation algorithm to introduce speed-ups. In the distribution module, a generative adversarial network is embedded for efficient learning and loading of asset distributions, which precisely capture the market trends. This work is a step forward in the development of specialized photonic processors for applications in finance, with the potential to improve the efficiency and quality of financial services. △ Less

Submitted 8 August, 2023; originally announced August 2023.

Comments: 11 pages, 7 figures

Journal ref: Photonics Research 10.1364/PRJ.493865 (2023)

Towards Quantum Federated Learning

Authors: Chao Ren, Rudai Yan, Huihui Zhu, Han Yu, Minrui Xu, Yuan Shen, Yan Xu, Ming Xiao, Zhao Yang Dong, Mikael Skoglund, Dusit Niyato, Leong Chuan Kwek

Abstract: Quantum Federated Learning (QFL) is an emerging interdisciplinary field that merges the principles of Quantum Computing (QC) and Federated Learning (FL), with the goal of leveraging quantum technologies to enhance privacy, security, and efficiency in the learning process. Currently, there is no comprehensive survey for this interdisciplinary field. This review offers a thorough, holistic examinati… ▽ More Quantum Federated Learning (QFL) is an emerging interdisciplinary field that merges the principles of Quantum Computing (QC) and Federated Learning (FL), with the goal of leveraging quantum technologies to enhance privacy, security, and efficiency in the learning process. Currently, there is no comprehensive survey for this interdisciplinary field. This review offers a thorough, holistic examination of QFL. We aim to provide a comprehensive understanding of the principles, techniques, and emerging applications of QFL. We discuss the current state of research in this rapidly evolving field, identify challenges and opportunities associated with integrating these technologies, and outline future directions and open research questions. We propose a unique taxonomy of QFL techniques, categorized according to their characteristics and the quantum techniques employed. As the field of QFL continues to progress, we can anticipate further breakthroughs and applications across various industries, driving innovation and addressing challenges related to data privacy, security, and resource optimization. This review serves as a first-of-its-kind comprehensive guide for researchers and practitioners interested in understanding and advancing the field of QFL. △ Less

Submitted 19 August, 2024; v1 submitted 16 June, 2023; originally announced June 2023.

Comments: Survey of quantum federated learning (QFL)

Digital Quantum Simulation of the Spin-Boson Model under Open System Dynamics

Authors: Andreas Burger, Leong Chuan Kwek, Dario Poletti

Abstract: Digital quantum computers have the potential to simulate complex quantum systems. The spin-boson model is one of such systems, used in disparate physical domains. Importantly, in a number of setups, the spin-boson model is open, i.e. the system is in contact with an external environment which can, for instance, cause the decay of the spin state. Here we study how to simulate such open quantum dyna… ▽ More Digital quantum computers have the potential to simulate complex quantum systems. The spin-boson model is one of such systems, used in disparate physical domains. Importantly, in a number of setups, the spin-boson model is open, i.e. the system is in contact with an external environment which can, for instance, cause the decay of the spin state. Here we study how to simulate such open quantum dynamics in a digital quantum computer, for which we use one of IBM's hardware. We consider in particular how accurate different implementations of the evolution result as a function of the level of noise in the hardware and of the parameters of the open dynamics. For the regimes studied, we show that the key aspect is to simulate the unitary portion of the dynamics, while the dissipative part can lead to a more noise-resistant simulation. We consider both a single spin coupled to a harmonic oscillator, and also two spins coupled to the oscillator. In the latter case, we show that it is possible to simulate the emergence of correlations between the spins via the oscillator. △ Less

Submitted 29 November, 2022; v1 submitted 28 October, 2022; originally announced October 2022.

Symmetry-protected topological corner modes in a periodically driven interacting spin lattice

Authors: Kelvin Koor, Raditya Weda Bomantara, Leong Chuan Kwek

Abstract: Periodic driving has the longstanding reputation for generating exotic phases of matter with no static counterparts. This work explores the interplay among periodic driving, interaction effects, and $\mathbb{Z}_2$ symmetry that leads to the emergence of Floquet symmetry protected second-order topological phases in a simple but insightful two-dimensional spin-1/2 lattice. Through a combination of a… ▽ More Periodic driving has the longstanding reputation for generating exotic phases of matter with no static counterparts. This work explores the interplay among periodic driving, interaction effects, and $\mathbb{Z}_2$ symmetry that leads to the emergence of Floquet symmetry protected second-order topological phases in a simple but insightful two-dimensional spin-1/2 lattice. Through a combination of analytical and numerical treatments, we verify the formation of 0 and $π$ modes, i.e., corner localized $\mathbb{Z}_2$ symmetry broken operators that respectively commute and anticommute with the one-period time evolution operator. We further verify the topological nature of these modes by demonstrating their presence over a wide range of parameter values and explicitly deriving their associated topological invariants under special conditions. Finally, we propose a means to detect the signature of such modes in experiments and discuss the effect of imperfections. △ Less

Submitted 16 November, 2022; v1 submitted 14 June, 2022; originally announced June 2022.

Comments: 16 pages, 10 figures. Comments are most welcome

Journal ref: Phys. Rev. B 106, 195122 (2022)

Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity

Authors: A. Chia, W. -K. Mok, C. Noh, L. C. Kwek

Abstract: It is universally accepted that noise may bring order to complex nonequilibrium systems. Most strikingly, entirely new states not seen in the noiseless system can be induced purely by including multiplicative noise -- an effect known as pure noise-induced transitions. It was first observed in superfluids in the 1980s. Recent results in complex nonequilibrium systems have also shown how new collect… ▽ More It is universally accepted that noise may bring order to complex nonequilibrium systems. Most strikingly, entirely new states not seen in the noiseless system can be induced purely by including multiplicative noise -- an effect known as pure noise-induced transitions. It was first observed in superfluids in the 1980s. Recent results in complex nonequilibrium systems have also shown how new collective states emerge from such pure noise-induced transitions, such as the foraging behavior of insect colonies, and schooling in fish. Here we report such effects of noise in a quantum-mechanical system without a classical limit. We use a minimal model of a nonlinearly damped oscillator in a fluctuating environment that is analytically tractable, and whose microscopic physics can be understood. When multiplicative environmental noise is included, the system is seen to transition to a limit-cycle state. The noise-induced quantum limit cycle also exhibits other genuinely nonclassical traits, such as Wigner negativity and number-parity sensitive circulation in phase space. Such quantum limit cycles are also conservative. These properties are in stark contrast to those of a widely used limit cycle in the literature, which is dissipative and loses all Wigner negativity. Our results establish the existence of a pure noise-induced transition that is nonclassical and unique to open quantum systems. They illustrate a fundamental difference between quantum and classical noise. △ Less

Submitted 8 June, 2023; v1 submitted 7 April, 2022; originally announced April 2022.

