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    SPECIAL TOPIC — Quantum computation and quantum simulation

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    Quantum walk under coherence non-generating channels
    Zishi Chen(陈子石) and Xueyuan Hu(胡雪元)
    Chin. Phys. B, 2021, 30 (3): 030305.   DOI: 10.1088/1674-1056/abd74d
    Abstract140)   HTML1)    PDF (645KB)(99)      
    We investigate the probability distribution of the quantum walk under coherence non-generating channels. We define a model called generalized classical walk with memory. Under certain conditions, generalized classical random walk with memory can degrade into classical random walk and classical random walk with memory. Based on its various spreading speed, the model may be a useful tool for building algorithms. Furthermore, the model may be useful for measuring the quantumness of quantum walk. The probability distributions of quantum walks are generalized classical random walks with memory under a class of coherence non-generating channels. Therefore, we can simulate classical random walk and classical random walk with memory by coherence non-generating channels. Also, we find that for another class of coherence non-generating channels, the probability distributions are influenced by the coherence in the initial state of the coin. Nevertheless, the influence degrades as the number of steps increases. Our results could be helpful to explore the relationship between coherence and quantum walk.
    A proposal for preparation of cluster states with linear optics
    Le Ju(鞠乐), Ming Yang(杨名), and Peng Xue(薛鹏)
    Chin. Phys. B, 2021, 30 (3): 030306.   DOI: 10.1088/1674-1056/abd74b
    Abstract95)   HTML3)    PDF (478KB)(113)      
    Measurement-based quantum computation in an optical setup shows great promise towards the implementation of large-scale quantum computation. The difficulty of measurement-based quantum computation lies in the preparation of cluster state. In this paper, we propose the method of generating the large-scale cluster state, which is a platform for measurement-based quantum computation. In order to achieve more complex quantum circuits, the preparation protocol of N-photon cluster state will be proposed as a generalization of the preparation of four-and five-photon cluster states. Furthermore, our proposal is experimentally feasible.
    Fast generation of W state via superadiabatic-based shortcut in circuit quantum electrodynamics
    Xue-Mei Wang(王雪梅), An-Qi Zhang(张安琪), Peng Xu(许鹏, and Sheng-Mei Zhao(赵生妹)
    Chin. Phys. B, 2021, 30 (3): 030307.   DOI: 10.1088/1674-1056/abd75b
    Abstract114)   HTML1)    PDF (1603KB)(77)      
    We propose a scheme to fast prepare the three-qubit W state via superadiabatic-based shortcuts in a circuit quantum electrodynamics (circuit QED) system. We derive the effective Hamiltonian to suppress the unwanted transitions between different eigenstates by counterdiabatic driving, and obtain the W state with high-fidelity based on the superadiabatic passage. The numerical simulation results demonstrate that the proposed scheme can accelerate the evolution, and is more efficient than that with the adiabatic passage. In addition, the proposed scheme is robust to the decoherence caused by the resonator decay and qubit relaxation, and does not need additional parameters, which could be feasible in experiment.
    Scheme to measure the expectation value of a physical quantity in weak coupling regime
    Jie Zhang(张杰), Chun-Wang Wu(吴春旺), Yi Xie(谢艺), Wei Wu(吴伟), and Ping-Xing Chen(陈平形)
    Chin. Phys. B, 2021, 30 (3): 033201.   DOI: 10.1088/1674-1056/abd772
    Abstract93)   HTML0)    PDF (513KB)(97)      
    In quantum mechanics, the expectation value of an operator can be measured by using the projective measurement, if the coupling between the measured system and pointer is strong enough. However in the weak coupling regime, the pointer can not show all the eigenvalue of the physical quantity directly due to the overlapping among the pointer states, which makes the measurement of the expectation value difficult. In this paper, we propose an expectation value measurement method in the weak coupling regime inspired by the weak measurement scheme. Compared to the projective measurement, our scheme has two obvious advantages. Experimentally we use the internal state and motional state of a single trapped 40Ca+ to establish the measurement scheme and realize the proof of principle demonstration of the scheme.
