Contracting Arbitrary Tensor Networks: General Approximate Algorithm and Applications in Graphical Models and Quantum Circuit Simulations

Pan, Feng; Zhou, Pengfei; Li, Sujie; Zhang, Pan

doi:10.1103/physrevlett.125.060503

Cited by 54 publications

(41 citation statements)

References 28 publications

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“…II B) is L = 2 20 groups of amplitudes, each group contains l = 2 6 = 64 bitstring amplitudes. That is, we have computed approximate amplitudes for 2 26 = 67, 108, 864 bitstrings and finally sampled 2 20 uncorrelated bitstrings from them.…”

Section: B Contraction Of the 3-dimensional Tensor Network To Obtain ...mentioning

confidence: 99%

“…amplitudes (in the practical computations we choose L = 2 20 and l = 2 6 ). They are given according to a generation process (e.g.…”

Section: B Contraction Of the 3-dimensional Tensor Network To Obtain ...mentioning

confidence: 99%

“…Specifically, the parameters in Google's experiments [1] are tuned to θ ≈ π/2 in order to keep the decomposition rank equal to 4 with a near-flat spectrum. This setting increases significantly the cost of classical simulations when compared with Controlled-Z gates which has decompositional rank 2, in exact simulations as well as in approximate simulations [19,20]. It has been reported in [1] that due to the flat spectrum of the fSim gates, there is almost no space to make use of the spectrum imbalances for speeding up the simulation in e.g.…”

Section: Exploring Low-rank Structuresmentioning

confidence: 99%

“…Our algorithm is massively more efficient than existing algorithms in producing a large number of uncorrelated approximate samples. On the Sycamore circuits with n = 53 qubits and m = 20 cycles, we have successfully generated L = 2 20 approximate samples with fidelity F ≈ 0.0037 in about 15 hours using 512 GPUs. We remark that to the best of our knowledge this is the first time that the sampling problem of the Sycamore quantum supremacy circuits (with fidelity larger than Google's hardware samples) with n = 53 qubits and m = 20 cycles is solved in practice classically.…”

Section: Introductionmentioning

confidence: 99%

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Solving the sampling problem of the Sycamore quantum supremacy circuits

Pan,

Chen,

Zhang

2021

Preprint

Self Cite

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We study the problem of generating independent samples from the output distribution of Google's Sycamore quantum circuits with a target fidelity, which is believed to be beyond the reach of classical supercomputers and has been used to demonstrate quantum supremacy. We propose a new method to classically solve this problem by contracting the corresponding tensor network just once, and is massively more efficient than existing methods in obtaining a large number of uncorrelated samples with a target fidelity. For the Sycamore quantum supremacy circuit with 53 qubits and 20 cycles, we have generated one million uncorrelated bitstrings s which are sampled from a distribution P(s) = | ψ(s)| 2 , where the approximate state ψ has fidelity F ≈ 0.0037. The whole computation has cost about 15 hours on a computational cluster with 512 GPUs. The obtained one million samples, the contraction code and contraction order are made public. If our algorithm could be implemented with high efficiency on a modern supercomputer with ExaFLOPS performance, we estimate that ideally, the simulation would cost a few dozens of seconds, which is faster than Google's quantum hardware.

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Section: B Contraction Of the 3-dimensional Tensor Network To Obtain ...mentioning

confidence: 99%

“…amplitudes (in the practical computations we choose L = 2 20 and l = 2 6 ). They are given according to a generation process (e.g.…”

Section: B Contraction Of the 3-dimensional Tensor Network To Obtain ...mentioning

confidence: 99%

Section: Exploring Low-rank Structuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Solving the sampling problem of the Sycamore quantum supremacy circuits

Pan,

Chen,

Zhang

2021

Preprint

Self Cite

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show abstract

“…Thus, tensor network algorithms developed in the quantum many-body community are potentially useful for simulating quantum circuits, especially the shallow ones with a large number of qubits where the state vector does not fit into memory [100][101][102]. In this sense, one can perform more efficient simulations at a larger scale by exploring low-rank structures in the tensor networks with a trade-off of almost negligible errors [103].…”

Section: Tensor Network Backendmentioning

confidence: 99%

Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design

Luo

Liu

Zhang

et al. 2020

Quantum

Self Cite

118

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We introduce Yao, an extensible, efficient open-source framework for quantum algorithm design. Yao features generic and differentiable programming of quantum circuits. It achieves state-of-the-art performance in simulating small to intermediate-sized quantum circuits that are relevant to near-term applications. We introduce the design principles and critical techniques behind Yao. These include the quantum block intermediate representation of quantum circuits, a builtin automatic differentiation engine optimized for reversible computing, and batched quantum registers with GPU acceleration. The extensibility and efficiency of Yao help boost innovation in quantum algorithm design.

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Fast Emulation of Fermionic Circuits with Matrix Product States

Provazza,

Gunst,

Zhai

et al. 2024

J. Chem. Theory Comput.

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We describe a matrix product state (MPS) extension for the Fermionic Quantum Emulator (FQE) software library. We discuss the theory behind symmetry-adapted MPSs for approximating many-body wave functions of spin-1/2 Fermions, and we present an open-source, MPS-enabled implementation of the FQE interface (MPS-FQE). The software uses the open-source pyblock3 and block2 libraries for most elementary tensor operations, and it can largely be used as a drop-in replacement for FQE that allows for more efficient but approximate emulation of larger Fermionic circuits. Finally, we show several applications relevant to both near-term and fault-tolerant quantum algorithms where approximate emulation of larger systems is expected to be useful: characterization of state preparation strategies for quantum phase estimation, the testing of different variational quantum eigensolver ansaẗze, the numerical evaluation of Trotter errors, and the simulation of general quantum dynamics problems. In all these examples, approximate emulation with MPS-FQE allows us to treat systems that are significantly larger than those accessible with a full statevector emulator.

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Contracting Arbitrary Tensor Networks: General Approximate Algorithm and Applications in Graphical Models and Quantum Circuit Simulations

Cited by 54 publications

References 28 publications

Solving the sampling problem of the Sycamore quantum supremacy circuits

Solving the sampling problem of the Sycamore quantum supremacy circuits

Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design

Fast Emulation of Fermionic Circuits with Matrix Product States

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