Publication

2024

1. PRB

   Noise-induced phase transitions in hybrid quantum circuits

   Shuo Liu, Ming-Rui Li, Shi-Xin Zhang^†, Shao-Kai Jian^†, and Hong Yao^†

   Phys. Rev. B, Aug 2024

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   The presence of quantum noises inherent to real physical systems can strongly impact the physics in hybrid quantum circuits with local random unitaries and midcircuit measurements. The quantum noises with a size-independent occurring probability can lead to the disappearance of a measurement-induced entanglement phase transition and the emergence of a single area-law phase. In this work, we investigate the effects of quantum noises with size-dependent probabilities 𝑞=𝑝/𝐿𝛼, where 𝛼 represents the scaling exponent. We have identified a noise-induced entanglement phase transition from a volume law to a power (area) law in the presence (absence) of measurements as 𝑝 increases when 𝛼=1. With the help of an effective statistical model, we reveal that the phase transition is of first order arising from the competition between two types of spin configurations and shares the same analytical understanding as the noise-induced coding transition. This unified picture further deepens the understanding of the connection between entanglement behavior and the capacity of information protection. When 𝛼≠1, one spin configuration always dominates regardless of 𝑝 and thus the phase transition disappears. Moreover, we highlight the difference between the effects of size-dependent bulk noise and boundary noises. We validate our analytical predictions with extensive numerical results from stabilizer circuit simulations.

   @article{Liu2024_MIPT2,
     author = {Liu, Shuo and Li, Ming-Rui and Zhang, Shi-Xin and Jian, Shao-Kai and Yao, Hong},
     doi = {10.1103/PhysRevB.110.064323},
     issn = {2469-9950},
     journal = {Phys. Rev. B},
     month = aug,
     number = {6},
     pages = {064323},
     title = {{Noise-induced phase transitions in hybrid quantum circuits}},
     url = {https://link.aps.org/doi/10.1103/PhysRevB.110.064323},
     volume = {110},
     year = {2024}
   }

2. PRL

   

   Entanglement Structure and Information Protection in Noisy Hybrid Quantum Circuits

   Shuo Liu, Ming-Rui Li, Shi-Xin Zhang^†, and Shao-Kai Jian^†

   Phys. Rev. Lett., Jun 2024

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   In the context of measurement-induced entanglement phase transitions, the influence of quantum noises, which are inherent in real physical systems, is of great importance and experimental relevance. In this Letter, we present a comprehensive theoretical analysis of the effects of both temporally uncorrelated and correlated quantum noises on entanglement generation and information protection. This investigation reveals that entanglement within the system follows q^-1/3 scaling for both types of quantum noises, where q represents the noise probability. The scaling arises from the Kardar-Parisi-Zhang fluctuation with effective length scale L_\texteff ∼q^-1. More importantly, the information protection timescales of the steady states are explored and shown to follow q^-1/2 and q^-2/3 scaling for temporally uncorrelated and correlated noises, respectively. The former scaling can be interpreted as a Hayden-Preskill protocol, while the latter is a direct consequence of Kardar-Parisi-Zhang fluctuations. We conduct extensive numerical simulations using stabilizer formalism to support the theoretical understanding. This Letter not only contributes to a deeper understanding of the interplay between quantum noises and measurement-induced phase transition but also provides a new perspective to understand the effects of Markovian and non-Markovian noises on quantum computation.

   @article{Liu2024_MIPT1,
     archiveprefix = {arXiv},
     arxivid = {2401.01593},
     author = {Liu, Shuo and Li, Ming-Rui and Zhang, Shi-Xin and Jian, Shao-Kai},
     doi = {10.1103/PhysRevLett.132.240402},
     eprint = {2401.01593},
     issn = {0031-9007},
     journal = {Phys. Rev. Lett.},
     month = jun,
     number = {24},
     pages = {240402},
     title = {{Entanglement Structure and Information Protection in Noisy Hybrid Quantum Circuits}},
     url = {https://link.aps.org/doi/10.1103/PhysRevLett.132.240402},
     volume = {132},
     year = {2024},
   }