    Nonlocal advantage of quantum coherence in a dephasing channel with memory
    Ming-Liang Hu(胡明亮), Yu-Han Zhang(张宇晗), and Heng Fan(范桁)
    Chin. Phys. B, 2021, 30 (3): 030308.   DOI: 10.1088/1674-1056/abcf4a
    Abstract153)   HTML0)    PDF (587KB)(117)      
    We investigate nonlocal advantage of quantum coherence (NAQC) in a correlated dephasing channel modeled by the multimode bosonic reservoir. We obtain analytically the dephasing and memory factors of this channel for the reservoir having a Lorentzian spectral density, and analyze how they affect the NAQC defined by the l1 norm and relative entropy. It is shown that the memory effects of this channel on NAQC are state-dependent, and they suppress noticeably the rapid decay of NAQC for the family of input Bell-like states with one excitation. For the given transmission time of each qubit, we also obtain the regions of the dephasing and memory factors during which there is NAQC in the output states.
    A concise review of Rydberg atom based quantum computation and quantum simulation
    Xiaoling Wu(吴晓凌), Xinhui Liang(梁昕晖), Yaoqi Tian(田曜齐), Fan Yang(杨帆), Cheng Chen(陈丞), Yong-Chun Liu(刘永椿), Meng Khoon Tey(郑盟锟), and Li You(尤力)
    Chin. Phys. B, 2021, 30 (2): 020305.   DOI: 10.1088/1674-1056/abd76f
    Abstract354)   HTML15)    PDF (3178KB)(369)      
    Quantum information processing based on Rydberg atoms emerged as a promising direction two decades ago. Recent experimental and theoretical progresses have shined exciting light on this avenue. In this concise review, we will briefly introduce the basics of Rydberg atoms and their recent applications in associated areas of neutral atom quantum computation and simulation. We shall also include related discussions on quantum optics with Rydberg atomic ensembles, which are increasingly used to explore quantum computation and quantum simulation with photons.
    Selected topics of quantum computing for nuclear physics
    Dan-Bo Zhang(张旦波), Hongxi Xing(邢宏喜), Hui Yan(颜辉), Enke Wang(王恩科), and Shi-Liang Zhu(朱诗亮)
    Chin. Phys. B, 2021, 30 (2): 020306.   DOI: 10.1088/1674-1056/abd761
    Abstract158)   HTML6)    PDF (915KB)(143)      
    Nuclear physics, whose underling theory is described by quantum gauge field coupled with matter, is fundamentally important and yet is formidably challenge for simulation with classical computers. Quantum computing provides a perhaps transformative approach for studying and understanding nuclear physics. With rapid scaling-up of quantum processors as well as advances on quantum algorithms, the digital quantum simulation approach for simulating quantum gauge fields and nuclear physics has gained lots of attention. In this review, we aim to summarize recent efforts on solving nuclear physics with quantum computers. We first discuss a formulation of nuclear physics in the language of quantum computing. In particular, we review how quantum gauge fields (both Abelian and non-Abelian) and their coupling to matter field can be mapped and studied on a quantum computer. We then introduce related quantum algorithms for solving static properties and real-time evolution for quantum systems, and show their applications for a broad range of problems in nuclear physics, including simulation of lattice gauge field, solving nucleon and nuclear structures, quantum advantage for simulating scattering in quantum field theory, non-equilibrium dynamics, and so on. Finally, a short outlook on future work is given.
    Quantum dynamics on a lossy non-Hermitian lattice
    Li Wang(王利), Qing Liu(刘青), and Yunbo Zhang(张云波)
    Chin. Phys. B, 2021, 30 (2): 020506.   DOI: 10.1088/1674-1056/abd765
    Abstract134)   HTML2)    PDF (3294KB)(104)      
    We investigate quantum dynamics of a quantum walker on a finite bipartite non-Hermitian lattice, in which the particle can leak out with certain rate whenever it visits one of the two sublattices. Quantum walker initially located on one of the non-leaky sites will finally totally disappear after a length of evolution time and the distribution of decay probability on each unit cell is obtained. In one regime, the resultant distribution shows an expected decreasing behavior as the distance from the initial site increases. However, in the other regime, we find that the resultant distribution of local decay probability is very counterintuitive, in which a relatively high population of decay probability appears on the edge unit cell which is the farthest from the starting point of the quantum walker. We then analyze the energy spectrum of the non-Hermitian lattice with pure loss, and find that the intriguing behavior of the resultant decay probability distribution is intimately related to the existence and specific property of the edge states, which are topologically protected and can be well predicted by the non-Bloch winding number. The exotic dynamics may be observed experimentally with arrays of coupled resonator optical waveguides.