Comments: Comments welcome. Supplementary material included

Journal ref: SciPost Phys. 15, 121 (2023)

Fast-Forwarding with NISQ Processors without Feedback Loop

Authors: Kian Hwee Lim, Tobias Haug, Leong Chuan Kwek, Kishor Bharti

Abstract: Simulating quantum dynamics is expected to be performed more easily on a quantum computer than on a classical computer. However, the currently available quantum devices lack the capability to implement fault-tolerant quantum algorithms for quantum simulation. Hybrid classical quantum algorithms such as the variational quantum algorithms have been proposed to effectively use current term quantum de… ▽ More Simulating quantum dynamics is expected to be performed more easily on a quantum computer than on a classical computer. However, the currently available quantum devices lack the capability to implement fault-tolerant quantum algorithms for quantum simulation. Hybrid classical quantum algorithms such as the variational quantum algorithms have been proposed to effectively use current term quantum devices. One promising approach to quantum simulation in the noisy intermediate-scale quantum (NISQ) era is the diagonalisation based approach, with some of the promising examples being the subspace Variational Quantum Simulator (SVQS), Variational Fast Forwarding (VFF), fixed-state Variational Fast Forwarding (fs-VFF), and the Variational Hamiltonian Diagonalisation (VHD) algorithms. However, these algorithms require a feedback loop between the classical and quantum computers, which can be a crucial bottleneck in practical application. Here, we present the Classical Quantum Fast Forwarding (CQFF) as an alternative diagonalisation based algorithm for quantum simulation. CQFF shares some similarities with SVQS, VFF, fs-VFF and VHD but removes the need for a classical-quantum feedback loop and controlled multi-qubit unitaries. The CQFF algorithm does not suffer from the barren plateau problem and the accuracy can be systematically increased. Furthermore, if the Hamiltonian to be simulated is expressed as a linear combination of tensored-Pauli matrices, the CQFF algorithm reduces to the task of sampling some many-body quantum state in a set of Pauli-rotated bases, which is easy to do in the NISQ era. We run the CQFF algorithm on existing quantum processors and demonstrate the promise of the CQFF algorithm for current-term quantum hardware. Our work provides a $10^4$ improvement over the previous record. △ Less

Submitted 21 September, 2021; v1 submitted 5 April, 2021; originally announced April 2021.

Comments: 12 pages, 7 figures

Journal ref: Quantum Sci. Technol. 7 015001 (2021)

NISQ Algorithm for Hamiltonian Simulation via Truncated Taylor Series

Authors: Jonathan Wei Zhong Lau, Tobias Haug, Leong Chuan Kwek, Kishor Bharti

Abstract: Simulating the dynamics of many-body quantum systems is believed to be one of the first fields that quantum computers can show a quantum advantage over classical computers. Noisy intermediate-scale quantum (NISQ) algorithms aim at effectively using the currently available quantum hardware. For quantum simulation, various types of NISQ algorithms have been proposed with individual advantages as wel… ▽ More Simulating the dynamics of many-body quantum systems is believed to be one of the first fields that quantum computers can show a quantum advantage over classical computers. Noisy intermediate-scale quantum (NISQ) algorithms aim at effectively using the currently available quantum hardware. For quantum simulation, various types of NISQ algorithms have been proposed with individual advantages as well as challenges. In this work, we propose a new algorithm, truncated Taylor quantum simulator (TTQS), that shares the advantages of existing algorithms and alleviates some of the shortcomings. Our algorithm does not have any classical-quantum feedback loop and bypasses the barren plateau problem by construction. The classical part in our hybrid quantum-classical algorithm corresponds to a quadratically constrained quadratic program (QCQP) with a single quadratic equality constraint, which admits a semidefinite relaxation. The QCQP based classical optimization was recently introduced as the classical step in quantum assisted eigensolver (QAE), a NISQ algorithm for the Hamiltonian ground state problem. Thus, our work provides a conceptual unification between the NISQ algorithms for the Hamiltonian ground state problem and the Hamiltonian simulation. We recover differential equation-based NISQ algorithms for Hamiltonian simulation such as quantum assisted simulator (QAS) and variational quantum simulator (VQS) as particular cases of our algorithm. We test our algorithm on some toy examples on current cloud quantum computers. We also provide a systematic approach to improve the accuracy of our algorithm. △ Less

Submitted 18 May, 2021; v1 submitted 9 March, 2021; originally announced March 2021.

Comments: 8 pages, 5 figures

Noisy intermediate scale quantum simulation of time dependent Hamiltonians

Authors: Jonathan Wei Zhong Lau, Kishor Bharti, Tobias Haug, Leong Chuan Kwek

Abstract: Quantum computers are expected to help us to achieve accurate simulation of the dynamics of many-body quantum systems. However, the limitations of current NISQ devices prevents us from realising this goal today. Recently an algorithm for performing quantum simulations called quantum assisted simulator has been proposed that promises realization on current experimental devices. In this work, we ext… ▽ More Quantum computers are expected to help us to achieve accurate simulation of the dynamics of many-body quantum systems. However, the limitations of current NISQ devices prevents us from realising this goal today. Recently an algorithm for performing quantum simulations called quantum assisted simulator has been proposed that promises realization on current experimental devices. In this work, we extend the quantum assisted simulator to simulate the dynamics of a class of time-dependent Hamiltonians. We show that the quantum assisted simulator is easier to implement as well as can realize multi-qubit interactions and challenging driving protocols that are difficult with other existing methods. We demonstrate this for a time-dependent Hamiltonian on the IBM Quantum Experience cloud quantum computer by showing superior performance of the quantum assisted simulator compared to Trotterization and variational quantum simulation. Further, we demonstrate the capability to simulate the dynamics of Hamiltonians consisting of 10000 qubits. Our results indicate that quantum assisted simulator is a promising algorithm for current term quantum hardware. △ Less

Submitted 14 August, 2021; v1 submitted 19 January, 2021; originally announced January 2021.

Comments: 15 pages, 14 figures

Simulating Energy Transfer in Molecular Systems with Digital Quantum Computers

Authors: Chee-Kong Lee, Jonathan Wei Zhong Lau, Liang Shi, Leong Chuan Kwek

Abstract: Quantum computers have the potential to simulate chemical systems beyond the capability of classical computers. Recent developments in hybrid quantum-classical approaches enable the determinations of the ground or low energy states of molecular systems. Here, we extend near-term quantum simulations of chemistry to time-dependent processes by simulating energy transfer in organic semiconducting mol… ▽ More Quantum computers have the potential to simulate chemical systems beyond the capability of classical computers. Recent developments in hybrid quantum-classical approaches enable the determinations of the ground or low energy states of molecular systems. Here, we extend near-term quantum simulations of chemistry to time-dependent processes by simulating energy transfer in organic semiconducting molecules. We developed a multi-scale modeling workflow that combines conventional molecular dynamics and quantum chemistry simulations with hybrid variational quantum algorithm to compute the exciton dynamics in both the single excitation subspace (i.e. Frenkel Hamiltonian) and the full-Hilbert space (i.e. multi-exciton) regimes. Our numerical examples demonstrate the feasibility of our approach, and simulations on IBM Q devices capture the qualitative behaviors of exciton dynamics, but with considerable errors. We present an error mitigation technique that combines experimental results from the variational and Trotter algorithms, and obtain significantly improved quantum dynamics. Our approach opens up new opportunities for modeling quantum dynamics in chemical, biological and material systems with quantum computers. △ Less

Submitted 2 December, 2021; v1 submitted 18 January, 2021; originally announced January 2021.