3. Comm Phys

   Quantum approximate optimization via learning-based adaptive optimization

   Lixue Cheng^†, Yu-Qin Chen, Shi-Xin Zhang^† , and Shengyu Zhang^†

   Communications Physics, Mar 2024

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   Combinatorial optimization problems are ubiquitous and computationally hard to solve in general. Quantum approximate optimization algorithm (QAOA), one of the most representative quantum-classical hybrid algorithms, is designed to solve combinatorial optimization problems by transforming the discrete optimization problem into a classical optimization problem over continuous circuit parameters. QAOA objective landscape is notorious for pervasive local minima, and its viability significantly relies on the efficacy of the classical optimizer. In this work, we design double adaptive-region Bayesian optimization (DARBO) for QAOA. Our numerical results demonstrate that the algorithm greatly outperforms conventional optimizers in terms of speed, accuracy, and stability. We also address the issues of measurement efficiency and the suppression of quantum noise by conducting the full optimization loop on a superconducting quantum processor as a proof of concept. This work helps to unlock the full power of QAOA and paves the way toward achieving quantum advantage in practical classical tasks.

   @article{Cheng2024,
     author = {Cheng, Lixue and Chen, Yu-Qin and Zhang, Shi-Xin and Zhang, Shengyu},
     doi = {10.1038/s42005-024-01577-x},
     issn = {2399-3650},
     journal = {Communications Physics},
     month = mar,
     number = {1},
     pages = {83},
     title = {{Quantum approximate optimization via learning-based adaptive optimization}},
     url = {https://www.nature.com/articles/s42005-024-01577-x},
     volume = {7},
     year = {2024},
   }

4. PRApplied

   Neural-network-encoded variational quantum algorithms

   Jiaqi Miao, Chang-Yu Hsieh^†, and Shi-Xin Zhang^†

   Phys. Rev. Appl., Jan 2024

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   We introduce a general framework called neural-network- (NN) encoded variational quantum algorithms (VQAs), or NNVQA for short, to address the challenges of implementing VQAs on noisy intermediate-scale quantum (NISQ) computers. Specifically, NNVQA feeds input (such as parameters of a Hamiltonian) from a given problem to a neural network and uses its outputs to parameterize an ansatz circuit for the standard VQA. Combining the strengths of NN and parameterized quantum circuits, NNVQA can accelerate the training process of VQAs and handle a broad family of related problems with varying input parameters with the pretrained NN. To concretely illustrate the merits of NNVQA, we present results on a NN variational quantum eigensolver (VQE) for solving the ground state of parameterized ?⁢?⁢? spin models in one and two dimensions. Our results demonstrate that NNVQE is able to estimate the ground-state energies of parameterized Hamiltonians with high precision without fine tuning, and significantly reduce the overall training cost to estimate ground-state properties across the phases of the given Hamiltonian. We also employ an active learning strategy to further increase the training efficiency while maintaining prediction accuracy. These encouraging results demonstrate that NNVQAs offer an alternative hybrid quantum-classical paradigm to utilize NISQ resources for solving more realistic and challenging computational problems.

   @article{Miao2024,
     author = {Miao, Jiaqi and Hsieh, Chang-Yu and Zhang, Shi-Xin},
     doi = {10.1103/PhysRevApplied.21.014053},
     issn = {2331-7019},
     journal = {Phys. Rev. Appl.},
     month = jan,
     number = {1},
     pages = {014053},
     title = {{Neural-network-encoded variational quantum algorithms}},
     url = {https://link.aps.org/doi/10.1103/PhysRevApplied.21.014053},
     volume = {21},
     year = {2024},
   }

2023

1. PRL

   Discrete Time Crystal Enabled by Stark Many-Body Localization

   Shuo Liu, Shi-Xin Zhang^†, Chang-Yu Hsieh , Shengyu Zhang, and Hong Yao^†

   Phys. Rev. Lett., Mar 2023

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   Discrete time crystal (DTC) has recently attracted increasing attention, but most DTC models and their properties are only revealed after disorder average. In this Letter, we propose a simple disorder-free periodically driven model that exhibits nontrivial DTC order stabilized by Stark many-body localization (MBL). We demonstrate the existence of DTC phase by analytical analysis from perturbation theory and convincing numerical evidence from observable dynamics. The new DTC model paves a new promising way for further experiments and deepens our understanding of DTC. Since the DTC order doesn’t require special quantum state preparation and the strong disorder average, it can be naturally realized on the noisy intermediate-scale quantum (NISQ) hardware with much fewer resources and repetitions. Moreover, besides the robust subharmonic response, there are other novel robust beating oscillations in Stark-MBL DTC phase which are absent in random or quasi-periodic MBL DTC.