    Dissipative preparation of multipartite Greenberger-Horne-Zeilinger states of Rydberg atoms
    Chong Yang(杨崇), Dong-Xiao Li(李冬啸), and Xiao-Qiang Shao(邵晓强)
    Chin. Phys. B, 2021, 30 (2): 023201.   DOI: 10.1088/1674-1056/abd755
    Abstract104)   HTML2)    PDF (782KB)(232)      
    The multipartite Greenberger-Horne-Zeilinger (GHZ) states play an important role in large-scale quantum information processing. We utilize the polychromatic driving fields and the engineered spontaneous emissions of Rydberg states to dissipatively drive three-and four-partite neutral atom systems into the steady GHZ states, at the presence of the next-nearest neighbor interaction of excited Rydberg states. Furthermore, the introduction of quantum Lyapunov control can help us optimize the dissipative dynamics of the system so as to shorten the convergence time of the target state, improve the robustness against the spontaneous radiations of the excited Rydberg states, and release the limiting condition for the strengths of the polychromatic driving fields. Under the feasible experimental conditions, the fidelities of three-and four-partite GHZ states can be stabilized at 99.24% and 98.76%, respectively.
    Phase-sensitive Landau-Zener-Stückelberg interference in superconducting quantum circuit
    Zhi-Xuan Yang(杨智璇), Yi-Meng Zhang(张一萌), Yu-Xuan Zhou(周宇轩), Li-Bo Zhang(张礼博), Fei Yan(燕飞), Song Liu(刘松), Yuan Xu(徐源), and Jian Li(李剑)
    Chin. Phys. B, 2021, 30 (2): 024212.   DOI: 10.1088/1674-1056/abd753
    Abstract168)   HTML2)    PDF (1157KB)(117)      
    Superconducting circuit quantum electrodynamics (QED) architecture composed of superconducting qubit and resonator is a powerful platform for exploring quantum physics and quantum information processing. By employing techniques developed for superconducting quantum computing, we experimentally investigate phase-sensitive Landau-Zener-Stückelberg (LZS) interference phenomena in a circuit QED. Our experiments cover an extensive range of LZS transition parameters and demonstrate the LZS induced Rabi-like oscillation as well as phase-dependent steady-state population.
    Quench dynamics in 1D model with 3rd-nearest-neighbor hoppings
    Shuai Yue(岳帅), Xiang-Fa Zhou(周祥发), and Zheng-Wei Zhou(周正威)
    Chin. Phys. B, 2021, 30 (2): 026402.   DOI: 10.1088/1674-1056/abd742
    Abstract101)   HTML4)    PDF (1731KB)(76)      
    The non-equilibrium dynamics of a one-dimensional (1D) topological system with 3rd-nearest-neighbor hopping has been investigated by analytical and numerical methods. An analytical form of topological defect density under the periodic boundary conditions (PBC) is obtained by using the Landau-Zener formula (LZF), which is consistent with the scaling of defect production provided by the Kibble-Zurek mechanism (KZM). Under the open boundary conditions (OBC), quench dynamics becomes more complicated due to edge states. The behaviors of the system quenching across different phases show that defect production no longer satisfies the KZM paradigm since complicated couplings exist under OBC. Some new dynamical features are revealed.
    Review of quantum simulation based on Rydberg many-body system
    Zheng-Yuan Zhang(张正源), Dong-Sheng Ding(丁冬生), and Bao-Sen Shi(史保森)
    Chin. Phys. B, 2021, 30 (2): 020307.   DOI: 10.1088/1674-1056/abd744
    Abstract158)   HTML7)    PDF (3357KB)(152)      
    Quantum simulation has been developed extensively over the past decades, widely applied to different models to explore dynamics in the quantum regime. Rydberg atoms have strong dipole-dipole interactions and interact with each other over a long distance, which makes it straightforward to build many-body interacting quantum systems to simulate specific models. Additionally, neutral atoms are easily manipulated due to their weak interactions. These advantages make Rydberg many-body system an ideal platform to implement quantum simulations. This paper reviews several quantum simulations for different models based on Rydberg many-body systems, including quantum Ising models in one dimension and two dimensions mainly for quantum magnetism, XY model for excitation transport, SSH model for symmetry-protected topological phases, and critical self-organized behaviors in many-body systems. Besides, some challenges and promising directions of quantum simulations based on Rydberg many-body system are discussed in this paper.