Comments: Including full-Hilbert space (i.e. multi-exciton) treatment of energy transfer

Reply to "Comment on `Noise, not squeezing, boosts synchronization in the deep quantum regime' "

Authors: Wai Keong Mok, Leong Chuan Kwek, Hermanni Heimonen

Abstract: In this reply we clarify the main points of our manuscript and respond to the critique in the Comment arXiv:2002.11514. In particular, we emphasize that our conclusion "squeezing loses effectiveness in the deep quantum regime" does not contradict the previous work arXiv:1801.10383, but instead adds to it, and raises fundamental questions on classifying parameter regimes for quantum synchronization… ▽ More In this reply we clarify the main points of our manuscript and respond to the critique in the Comment arXiv:2002.11514. In particular, we emphasize that our conclusion "squeezing loses effectiveness in the deep quantum regime" does not contradict the previous work arXiv:1801.10383, but instead adds to it, and raises fundamental questions on classifying parameter regimes for quantum synchronization. Moreover, we address the concern brought up on the validity of the master equation in the deep quantum regime, and show that our noise-enhanced synchronization differs from previous literature. Through numerical examples, we also demonstrate that the choice of ansatz, while appearing inconsistent, does not lead to erroneous conclusions. Lastly, we expound on the physics of noise-boosted synchronization, and show that it is indeed a genuine feature unique to the deep quantum regime. However, we note that single photon dissipation is a more accurate term, and will move to using that. △ Less

Submitted 19 April, 2020; originally announced April 2020.

Suppressing Decoherence in Quantum Plasmonic Systems by Spectral Hole Burning Effect

Authors: Jia-Bin You, Xiao Xiong, Ping Bai, Zhang-Kai Zhou, Wan-Li Yang, Ching Eng Png, Leong Chuan Kwek, Lin Wu

Abstract: Quantum plasmonic systems suffer from significant decoherence due to the intrinsically large dissipative and radiative dampings. Based on our quantum simulations via a quantum tensor network algorithm, we numerically demonstrate the mitigation of this restrictive drawback by hybridizing a plasmonic nanocavity with an emitter ensemble with inhomogeneously-broadened transition frequencies. By burnin… ▽ More Quantum plasmonic systems suffer from significant decoherence due to the intrinsically large dissipative and radiative dampings. Based on our quantum simulations via a quantum tensor network algorithm, we numerically demonstrate the mitigation of this restrictive drawback by hybridizing a plasmonic nanocavity with an emitter ensemble with inhomogeneously-broadened transition frequencies. By burning two narrow spectral holes in the spectral density of the emitter ensemble, the coherent time of Rabi oscillation for the hybrid system is increased tenfold. With the suppressed decoherence, we move one step further in bringing plasmonic systems into practical quantum applications. △ Less

Submitted 8 June, 2021; v1 submitted 23 March, 2020; originally announced March 2020.

Journal ref: Phys. Rev. A 103, 053517 (2021)

Noise, not squeezing, boosts synchronization in the deep quantum regime

Authors: Wai Keong Mok, Leong Chuan Kwek, Hermanni Heimonen

Abstract: Synchronization occurs ubiquitously in nature. The van der Pol oscillator has been a favorite model to investigate synchronization. Here we study the oscillator in the deep quantum regime, where nonclassical effects dominate the dynamics. Our results show: (i) squeezed driving loses its effect, (ii) noise boosts synchronization, (iii) synchronization is bounded, and (iv) the limit-cycle is insensi… ▽ More Synchronization occurs ubiquitously in nature. The van der Pol oscillator has been a favorite model to investigate synchronization. Here we study the oscillator in the deep quantum regime, where nonclassical effects dominate the dynamics. Our results show: (i) squeezed driving loses its effect, (ii) noise boosts synchronization, (iii) synchronization is bounded, and (iv) the limit-cycle is insensitive to strong driving. We propose a synchronization measure and analytically calculate it. These results reflect intrinsic differences between synchronization in the quantum and deep quantum regimes. △ Less

Submitted 18 February, 2020; originally announced February 2020.

Journal ref: Phys. Rev. Research 2, 033422 (2020)

Phase-preserving linear amplifiers not simulable by the parametric amplifier

Authors: A. Chia, M. Hajdusek, R. Nair, R. Fazio, L. C. Kwek, V. Vedral

Abstract: It is commonly accepted that a parametric amplifier can simulate a phase-preserving linear amplifier regardless of how the latter is realized [Caves et al., Phys. Rev. A 86, 063802 (2012)]. If true, this reduces all phase-preserving linear amplifiers to a single familiar model. Here we disprove this claim by constructing two counterexamples. A detailed discussion of the physics of our counterexamp… ▽ More It is commonly accepted that a parametric amplifier can simulate a phase-preserving linear amplifier regardless of how the latter is realized [Caves et al., Phys. Rev. A 86, 063802 (2012)]. If true, this reduces all phase-preserving linear amplifiers to a single familiar model. Here we disprove this claim by constructing two counterexamples. A detailed discussion of the physics of our counterexamples is provided. It is shown that a Heisenberg-picture analysis facilitates a microscopic explanation of the physics. This also resolves a question about the nature of amplifier-added noise in degenerate two-photon amplification. △ Less

Submitted 17 October, 2020; v1 submitted 22 March, 2019; originally announced March 2019.

Comments: Comments welcome

Journal ref: Phys. Rev. Lett. 125, 163603 (2020)

Quantum transistor realized with a single $Λ$-level atom coupled to the microtoroidal cavity

Authors: Davit Aghamalyan, Jia-Bin You, Hong-Son Chu, Ching Eng Png, Leonid Krivitsky, Leong Chuan Kwek

Abstract: We propose a realization of the quantum transistor for coherent light fields for the fibre-coupled microdisk cavities. We demonstrate by combining numerical and analytical methods that both in strong coupling and bad cavity limits it is possible to change system's behaviour from being fully transparent to being fully reflective by varying the amplitude of the external control field. We remark that… ▽ More We propose a realization of the quantum transistor for coherent light fields for the fibre-coupled microdisk cavities. We demonstrate by combining numerical and analytical methods that both in strong coupling and bad cavity limits it is possible to change system's behaviour from being fully transparent to being fully reflective by varying the amplitude of the external control field. We remark that tuning the amplitude of the control field is significantly easier in the experimental setting than tuning cavity-atom coupling strength which was suggested in [Phys. Rev. A 90, 053822 (2014)] for two-level atoms and works only in the strong coupling limit. We also demonstrate the possibility of controlling the statistics of the input coherent field with the control field which opens the venue for obtaining quantum states of light. △ Less

Submitted 28 February, 2019; originally announced February 2019.

Journal ref: Phys. Rev. A 100, 053851 (2019)

Environment mediated multipartite and multidimensional entanglement

Authors: Chee Kong Lee, Mojdeh Shikhali Najafabadi, Daniel Schumayer, Leong Chuan Kwek, David A. W. Hutchinson

Abstract: Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only throug… ▽ More Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only through their mutual coupling to a reservoir. We explore the entanglement of multipartite and multidimensional system as mediated by the bath and show that at low temperatures and intermediate coupling strengths multipartite entanglement may form between qubits and between higher spins, i.e., qudits. We characterise the multipartite entanglement using an entanglement witness based upon the structure factor and demonstrate its validity versus the directly calculated entanglement of formation, suggesting possible experiments for its measure. △ Less

Submitted 21 February, 2019; originally announced February 2019.