   @article{Liu2022_DTC,
     archiveprefix = {arXiv},
     arxivid = {2208.02866},
     author = {Liu, Shuo and Zhang, Shi-Xin and Hsieh, Chang-Yu and Zhang, Shengyu and Yao, Hong},
     doi = {10.1103/PhysRevLett.130.120403},
     eprint = {2208.02866},
     issn = {0031-9007},
     journal = {Phys. Rev. Lett.},
     month = mar,
     number = {12},
     pages = {120403},
     title = {{Discrete Time Crystal Enabled by Stark Many-Body Localization}},
     url = {https://link.aps.org/doi/10.1103/PhysRevLett.130.120403},
     volume = {130},
     year = {2023},
   }

2. Quantum

   TensorCircuit: a Quantum Software Framework for the NISQ Era

   Shi-Xin Zhang, Jonathan Allcock, Zhou-Quan Wan, Shuo Liu, Jiace Sun, Hao Yu, and 10 more authors

   Quantum, Feb 2023

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   TensorCircuit is an open source quantum circuit simulator based on tensor network contraction, designed for speed, flexibility and code efficiency. Written purely in Python, and built on top of industry-standard machine learning frameworks, TensorCircuit supports automatic differentiation, just-in-time compilation, vectorized parallelism and hardware acceleration. These features allow TensorCircuit to simulate larger and more complex quantum circuits than existing simulators, and are especially suited to variational algorithms based on parameterized quantum circuits. TensorCircuit enables orders of magnitude speedup for various quantum simulation tasks compared to other common quantum software, and can simulate up to 600 qubits with moderate circuit depth and low-dimensional connectivity. With its time and space efficiency, flexible and extensible architecture and compact, user-friendly API, TensorCircuit has been built to facilitate the design, simulation and analysis of quantum algorithms in the Noisy Intermediate-Scale Quantum (NISQ) era.

   @article{Zhang2022_tc,
     archiveprefix = {arXiv},
     arxivid = {2205.10091},
     author = {Zhang, Shi-Xin and Allcock, Jonathan and Wan, Zhou-Quan and Liu, Shuo and Sun, Jiace and Yu, Hao and Yang, Xing-Han and Qiu, Jiezhong and Ye, Zhaofeng and Chen, Yu-Qin and Lee, Chee-Kong and Zheng, Yi-Cong and Jian, Shao-Kai and Yao, Hong and Hsieh, Chang-Yu and Zhang, Shengyu},
     doi = {10.22331/q-2023-02-02-912},
     eprint = {2205.10091},
     issn = {2521-327X},
     journal = {Quantum},
     month = feb,
     pages = {912},
     title = {{TensorCircuit: a Quantum Software Framework for the NISQ Era}},
     url = {https://quantum-journal.org/papers/q-2023-02-02-912/},
     volume = {7},
     year = {2023},
   }

3. PRB

   Probing many-body localization by excited-state variational quantum eigensolver

   Shuo Liu, Shi-Xin Zhang^†, Chang-Yu Hsieh^† , Shengyu Zhang, and Hong Yao^†

   Phys. Rev. B, Jan 2023

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   Non-equilibrium physics including many-body localization (MBL) has attracted increasing attentions, but theoretical approaches of reliably studying non-equilibrium properties remain quite limited. In this Letter, we propose a systematic approach to probe MBL phases via the excited-state variational quantum eigensolver (VQE) and demonstrate convincing results of MBL on a quantum hardware, which we believe paves a promising way for future simulations of non-equilibrium systems beyond the reach of classical computations in the noisy intermediate-scale quantum (NISQ) era. Moreover, the MBL probing protocol based on excited-state VQE is NISQ-friendly, as it can successfully differentiate the MBL phase from thermal phases with relatively-shallow quantum circuits, and it is also robust against the effect of quantum noises.

