Simulating noisy quantum circuits with matrix product density operators

Cheng, Song; Cao, Chenfeng; Zhang, Chao; Liu, Yongxiang; Hou, Shi-Yao; Xu, Pengxiang; Zeng, Bei

doi:10.1103/physrevresearch.3.023005

Cited by 15 publications

(10 citation statements)

References 26 publications

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“…During the process, we can even make an approximation by cutting the bond dimension of the working tensor network TN i . [71,73] In this way, the time complexity of the contraction process can be restricted to polynomial scaling with the size of the circuit. However, the approximation error should be small enough to pass the corresponding verification test of quantum advantage.…”

Section: Simulation Methods Based On Tensor Networkmentioning

confidence: 99%

Noisy Random Quantum Circuit Sampling and its Classical Simulation

Zhang

Wang²,

Han

2023

Adv Quantum Tech

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Demonstrating quantum advantage on noisy quantum devices is one of the most important tasks of quantum computing research in the near future. Random quantum circuit sampling is proposed as the most promising approach to the task and has been implemented in experiments for achieving quantum advantage. A series of encouraging computational complexity results, based on some plausible assumptions, show that this task is impossible to complete efficiently by classical computers. However, in practical experiments on noisy quantum devices, the approximate average‐case hardness and the effects of the noise need to be further checked. The competition between the classical simulation algorithm (mainly based on tensor network algorithms) and noisy quantum devices is the explicit way to understand quantum advantage in practice. This review briefly overviews the computational complexity arguments for the hardness of classical simulation of random quantum circuits sampling, then focus on various methods of classical simulation of quantum circuits based on tensor network method.

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Section: Simulation Methods Based On Tensor Networkmentioning

confidence: 99%

Noisy Random Quantum Circuit Sampling and its Classical Simulation

Zhang

Wang²,

Han

2023

Adv Quantum Tech

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“…We stress that the engine does not perform any truncation to the target density matrix, which is different from a number of preceding works. 79,80 In the presence of noise, unfortunately, symmetries encoded in the ansatz are broken and cannot be exploited. In TENSORCIRCUIT, noise channels are defined by their corresponding Kraus operators K i , i.e.,…”

Section: Engines and Backendsmentioning

confidence: 99%

TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era

Allcock

Cheng

et al. 2023

J. Chem. Theory Comput.

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TenCirChem is an open-source Python library for simulating variational quantum algorithms for quantum computational chemistry. TenCirChem shows high-performance in the simulation of unitary coupled-cluster circuits, using compact representations of quantum states and excitation operators. Additionally, TenCirChem supports noisy circuit simulation and provides algorithms for variational quantum dynamics. TenCirChem’s capabilities are demonstrated through various examples, such as the calculation of the potential energy curve of H2O with a 6-31G(d) basis set using a 34-qubit quantum circuit, the examination of the impact of quantum gate errors on the variational energy of the H2 molecule, and the exploration of the Marcus inverted region for charge transfer rate based on variational quantum dynamics. Furthermore, TenCirChem is capable of running real quantum hardware experiments, making it a versatile tool for both simulation and experimentation in the field of quantum computational chemistry.

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“…VarQEC can also be directly revised to a classical algorithm. When a NISQ processor is not accessible, one can replace the VQCs with classical variational ansatzes like tensor networks [93][94][95] or neural network quantum states [96], and then similarly implement optimization and search for eligible quantum codes merely with a classical computer. However, the encoding circuits can not be naturally obtained.…”

Section: Conclusion and Outlooksmentioning

confidence: 99%

Quantum variational learning for quantum error-correcting codes

Cao

Zhang

et al. 2022

Quantum

Self Cite

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Quantum error correction is believed to be a necessity for large-scale fault-tolerant quantum computation. In the past two decades, various constructions of quantum error-correcting codes (QECCs) have been developed, leading to many good code families. However, the majority of these codes are not suitable for near-term quantum devices. Here we present VarQEC, a noise-resilient variational quantum algorithm to search for quantum codes with a hardware-efficient encoding circuit. The cost functions are inspired by the most general and fundamental requirements of a QECC, the Knill-Laflamme conditions. Given the target noise channel (or the target code parameters) and the hardware connectivity graph, we optimize a shallow variational quantum circuit to prepare the basis states of an eligible code. In principle, VarQEC can find quantum codes for any error model, whether additive or non-additive, degenerate or non-degenerate, pure or impure. We have verified its effectiveness by (re)discovering some symmetric and asymmetric codes, e.g., ((n,2n−6,3))2 for n from 7 to 14. We also found new ((6,2,3))2 and ((7,2,3))2 codes that are not equivalent to any stabilizer code, and extensive numerical evidence with VarQEC suggests that a ((7,3,3))2 code does not exist. Furthermore, we found many new channel-adaptive codes for error models involving nearest-neighbor correlated errors. Our work sheds new light on the understanding of QECC in general, which may also help to enhance near-term device performance with channel-adaptive error-correcting codes.

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Simulating noisy quantum circuits with matrix product density operators

Cited by 15 publications

References 26 publications

Noisy Random Quantum Circuit Sampling and its Classical Simulation

Noisy Random Quantum Circuit Sampling and its Classical Simulation

TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era

Quantum variational learning for quantum error-correcting codes

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