Comments: 9 pages, 10 figures

Journal ref: Scientific Reports 9, 9147 (2019)

Non-classical Correlations in n-Cycle Setting

Authors: Kishor Bharti, Maharshi Ray, Leong Chuan Kwek

Abstract: We explore non-classical correlations in n-cycle setting. In particular, we focus on correlations manifested by Kochen-Specker-Klyachko box (KS box), scenarios involving n-cycle non-contextuality inequalities and Popescu-Rohlrich boxes (PR box). We provide the criteria for optimal classical simulation of a KS box of arbitrary n dimension. The non-contextuality inequalities are analysed for n-cycle… ▽ More We explore non-classical correlations in n-cycle setting. In particular, we focus on correlations manifested by Kochen-Specker-Klyachko box (KS box), scenarios involving n-cycle non-contextuality inequalities and Popescu-Rohlrich boxes (PR box). We provide the criteria for optimal classical simulation of a KS box of arbitrary n dimension. The non-contextuality inequalities are analysed for n-cycle setting, and the condition for the quantum violation for odd as well as even n-cycle is discussed. We offer a simple extension of even cycle non-contextuality inequalities to the continuous variable case. Furthermore, we simulate a generalized PR box using KS box and provide some interesting insights. Towards the end, we discuss a few possible interesting open problems for future research. △ Less

Submitted 12 December, 2018; originally announced December 2018.

Comments: 12 pages

Journal ref: Entropy 2019, 21(2)

Phase diffusion and the small-noise approximation in linear amplifiers: Limitations and beyond

Authors: A. Chia, M. Hajdusek, R. Fazio, L. C. Kwek, V. Vedral

Abstract: The phase of an optical field inside a linear amplifier is widely known to diffuse with a diffusion coefficient that is inversely proportional to the photon number. The same process occurs in lasers which limits its intrinsic linewidth and makes the phase uncertainty difficult to calculate. The most commonly used simplification is to assume a narrow photon-number distribution for the optical field… ▽ More The phase of an optical field inside a linear amplifier is widely known to diffuse with a diffusion coefficient that is inversely proportional to the photon number. The same process occurs in lasers which limits its intrinsic linewidth and makes the phase uncertainty difficult to calculate. The most commonly used simplification is to assume a narrow photon-number distribution for the optical field (which we call the small-noise approximation). For coherent light, this condition is determined by the average photon number. The small-noise approximation relies on (i) the input to have a good signal-to-noise ratio, and (ii) that such a signal-to-noise ratio can be maintained throughout the amplification process. Here we ask: For a coherent input, how many photons must be present in the input to a quantum linear amplifier for the phase noise at the output to be amenable to a small-noise analysis? We address these questions by showing how the phase uncertainty can be obtained without recourse to the small-noise approximation. It is shown that for an ideal linear amplifier (i.e. an amplifier most favourable to the small-noise approximation), the small-noise approximation breaks down with only a few photons on average. Interestingly, when the input strength is increased to tens of photons, the small-noise approximation can be seen to perform much better and the process of phase diffusion permits a small-noise analysis. This demarcates the limit of the small-noise assumption in linear amplifiers as such an assumption is less true for a nonideal amplifier. △ Less

Submitted 25 October, 2019; v1 submitted 20 November, 2018; originally announced November 2018.

Journal ref: Quantum 3, 200 (2019)

All fundamental non-contextuality inequalities are unique

Authors: Kishor Bharti, Atul Singh Arora, Leong Chuan Kwek, Jérémie Roland

Abstract: Contextuality is one way of capturing the non-classicality of quantum theory. The contextual nature of a theory is often witnessed via the violation of non-contextuality inequalities---certain linear inequalities involving probabilities of measurement events. Using the exclusivity graph approach (one of the two main graph theoretic approaches for studying contextuality), it was shown [PRA 88, 0321… ▽ More Contextuality is one way of capturing the non-classicality of quantum theory. The contextual nature of a theory is often witnessed via the violation of non-contextuality inequalities---certain linear inequalities involving probabilities of measurement events. Using the exclusivity graph approach (one of the two main graph theoretic approaches for studying contextuality), it was shown [PRA 88, 032104 (2013); Annals of mathematics, 51-299 (2006)] that a necessary and sufficient condition for witnessing contextuality is the presence of an odd number of events (greater than three) which are either cyclically or anti-cyclically exclusive. Thus, the non-contextuality inequalities whose underlying exclusivity structure is as stated, either cyclic or anti-cyclic, are fundamental to quantum theory. We show that there is a unique non-contextuality inequality for each non-trivial cycle and anti-cycle. In addition to the foundational interest, we expect this to aid the understanding of contextuality as a resource to quantum computing and its applications to local self-testing. △ Less

Submitted 22 December, 2019; v1 submitted 13 November, 2018; originally announced November 2018.

Comments: 17 pages (5 main, 12 appendix), 4 figures; In v2, generalised the result, upgraded the title, clarified the relation to prior work and rewrote the narrative

Journal ref: Phys. Rev. Research 2, 033010 (2020)

Charge-Qubit-Resonator-Interface-Based Nonlinear Circuit QED

Authors: Deshui Yu, Leong Chuan Kwek, Luigi Amico, Rainer Dumke

Abstract: We explore applications of nonlinear circuit QED with a charge qubit inductively coupled to a microwave LC resonator in the photonic engineering and ultrastrong-coupling multiphoton quantum optics. Simply sweeping the gate-voltage bias achieves arbitrary Fock-state pulsed maser, where the single qubit plays the role of artificial gain medium. Resonantly pumping the parametric qubit-resonator inter… ▽ More We explore applications of nonlinear circuit QED with a charge qubit inductively coupled to a microwave LC resonator in the photonic engineering and ultrastrong-coupling multiphoton quantum optics. Simply sweeping the gate-voltage bias achieves arbitrary Fock-state pulsed maser, where the single qubit plays the role of artificial gain medium. Resonantly pumping the parametric qubit-resonator interface leads to the squeezing of resonator field, which is utilizable to the quantum-limited microwave amplification. Moreover, upwards and downwards multiphoton quantum jumps may be observed in the steady state of the driving-free system. △ Less

Submitted 18 September, 2018; originally announced September 2018.