   @article{Liu2023_VQEX,
     archiveprefix = {arXiv},
     arxivid = {2111.13719},
     author = {Liu, Shuo and Zhang, Shi-Xin and Hsieh, Chang-Yu and Zhang, Shengyu and Yao, Hong},
     doi = {10.1103/PhysRevB.107.024204},
     eprint = {2111.13719},
     issn = {2469-9950},
     journal = {Phys. Rev. B},
     month = jan,
     number = {2},
     pages = {024204},
     title = {{Probing many-body localization by excited-state variational quantum eigensolver}},
     url = {https://link.aps.org/doi/10.1103/PhysRevB.107.024204},
     volume = {107},
     year = {2023},
   }

2022

1. QST

   Differentiable quantum architecture search

   Shi-Xin Zhang, Chang-Yu Hsieh^† , Shengyu Zhang, and Hong Yao^†

   Quantum Science and Technology, Oct 2022

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   Quantum architecture search (QAS) is the process of automating architecture engineering of quantum circuits. It has been desired to construct a powerful and general QAS platform which can significantly accelerate current efforts to identify quantum advantages of error-prone and depth-limited quantum circuits in the NISQ era. Hereby, we propose a general framework of differentiable quantum architecture search (DQAS), which enables automated designs of quantum circuits in an end-to-end differentiable fashion. We present several examples of circuit design problems to demonstrate the power of DQAS. For instance, unitary operations are decomposed into quantum gates, noisy circuits are re-designed to improve accuracy, and circuit layouts for quantum approximation optimization algorithm are automatically discovered and upgraded for combinatorial optimization problems. These results not only manifest the vast potential of DQAS being an essential tool for the NISQ application developments, but also present an interesting research topic from the theoretical perspective as it draws inspirations from the newly emerging interdisciplinary paradigms of differentiable programming, probabilistic programming, and quantum programming.

   @article{Zhang2020_DQAS,
     archiveprefix = {arXiv},
     arxivid = {2010.08561},
     author = {Zhang, Shi-Xin and Hsieh, Chang-Yu and Zhang, Shengyu and Yao, Hong},
     doi = {10.1088/2058-9565/ac87cd},
     eprint = {2010.08561},
     issn = {2058-9565},
     journal = {Quantum Science and Technology},
     month = oct,
     number = {4},
     pages = {045023},
     title = {{Differentiable quantum architecture search}},
     url = {https://iopscience.iop.org/article/10.1088/2058-9565/ac87cd},
     volume = {7},
     year = {2022},
   }

2. PRL

   

   Variational Quantum-Neural Hybrid Eigensolver

   Shi-Xin Zhang, Zhou-Quan Wan, Chee-Kong Lee, Chang-Yu Hsieh^† , Shengyu Zhang, and Hong Yao^†

   Phys. Rev. Lett., Mar 2022

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   The variational quantum eigensolver (VQE) is one of the most representative quantum algorithms in the noisy intermediate-size quantum (NISQ) era, and is generally speculated to deliver one of the first quantum advantages for the ground-state simulations of some non-trivial Hamiltonians. However, short quantum coherence time and limited availability of quantum hardware resources in the NISQ hardware strongly restrain the capacity and expressiveness of VQEs. In this Letter, we introduce the variational quantum-neural hybrid eigensolver (VQNHE) in which the shallow-circuit quantum ansatz can be further enhanced by classical post-processing with neural networks. We show that VQNHE consistently and significantly outperforms VQE in simulating ground-state energies of quantum spins and molecules given the same amount of quantum resources. More importantly, we demonstrate that for arbitrary post-processing neural functions, VQNHE only incurs an polynomial overhead of processing time and represents the first scalable method to exponentially accelerate VQE with non-unitary post-processing that can be efficiently implemented in the NISQ era.