    Quantum algorithm for a set of quantum 2SAT problems
    Yanglin Hu(胡杨林), Zhelun Zhang(张哲伦), and Biao Wu(吴飙)
    Chin. Phys. B, 2021, 30 (2): 020308.   DOI: 10.1088/1674-1056/abd741
    Abstract111)   HTML3)    PDF (543KB)(86)      
    We present a quantum adiabatic algorithm for a set of quantum 2-satisfiability (Q2SAT) problem, which is a generalization of 2-satisfiability (2SAT) problem. For a Q2SAT problem, we construct the Hamiltonian which is similar to that of a Heisenberg chain. All the solutions of the given Q2SAT problem span the subspace of the degenerate ground states. The Hamiltonian is adiabatically evolved so that the system stays in the degenerate subspace. Our numerical results suggest that the time complexity of our algorithm is O(n3.9) for yielding non-trivial solutions for problems with the number of clauses m=dn(n-1)/2 (\(d\lesssim 0.1\)). We discuss the advantages of our algorithm over the known quantum and classical algorithms.
    Low-temperature environments for quantum computation and quantum simulation
    Hailong Fu(付海龙), Pengjie Wang(王鹏捷), Zhenhai Hu(胡禛海), Yifan Li(李亦璠), and Xi Lin(林熙)
    Chin. Phys. B, 2021, 30 (2): 020702.   DOI: 10.1088/1674-1056/abd762
    Abstract217)   HTML4)    PDF (957KB)(150)      
    This review summarizes the requirement of low temperature conditions in existing experimental approaches to quantum computation and quantum simulation.
    Cluster mean-field study of spinor Bose-Hubbard ladder: Ground-state phase diagram and many-body population dynamics
    Li Zhang(张莉), Wenjie Liu(柳文洁), Jiahao Huang(黄嘉豪), and Chaohong Lee(李朝红)
    Chin. Phys. B, 2021, 30 (2): 026701.   DOI: 10.1088/1674-1056/abd760
    Abstract95)   HTML3)    PDF (2374KB)(76)      
    We present a cluster mean-field study for ground-state phase diagram and many-body dynamics of spin-1 bosons confined in a two-chain Bose-Hubbard ladder (BHL). For unbiased BHL, we find superfluid (SF) phase and integer filling Mott insulator (IntMI) phase. For biased BHL, in addition to the SF and IntMI phases, there appears half-integer filling Mott insulator (HIntMI) phase. The phase transition between the SF and IntMI phases can be first order at a part of phase boundaries, while the phase transition between the SF and HIntMI phases is always second order. By tuning the bias energy, we report on the change of the nature of SF-MI phase transitions. Furthermore, we study the effect of the spin-dependent interaction on the many-body population dynamics. The spin-dependent interaction can lead to rich dynamical behaviors, but does not influence the particle transfer efficiency. Our results indicate a way to tune the nature of the SF-MI phase transition and open a new avenue to study the many-body dynamics of spinor bosons in optical lattices.
    A two-dimensional quantum walk driven by a single two-side coin
    Quan Lin(林泉), Hao Qin(秦豪) Kun-Kun Wang(王坤坤), Lei Xiao(肖磊), and Peng Xue(薛鹏)
    Chin. Phys. B, 2020, 29 (11): 110303.   DOI: 10.1088/1674-1056/abaee8
    Abstract138)   HTML    PDF (823KB)(110)      

    We study a two-dimensional quantum walk with only one walker alternatively walking along the horizontal and vertical directions driven by a single two-side coin. We find the analytical expressions of the first two moments of the walker’s position distribution in the long-time limit, which indicates that the variance of the position distribution grows quadratically with walking steps, showing a ballistic spreading typically for quantum walks. Besides, we analyze the correlation by calculating the quantum mutual information and the measurement-induced disturbance respectively as the outcome of the walk in one dimension is correlated to the other with the coin as a bridge. It is shown that the quantum correlation between walker spaces increases gradually with the walking steps.

    Realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions
    Qing Yan(闫青) and Qing-Feng Sun(孙庆丰)
    Chin. Phys. B, 2021, 30 (4): 040303.   DOI: 10.1088/1674-1056/abe296
    Abstract116)   HTML1)    PDF (815KB)(125)      
    Quantum computers are in hot-spot with the potential to handle more complex problems than classical computers can. Realizing the quantum computation requires the universal quantum gate set {T, H, CNOT} so as to perform any unitary transformation with arbitrary accuracy. Here we first briefly review the Majorana fermions and then propose the realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions. Elementary cells consist of a quantum anomalous Hall insulator surrounded by a topological superconductor with electric gates and quantum-dot structures, which enable the braiding operation and the partial exchange operation. After defining a qubit by four chiral Majorana fermions, the single-qubit T and H quantum gates are realized via one partial exchange operation and three braiding operations, respectively. The entangled CNOT quantum gate is performed by braiding six chiral Majorana fermions. Besides, we design a powerful device with which arbitrary two-qubit quantum gates can be realized and take the quantum Fourier transform as an example to show that several quantum operations can be performed with this space-limited device. Thus, our proposal could inspire further utilization of mobile chiral Majorana edge states for faster quantum computation.
    Taking tomographic measurements for photonic qubits 88 ns before they are created
    Zhibo Hou(侯志博), Qi Yin(殷琪), Chao Zhang(张超), Han-Sen Zhong(钟翰森), Guo-Yong Xiang(项国勇), Chuan-Feng Li(李传锋), Guang-Can Guo(郭光灿), Geoff J. Pryde, and Anthony Laing
    Chin. Phys. B, 2021, 30 (4): 040304.   DOI: 10.1088/1674-1056/abe29c
    Abstract55)   HTML0)    PDF (1101KB)(54)      
    We experimentally demonstrate that tomographic measurements can be performed for states of qubits before they are prepared. A variant of the quantum teleportation protocol is used as a channel between two instants in time, allowing measurements for polarization states of photons to be implemented 88 ns before they are created. Measurement data taken at the early time and later unscrambled according to the results of the protocol's Bell measurements, produces density matrices with an average fidelity of 0.900.01 against the ideal states of photons created at the later time. Process tomography of the time reverse quantum channel finds an average process fidelity of 0.840.02. While our proof-of-principle implementation necessitates some post-selection, the general protocol is deterministic and requires no post-selection to sift desired states and reject a larger ensemble.
    Efficient self-testing system for quantum computations based on permutations
    Shuquan Ma(马树泉), Changhua Zhu(朱畅华), Min Nie(聂敏), and Dongxiao Quan(权东晓)
    Chin. Phys. B, 2021, 30 (4): 040305.   DOI: 10.1088/1674-1056/abe29a
    Abstract81)   HTML1)    PDF (590KB)(76)      
    Verification in quantum computations is crucial since quantum systems are extremely vulnerable to the environment. However, verifying directly the output of a quantum computation is difficult since we know that efficiently simulating a large-scale quantum computation on a classical computer is usually thought to be impossible. To overcome this difficulty, we propose a self-testing system for quantum computations, which can be used to verify if a quantum computation is performed correctly by itself. Our basic idea is using some extra ancilla qubits to test the output of the computation. We design two kinds of permutation circuits into the original quantum circuit: one is applied on the ancilla qubits whose output indicates the testing information, the other is applied on all qubits (including ancilla qubits) which is aiming to uniformly permute the positions of all qubits. We show that both permutation circuits are easy to achieve. By this way, we prove that any quantum computation has an efficient self-testing system. In the end, we also discuss the relation between our self-testing system and interactive proof systems, and show that the two systems are equivalent if the verifier is allowed to have some quantum capacity.
    Quantum annealing for semi-supervised learning
    Yu-Lin Zheng(郑玉鳞), Wen Zhang(张文), Cheng Zhou(周诚), and Wei Geng(耿巍)
    Chin. Phys. B, 2021, 30 (4): 040306.   DOI: 10.1088/1674-1056/abe298
    Abstract79)   HTML0)    PDF (1032KB)(48)      
    Recent advances in quantum technology have led to the development and the manufacturing of programmable quantum annealers that promise to solve certain combinatorial optimization problems faster than their classical counterparts. Semi-supervised learning is a machine learning technique that makes use of both labeled and unlabeled data for training, which enables a good classifier with only a small amount of labeled data. In this paper, we propose and theoretically analyze a graph-based semi-supervised learning method with the aid of the quantum annealing technique, which efficiently utilizes the quantum resources while maintaining good accuracy. We illustrate two classification examples, suggesting the feasibility of this method even with a small portion (30%) of labeled data involved.