Comments: 3 figures

Journal ref: Phys. Rev. A 98, 033833 (2018)

Relaxation of Rabi Dynamics in a Superconducting Multiple-Qubit Circuit

Authors: Deshui Yu, Leong Chuan Kwek, Rainer Dumke

Abstract: We investigate a superconducting circuit consisting of multiple capacitively-coupled charge qubits. The collective Rabi oscillation of qubits is numerically studied in detail by imitating environmental fluctuations according to the experimental measurement. For the quantum circuit composed of identical qubits, the energy relaxation of the system strongly depends on the interqubit coupling strength… ▽ More We investigate a superconducting circuit consisting of multiple capacitively-coupled charge qubits. The collective Rabi oscillation of qubits is numerically studied in detail by imitating environmental fluctuations according to the experimental measurement. For the quantum circuit composed of identical qubits, the energy relaxation of the system strongly depends on the interqubit coupling strength. As the qubit-qubit interaction is increased, the system's relaxation rate is enhanced firstly and then significantly reduced. In contrast, the inevitable inhomogeneity caused by the nonideal fabrication always accelerates the collective energy relaxation of the system and weakens the interqubit correlation. However, such an inhomogeneous quantum circuit is an interesting test bed for studying the effect of the system inhomogeneity in quantum many-body simulation. △ Less

Submitted 13 August, 2018; originally announced August 2018.

Comments: 15 pages, 5 figures

Journal ref: J. Phys. Commun. 2, 095001 (2018)

An experimental measurement of the topological charge of orbital angular momentum beams through weak measurement

Authors: Jing Zhu, Pei Zhang, Qichang Li, Feiran Wang, Chenhui Wang, Yingnan Zhou, Jinwen Wang, Hong Gao, L. C. Kwek, Fuli Li

Abstract: As a special experimental technique, weak measurement extracts very little information about the measured system and will not cause the measured state collapse. When coupling the orbital angular momentum (OAM) state with a well-defined pre-selected and post-selected system of a weak measurement process, there is an indirect coupling between position and topological charge (TC) of OAM state. Based… ▽ More As a special experimental technique, weak measurement extracts very little information about the measured system and will not cause the measured state collapse. When coupling the orbital angular momentum (OAM) state with a well-defined pre-selected and post-selected system of a weak measurement process, there is an indirect coupling between position and topological charge (TC) of OAM state. Based on these ideas, we propose an experimental scheme that experimentally measure the TC of OAM beams from -14 to 14 through weak measurement. △ Less

Submitted 22 January, 2018; originally announced January 2018.

Comments: 5 pages, 2 figures. Comments are welcome

Stabilizing Rabi Oscillation of a Charge Qubit via Atomic Clock Technique

Authors: Deshui Yu, Alessandro Landra, Leong Chuan Kwek, Luigi Amico, Rainer Dumke

Abstract: We propose a superconducting circuit-atom hybrid, where the Rabi oscillation of single excess Cooper pair in the island is stabilized via the common atomic-clock technique. The noise in the superconducting circuit is mapped onto the voltage source which biases the Cooper-pair box via an inductor and a gate capacitor. The fast fluctuations of the gate charge are significantly suppressed by an induc… ▽ More We propose a superconducting circuit-atom hybrid, where the Rabi oscillation of single excess Cooper pair in the island is stabilized via the common atomic-clock technique. The noise in the superconducting circuit is mapped onto the voltage source which biases the Cooper-pair box via an inductor and a gate capacitor. The fast fluctuations of the gate charge are significantly suppressed by an inductor-capacitor resonator, leading to a long-relaxation-time Rabi oscillation. More importantly, the residual low-frequency fluctuations are further reduced by using the general feedback-control method, in which the voltage bias is stabilized via continuously measuring the dc-Stark-shift-induced atomic Ramsey signal. The stability and coherence time of the resulting charge-qubit Rabi oscillation are both enhanced. The principal structure of this Cooper-pair-box oscillator is studied in detail. △ Less

Submitted 4 January, 2018; originally announced January 2018.

Comments: 4 figures

Journal ref: New J. Phys. 20, 023031 (2018)

Population mixing due to dipole-dipole interactions in a 1D array of multilevel atoms

Authors: Ewan Munro, Ana Asenjo-Garcia, Yiheng Lin, Leong Chuan Kwek, Cindy A. Regal, Darrick E. Chang

Abstract: We examine theoretically how dipole-dipole interactions arising from multiple photon scattering lead to a modified distribution of ground state populations in a driven, ordered 1D array of multilevel atoms. Specifically, we devise a level configuration in which a ground-state population accumulated due solely to dipole-dipole interactions can be up to 20\% in regimes accessible to current experime… ▽ More We examine theoretically how dipole-dipole interactions arising from multiple photon scattering lead to a modified distribution of ground state populations in a driven, ordered 1D array of multilevel atoms. Specifically, we devise a level configuration in which a ground-state population accumulated due solely to dipole-dipole interactions can be up to 20\% in regimes accessible to current experiments with neutral atom arrays. For much larger systems, the steady state can consist of an equal distribution of population across the ground state manifold. Our results illustrate how dipole-dipole interactions can be accentuated through interference, and regulated by the geometry of ordered atom arrays. More generally, control techniques for multilevel atoms that can be degraded by multiple scattering, such as optical pumping, will benefit from an improved understanding and control of dipole-dipole interactions available in ordered arrays. △ Less

Submitted 17 September, 2018; v1 submitted 6 December, 2017; originally announced December 2017.

Comments: paper is now identical to published version

Journal ref: Phys. Rev. A 98, 033815 (2018)

Relaxation oscillations and frequency entrainment in quantum mechanics

Authors: A. Chia, L. C. Kwek, C. Noh

Abstract: Frequency entrainment of continuous-variable oscillators has to date been restrained to the weakly nonlinear regime. Here we overcome this bottleneck and extend frequency entrainment of quantum continuous-variable oscillators to arbitrary nonlinearities. The previously known steady state of such quantum oscillators in the weakly nonlinear regime (also known as a Stuart-Landau oscillator) is shown… ▽ More Frequency entrainment of continuous-variable oscillators has to date been restrained to the weakly nonlinear regime. Here we overcome this bottleneck and extend frequency entrainment of quantum continuous-variable oscillators to arbitrary nonlinearities. The previously known steady state of such quantum oscillators in the weakly nonlinear regime (also known as a Stuart-Landau oscillator) is shown to emerge as a special case. Most importantly, the hallmark of strong nonlinearity--relaxation oscillations--is shown in quantum mechanics. Depending on the oscillator's nonlinearity, relaxation oscillations are found to occur via two distinct mechanisms in phase space. △ Less

Submitted 16 October, 2020; v1 submitted 20 November, 2017; originally announced November 2017.

Comments: Comments welcome

Journal ref: Phys. Rev. E 102, 042213 (2020)

Superconducting Qubit-Resonator-Atom Hybrid System

Authors: Deshui Yu, Leong Chuan Kwek, Luigi Amico, Rainer Dumke

Abstract: We propose a hybrid quantum system, where an $LC$ resonator inductively interacts with a flux qubit and is capacitively coupled to a Rydberg atom. Varying the external magnetic flux bias controls the flux-qubit flipping and the flux qubit-resonator interface. The atomic spectrum is tuned via an electrostatic field, manipulating the qubit-state transition of atom and the atom-resonator coupling. Di… ▽ More We propose a hybrid quantum system, where an $LC$ resonator inductively interacts with a flux qubit and is capacitively coupled to a Rydberg atom. Varying the external magnetic flux bias controls the flux-qubit flipping and the flux qubit-resonator interface. The atomic spectrum is tuned via an electrostatic field, manipulating the qubit-state transition of atom and the atom-resonator coupling. Different types of entanglement of superconducting, photonic, and atomic qubits can be prepared via simply tuning the flux bias and electrostatic field, leading to the implementation of three-qubit Toffoli logic gate. △ Less

Submitted 28 June, 2017; originally announced June 2017.

