Overhead for simulating a non-local channel with local channels by quasiprobability sampling

Kosuke Mitarai1,2,3 and Keisuke Fujii1,2,4

1Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan.
2Center for Quantum Information and Quantum Biology, Institute for Open and Transdisciplinary Research Initiatives, Osaka University, Japan.
3JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan.
4Center for Emergent Matter Science, RIKEN, Wako Saitama 351-0198, Japan

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As the hardware technology for quantum computing advances, its possible applications are actively searched and developed. However, such applications still suffer from the noise on quantum devices, in particular when using two-qubit gates whose fidelity is relatively low. One way to overcome this difficulty is to substitute such non-local operations by local ones. Such substitution can be performed by decomposing a non-local channel into a linear combination of local channels and simulating the original channel with a quasiprobability-based method. In this work, we first define a quantity that we call channel robustness of non-locality, which quantifies the cost for the decomposition. While this quantity is challenging to calculate for a general non-local channel, we give an upper bound for a general two-qubit unitary channel by providing an explicit decomposition. The decomposition is obtained by generalizing our previous work whose application has been restricted to a certain form of two-qubit unitary. This work develops a framework for a resource reduction suitable for first-generation quantum devices.

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Cited by

[1] Keisuke Fujii, Kosuke Mitarai, Wataru Mizukami, and Yuya O. Nakagawa, "Deep Variational Quantum Eigensolver: a divide-and-conquer method for solving a larger problem with smaller size quantum computers", arXiv:2007.10917.

[2] Xiao Yuan, Jinzhao Sun, Junyu Liu, Qi Zhao, and You Zhou, "Quantum simulation with hybrid tensor networks", arXiv:2007.00958.

[3] Yasunari Suzuki, Suguru Endo, Keisuke Fujii, and Yuuki Tokunaga, "Quantum error mitigation for fault-tolerant quantum computing", arXiv:2010.03887.

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