   @article{Zhang2021_VQNHE,
     archiveprefix = {arXiv},
     arxivid = {2106.05105},
     author = {Zhang, Shi-Xin and Wan, Zhou-Quan and Lee, Chee-Kong and Hsieh, Chang-Yu and Zhang, Shengyu and Yao, Hong},
     doi = {10.1103/PhysRevLett.128.120502},
     eprint = {2106.05105},
     issn = {0031-9007},
     journal = {Phys. Rev. Lett.},
     month = mar,
     number = {12},
     pages = {120502},
     title = {{Variational Quantum-Neural Hybrid Eigensolver}},
     url = {https://link.aps.org/doi/10.1103/PhysRevLett.128.120502},
     volume = {128},
     year = {2022},
   }

2021

1. MLST

   

   Neural predictor based quantum architecture search

   Shi-Xin Zhang, Chang-Yu Hsieh^† , Shengyu Zhang, and Hong Yao^†

   Machine Learning: Science and Technology, Dec 2021

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   Variational quantum algorithms (VQAs) are widely speculated to deliver quantum advantages for practical problems under the quantum–classical hybrid computational paradigm in the near term. Both theoretical and practical developments of VQAs share many similarities with those of deep learning. For instance, a key component of VQAs is the design of task-dependent parameterized quantum circuits (PQCs) as in the case of designing a good neural architecture in deep learning. Partly inspired by the recent success of AutoML and neural architecture search (NAS), quantum architecture search (QAS) is a collection of methods devised to engineer an optimal task-specific PQC. It has been proven that QAS-designed VQAs can outperform expert-crafted VQAs in various scenarios. In this work, we propose to use a neural network based predictor as the evaluation policy for QAS. We demonstrate a neural predictor guided QAS can discover powerful quantum circuit ansatz, yielding state-of-the-art results for various examples from quantum simulation and quantum machine learning. Notably, neural predictor guided QAS provides a better solution than that by the random-search baseline while using an order of magnitude less of circuit evaluations. Moreover, the predictor for QAS as well as the optimal ansatz found by QAS can both be transferred and generalized to address similar problems.

   @article{Zhang2021_neural,
     author = {Zhang, Shi-Xin and Hsieh, Chang-Yu and Zhang, Shengyu and Yao, Hong},
     doi = {10.1088/2632-2153/ac28dd},
     issn = {2632-2153},
     journal = {Machine Learning: Science and Technology},
     month = dec,
     number = {4},
     pages = {045027},
     title = {{Neural predictor based quantum architecture search}},
     url = {https://iopscience.iop.org/article/10.1088/2632-2153/ac28dd},
     volume = {2},
     year = {2021},
   }

2018

1. PRL

   Universal Properties of Many-Body Localization Transitions in Quasiperiodic Systems

   Shi-Xin Zhang, and Hong Yao^†

   Phys. Rev. Lett., Dec 2018

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   Precise nature of MBL transitions in both random and quasiperiodic (QP) systems remains elusive so far. In particular, whether MBL transitions in QP and random systems belong to the same universality class or two distinct ones has not been decisively resolved. Here we investigate MBL transitions in one-dimensional (d\!=\!1) QP systems as well as in random systems by state-of-the-art real-space renormalization group (RG) calculation. Our real-space RG shows that MBL transitions in 1D QP systems are characterized by the critical exponent ν\!≈\!2.4, which respects the Harris-Luck bound (ν\!>\!1/d) for QP systems. Note that ν\!≈\! 2.4 for QP systems also satisfies the Harris-CCFS bound (ν\!>\!2/d) for random systems, which implies that MBL transitions in 1D QP systems are stable against weak quenched disorder since randomness is Harris irrelevant at the transition. We shall briefly discuss experimental means to measure νof QP-induced MBL transitions.

   @article{Zhang2018_MBL,
     archiveprefix = {arXiv},
     arxivid = {1805.05958},
     author = {Zhang, Shi-Xin and Yao, Hong},
     doi = {10.1103/PhysRevLett.121.206601},
     eprint = {1805.05958},
     issn = {10797114},
     journal = {Phys. Rev. Lett.},
     number = {20},
     pages = {206601},
     publisher = {American Physical Society},
     title = {{Universal Properties of Many-Body Localization Transitions in Quasiperiodic Systems}},
     url = {https://doi.org/10.1103/PhysRevLett.121.206601},
     volume = {121},
     year = {2018},
   }