Comments: 4 figures

Journal ref: Quantum Sci. Technol. 2, 035005 (2017)

Scaling of geometric phase versus band structure in cluster-Ising models

Authors: Wei Nie, Feng Mei, Luigi Amico, Leong Chuan Kwek

Abstract: We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be ordinary phases with local order parameter or exotic ones, known as symmetry protected topologically ordered phases. Quantum phase transitions with dynamical crit… ▽ More We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be ordinary phases with local order parameter or exotic ones, known as symmetry protected topologically ordered phases. Quantum phase transitions with dynamical critical exponents z = 1 or z = 2 are found. Quantum phase transitions are analyzed through finite-size scaling of the geometric phase accumulated when the spins of the lattice perform an adiabatic precession. In particular, we quantify the scaling behavior of the geometric phase in relation with the topology and low energy properties of the band structure of the system. △ Less

Submitted 1 March, 2017; v1 submitted 8 February, 2017; originally announced February 2017.

Journal ref: Phys. Rev. E 96, 020106 (2017)

Superconducting Resonator-Rydberg Atom Hybrid in the Strong Coupling Regime

Authors: Deshui Yu, Alessandro Landra, Maria Martinez Valado, Christoph Hufnagel, Leong Chuan Kwek, Luigi Amico, Rainer Dumke

Abstract: We propose a promising hybrid quantum system, where a highly-excited atom strongly interacts with a superconducting LC oscillator via the electric field of capacitor. An external electrostatic field is applied to tune the energy spectrum of atom. The atomic qubit is implemented by two eigenstates near an avoided-level crossing in the DC Stark map of Rydberg atom. Varying the electrostatic field br… ▽ More We propose a promising hybrid quantum system, where a highly-excited atom strongly interacts with a superconducting LC oscillator via the electric field of capacitor. An external electrostatic field is applied to tune the energy spectrum of atom. The atomic qubit is implemented by two eigenstates near an avoided-level crossing in the DC Stark map of Rydberg atom. Varying the electrostatic field brings the atomic-qubit transition on- or off-resonance to the microwave resonator, leading to a strong atom-resonator coupling with an extremely large cooperativity. Like the nonlinearity induced by Josephson junctions in superconducting circuits, the large atom-resonator interface disturbs the harmonic potential of resonator, resulting in an artificial two-level particle. Different universal two-qubit logic gates can also be performed on our hybrid system within the space where an atomic qubit couples to a single photon with an interaction strength much larger than any relaxation rates, opening the door to the cavity-mediated state transmission. △ Less

Submitted 16 November, 2016; originally announced November 2016.

Comments: 4 figures

Journal ref: Phys. Rev. A 94, 062301 (2016)

Quantum State Transmission in a Superconducting Charge Qubit-Atom Hybrid

Authors: Deshui Yu, Maria Martinez Valado, Christoph Hufnagel, Leong Chuan Kwek, Luigi Amico, Rainer Dumke

Abstract: Hybrids consisting of macroscopic superconducting circuits and microscopic components, such as atoms and spins, have the potential of transmitting an arbitrary state between different quantum species, leading to the prospective of high-speed operation and long-time storage of quantum information. Here we propose a novel hybrid structure, where a neutral-atom qubit directly interfaces with a superc… ▽ More Hybrids consisting of macroscopic superconducting circuits and microscopic components, such as atoms and spins, have the potential of transmitting an arbitrary state between different quantum species, leading to the prospective of high-speed operation and long-time storage of quantum information. Here we propose a novel hybrid structure, where a neutral-atom qubit directly interfaces with a superconducting charge qubit, to implement the qubit-state transmission. The highly-excited Rydberg atom located inside the gate capacitor strongly affects the behavior of Cooper pairs in the box while the atom in the ground state hardly interferes with the superconducting device. In addition, the DC Stark shift of the atomic states significantly depends on the charge-qubit states. By means of the standard spectroscopic techniques and sweeping the gate voltage bias, we show how to transfer an arbitrary quantum state from the superconducting device to the atom and vice versa. △ Less

Submitted 9 November, 2016; originally announced November 2016.

Comments: 3 figures, 1 table

Journal ref: Sci. Rep. 6, 38356 (2016)

Hitting statistics from quantum jumps

Authors: A. Chia, T. Paterek, L. C. Kwek

Abstract: We define the hitting time for a model of continuous-time open quantum walks in terms of quantum jumps. Our starting point is a master equation in Lindblad form, which can be taken as the quantum analogue of the rate equation for a classical continuous-time Markov chain. The quantum jump method is well known in the quantum optics community and has also been applied to simulate open quantum walks i… ▽ More We define the hitting time for a model of continuous-time open quantum walks in terms of quantum jumps. Our starting point is a master equation in Lindblad form, which can be taken as the quantum analogue of the rate equation for a classical continuous-time Markov chain. The quantum jump method is well known in the quantum optics community and has also been applied to simulate open quantum walks in discrete time. This method however, is well-suited to continuous-time problems. It is shown here that a continuous-time hitting problem is amenable to analysis via quantum jumps: The hitting time can be defined as the time of the first jump. Using this fact, we derive the distribution of hitting times and explicit exressions for its statistical moments. Simple examples are considered to illustrate the final results. We then show that the hitting statistics obtained via quantum jumps is consistent with a previous definition for a measured walk in discrete time [Phys.~Rev.~A~{\bf 73}, 032341 (2006)] (when generalised to allow for non-unitary evolution and in the limit of small time steps). A caveat of the quantum-jump approach is that it relies on the final state (the state which we want to hit) to share only incoherent edges with other vertices in the graph. We propose a simple remedy to restore the applicability of quantum jumps when this is not the case and show that the hitting-time statistics will again converge to that obtained from the measured discrete walk in appropriate limits. △ Less

Submitted 14 July, 2017; v1 submitted 19 August, 2016; originally announced August 2016.

Comments: Version to be published

Journal ref: Quantum 1, 19 (2017)

Entanglement Detection with Single Hong-Ou-Mandel Interferometry

Authors: Chang Jian Kwong, Simone Felicetti, Leong Chuan Kwek, Joonwoo Bae

Abstract: Entanglement is not only fundamental for understanding multipartite quantum systems but also generally useful for quantum information applications. Despite much effort devoted so far, little is known about minimal resources for detecting entanglement and also comparisons to tomography which reveals the full characterization. Here, we show that all entangled states can in general be detected in an… ▽ More Entanglement is not only fundamental for understanding multipartite quantum systems but also generally useful for quantum information applications. Despite much effort devoted so far, little is known about minimal resources for detecting entanglement and also comparisons to tomography which reveals the full characterization. Here, we show that all entangled states can in general be detected in an experimental scheme that estimates the fidelity of two pure quantum states. An experimental proposal is presented with a single Hong-Ou-Mandel interferometry in which only two detectors are applied regardless of the dimensions or the number of modes of quantum systems. This shows measurement settings for entanglement detection are in general inequivalent to tomography: the number of detectors in quantum tomography increases with the dimensions and the modes whereas it is not the case in estimation of fidelity which detects entangled states. △ Less

Submitted 1 June, 2016; originally announced June 2016.

Comments: 8 pages, 4 figures

Optical properties of an atomic ensemble coupled to a band edge of a photonic crystal waveguide

Authors: Ewan Munro, Leong Chuan Kwek, Darrick E. Chang

Abstract: We study the optical properties of an ensemble of two-level atoms coupled to a 1D photonic crystal waveguide (PCW), which mediates long-range coherent dipole-dipole interactions between the atoms. We show that the long-range interactions can dramatically alter the linear and nonlinear optical behavior, as compared to a typical atomic ensemble. In particular, in the linear regime, we find that the… ▽ More We study the optical properties of an ensemble of two-level atoms coupled to a 1D photonic crystal waveguide (PCW), which mediates long-range coherent dipole-dipole interactions between the atoms. We show that the long-range interactions can dramatically alter the linear and nonlinear optical behavior, as compared to a typical atomic ensemble. In particular, in the linear regime, we find that the transmission spectrum reveals multiple transmission dips, whose properties we show how to characterize. In the many-photon regime the system response can be highly non-linear, and under certain circumstances the ensemble can behave like a single two-level system, which is only capable of absorbing and emitting a single excitation at a time. Our results are of direct relevance to atom-PCW experiments that should soon be realizable. △ Less

Submitted 13 April, 2016; v1 submitted 11 April, 2016; originally announced April 2016.

Coherent transfer of singlet-triplet qubit states in an architecture of triple quantum dots

Authors: MengKe Feng, Chang Jian Kwong, Teck Seng Koh, Leong Chuan Kwek

Abstract: We propose two schemes to coherently transfer arbitrary quantum states of the two-electron singlet-triplet qubit across a chain of 3 quantum dots. The schemes are based on electrical control over the detuning energy of the quantum dots. The first is a pulse-gated scheme, requiring dc pulses and engineering of inter- and intra-dot Coulomb energies. The second scheme is based on the adiabatic theore… ▽ More We propose two schemes to coherently transfer arbitrary quantum states of the two-electron singlet-triplet qubit across a chain of 3 quantum dots. The schemes are based on electrical control over the detuning energy of the quantum dots. The first is a pulse-gated scheme, requiring dc pulses and engineering of inter- and intra-dot Coulomb energies. The second scheme is based on the adiabatic theorem, requiring time-dependent control of the detuning energy through avoided crossings at a rate that the system remains in the ground state. We simulate the transfer fidelity using typical experimental parameters for silicon quantum dots. Our results give state transfer fidelities between $94.3\% < \mathcal{F} < 99.5\%$ at sub-ns gate times for the pulse-gated scheme and between $75.4\% < \mathcal{F} < 99.0 \%$ at tens of ns for the adiabatic scheme. Taking into account dephasing from charge noise, we obtain state transfer fidelities between $94.0\% < \mathcal{F} < 99.2\%$ for the pulse-gated scheme and between $64.9\% < \mathcal{F} < 93.6\%$ for the adiabatic scheme. △ Less

Submitted 21 June, 2018; v1 submitted 27 February, 2016; originally announced February 2016.

Comments: Includes text and supplemental material, 11 Pages, 6 figures

Unattainable & attainable bounds for quantum sensors

Authors: Masahito Hayashi, Sai Vinjanampathy, L. C. Kwek

Abstract: In quantum metrology, it is widely believed that the quantum Cramer-Rao bound is attainable bound while it is not true. In order to clarify this point, we explain why the quantum Cramer-Rao bound cannot be attained geometrically. In this manuscript, we investigate noiseless channel estimation under energy constraint for states, using a physically reasonable error function, and present the optimal… ▽ More In quantum metrology, it is widely believed that the quantum Cramer-Rao bound is attainable bound while it is not true. In order to clarify this point, we explain why the quantum Cramer-Rao bound cannot be attained geometrically. In this manuscript, we investigate noiseless channel estimation under energy constraint for states, using a physically reasonable error function, and present the optimal state and the attainable bound. We propose the experimental generation of the optimal states for enhanced metrology using squeezing transformations. This makes the estimation of unitary channels physically implementable, while existing unitary estimation protocols do not work △ Less

Submitted 24 June, 2016; v1 submitted 23 February, 2016; originally announced February 2016.

Comments: 9 pages, 2 figures

Charge Qubit-Atom Hybrid

Authors: Deshui Yu, Maria Martinez Valado, Christoph Hufnagel, Leong Chuan Kwek, Luigi Amico, Rainer Dumke

Abstract: We investigate a novel hybrid system of a superconducting charge qubit interacting directly with a single neutral atom via electric dipole coupling. Interfacing of the macroscopic superconducting circuit with the microscopic atomic system is accomplished by varying the gate capacitance of the charge qubit. To achieve strong interaction, we employ two Rydberg states with an electric-dipole allowed… ▽ More We investigate a novel hybrid system of a superconducting charge qubit interacting directly with a single neutral atom via electric dipole coupling. Interfacing of the macroscopic superconducting circuit with the microscopic atomic system is accomplished by varying the gate capacitance of the charge qubit. To achieve strong interaction, we employ two Rydberg states with an electric-dipole allowed transition, which alters the polarizability of the dielectric medium of the gate capacitor. Sweeping the gate voltage with different rates leads to a precise control of hybrid quantum states. Furthermore, we show a possible implementation of a universal two-qubit gate. △ Less

Submitted 31 March, 2016; v1 submitted 4 February, 2016; originally announced February 2016.

Comments: accepted for publication in Physical Review A

Journal ref: Phys. Rev. A 93, 042329 (2016)

Entanglement witness via symmetric two-body correlations

Authors: Ernest Y. -Z. Tan, Dagomir Kaszlikowski, L. C. Kwek

Abstract: We construct an entanglement witness for many-qubit systems, based on symmetric two-body correlations with two measurement settings. This witness is able to detect the entanglement of some Dicke states for any number of particles, and such detection exhibits some robustness against white noise and thermal noise under the Lipkin-Meshkov-Glick Hamiltonian. In addition, it detects the entanglement of… ▽ More We construct an entanglement witness for many-qubit systems, based on symmetric two-body correlations with two measurement settings. This witness is able to detect the entanglement of some Dicke states for any number of particles, and such detection exhibits some robustness against white noise and thermal noise under the Lipkin-Meshkov-Glick Hamiltonian. In addition, it detects the entanglement of spin-squeezed states, with a detection strength that approaches the maximal value for sufficiently large numbers of particles. As spin-squeezed states can be experimentally generated, the properties of the witness with respect to these states may be amenable to experimental investigation. Finally, we show that while the witness is unable to detect GHZ states, it is instead able to detect superpositions of Dicke states with GHZ states. △ Less

Submitted 14 January, 2016; v1 submitted 8 November, 2015; originally announced November 2015.

Comments: Added references

Journal ref: Phys. Rev. A 93 (2016) 012341

Simulation and Detection of Photonic Chern Insulators in One-Dimensional Circuit Quantum Electrodynamics Lattice

Authors: Feng Mei, Jia-Bin You, Wei Nie, R. Fazio, Shi-Liang Zhu, L. C. Kwek

Abstract: We introduce a simple method to realize and detect photonic topological Chern insulators with one-dimensional circiut quantum electrodynamics arrays. By periodically modulating the couplings of the array, we show that this one-dimensional model can be mapped into a two-dimensional Chern insulator model. In addition to allowing the study of photonic Chern insulators, this approach also provides a n… ▽ More We introduce a simple method to realize and detect photonic topological Chern insulators with one-dimensional circiut quantum electrodynamics arrays. By periodically modulating the couplings of the array, we show that this one-dimensional model can be mapped into a two-dimensional Chern insulator model. In addition to allowing the study of photonic Chern insulators, this approach also provides a natural platform to realise experimentally Laughlin's pumping argument. Based on scattering theory of topological insulators and input-output formalism, we show that the photonic edge state can be probed directly and the topological invariant can be detected from the winding number of the reflection coefficient phase. △ Less

Submitted 14 October, 2015; v1 submitted 22 April, 2015; originally announced April 2015.

Comments: 5 pages, 3 figures

Journal ref: Phys. Rev. A 92, 041805 (2015)

Fast non-Abelian geometric gates via transitionless quantum driving

Authors: J. Zhang, Thi Ha Kyaw, D. M. Tong, Erik Sjöqvist, L. C. Kwek

Abstract: A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phase… ▽ More A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer. △ Less

Submitted 21 December, 2015; v1 submitted 8 December, 2014; originally announced December 2014.

Comments: 7 pages, 2 figures

Journal ref: Sci. Rep. 5, 18414 (2015)

Beating the Clauser-Horne-Shimony-Holt and the Svetlichny games with Optimal States

Authors: Hong-Yi Su, Changliang Ren, Jing-Ling Chen, Fu-Lin Zhang, Chunfeng Wu, Zhen-Peng Xu, Mile Gu, Sai Vinjanampathy, L. C. Kwek

Abstract: We study the relation between the maximal violation of Svetlichny's inequality and the mixedness of quantum states and obtain the optimal state (i.e., maximally nonlocal mixed states, or MNMS, for each value of linear entropy) to beat the Clauser-Horne-Shimony-Holt and the Svetlichny games. For the two-qubit and three-qubit MNMS, we showed that these states are also the most tolerant state against… ▽ More We study the relation between the maximal violation of Svetlichny's inequality and the mixedness of quantum states and obtain the optimal state (i.e., maximally nonlocal mixed states, or MNMS, for each value of linear entropy) to beat the Clauser-Horne-Shimony-Holt and the Svetlichny games. For the two-qubit and three-qubit MNMS, we showed that these states are also the most tolerant state against white noise, and thus serve as valuable quantum resources for such games. In particular, the quantum prediction of the MNMS decreases as the linear entropy increases, and then ceases to be nonlocal when the linear entropy reaches the critical points ${2}/{3}$ and ${9}/{14}$ for the two- and three-qubit cases, respectively. The MNMS are related to classical errors in experimental preparation of maximally entangled states. △ Less

Submitted 22 January, 2016; v1 submitted 29 April, 2014; originally announced April 2014.

Comments: 7 pages, 3 figures; minor changes; accepted in Physical Review A

Journal ref: Phys. Rev. A 93, 022110 (2016)

Beyond Gisin's Theorem and its Applications: Violation of Local Realism by Two-Party Einstein-Podolsky-Rosen Steering

Authors: Jing-Ling Chen, Hong-Yi Su, Zhen-Peng Xu, Yu-Chun Wu, Chunfeng Wu, Xiang-Jun Ye, Marek Zukowski, L. C. Kwek

Abstract: We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum en… ▽ More We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum entanglement (this is not so without this condition). This result leads to an enhanced version of Gisin's theorem (originally: all pure entangled states violate local realism). Local realism is violated by all mixed states with the above steering property. The new class of states allows one e.g. to perform three party secret sharing with just pairs of entangled qubits, instead of three qubit entanglements (which are currently available with low fidelity). This significantly increases the feasibility of having high performance versions of such protocols. Finally, we discuss some possible applications. △ Less

Submitted 10 March, 2015; v1 submitted 9 April, 2014; originally announced April 2014.

Comments: 9 pages, 1 figure

Randomized Graph States and their Entanglement Properties

Authors: Jun-Yi Wu, Matteo Rossi, Hermann Kampermann, Simone Severini, Leong Chuan Kwek, Chiara Macchiavello, Dagmar Bruß

Abstract: We introduce a class of mixed multiqubit states, that corresponds to a randomized version of graph states. Such states arise when a graph state is prepared with noisy or imperfect controlled-Z gates. We study the entanglement features of these states by investigating both bipartite and genuine multipartite entanglement. Bipartite entanglement is studied via the concepts of connectedness and persis… ▽ More We introduce a class of mixed multiqubit states, that corresponds to a randomized version of graph states. Such states arise when a graph state is prepared with noisy or imperfect controlled-Z gates. We study the entanglement features of these states by investigating both bipartite and genuine multipartite entanglement. Bipartite entanglement is studied via the concepts of connectedness and persistency, which are related to measurement based quantum computation. The presence of multipartite entanglement is instead revealed by the use of witness operators which are subsequently adapted to study nonlocal properties through the violation of suitable Bell inequalities. We also present results on the entanglement detection of particular randomized graph states, by deriving explicit thresholds for entanglement and nonlocality in terms of the noise parameter that characterizes the controlled-Z gates exploited for their generation. Finally, we propose a method to further improve the detection of genuine multipartite entanglement in this class of states. △ Less

Submitted 3 June, 2014; v1 submitted 15 March, 2014; originally announced March 2014.

Comments: This is the published version. We have added some text to clarify our results, corrected typos in references, and made some minor style modifications according to the journal

Journal ref: Phys. Rev. A 89:052335 (2014)

Transitions in the quantum computational power

Authors: Tzu-Chieh Wei, Ying Li, Leong Chuan Kwek

Abstract: We construct two spin models on lattices (both two and three-dimensional) to study the capability of quantum computational power as a function of temperature and the system parameter. There exists a finite region in the phase diagram such that the thermal equilibrium states are capable of providing a universal fault-tolerant resource for measurement-based quantum computation. Moreover, in such a r… ▽ More We construct two spin models on lattices (both two and three-dimensional) to study the capability of quantum computational power as a function of temperature and the system parameter. There exists a finite region in the phase diagram such that the thermal equilibrium states are capable of providing a universal fault-tolerant resource for measurement-based quantum computation. Moreover, in such a region the thermal resource states on the 3D lattices can enable topological protection for quantum computation. The two models behave similarly in terms of quantum computational power. However, they have different properties in terms of the usual phase transitions. The first model has a first-order phase transition only at zero temperature whereas there is no transition at all in the second model. Interestingly, the transition in the quantum computational power does not coincide with the phase transition in the first model. △ Less

Submitted 16 May, 2014; v1 submitted 18 February, 2014; originally announced February 2014.

Comments: 10 pages, 6 figures, close to published version

Journal ref: Phys. Rev. A 89, 052315 (2014)