Sampling-based quasiprobability simulation for fault-tolerant quantum error correction on the surface codes under coherent noise

Shigeo Hakkaku,Keisuke Fujii,Kosuke Mitarai

doi:10.1103/physrevresearch.3.043130

Abstract

We propose a sampling-based simulation for fault-tolerant quantum error correction under coherent noise. A mixture of incoherent and coherent noise, possibly due to over-rotation, is decomposed into Clifford channels with a quasiprobability distribution. Then, an unbiased estimator of the logical error probability is constructed by sampling Clifford channels with an appropriate postprocessing. We characterize the sampling cost via the channel robustness and find that the proposed sampling-based method is feasible even for planar surface codes with relatively large code distances intractable for full state-vector simulations. As a demonstration, we simulate repetitive faulty syndrome measurements on the planar surface code of distance 5 with 81 qubits. We find that the coherent error increases the logical error rate. This is a practical application of the quasiprobability simulation for a meaningful task and would be useful to explore experimental quantum error correction on the near-term quantum devices.

Highlights

Quantum error correction (QEC) is an essential ingredient for developing scalable fault-tolerant quantum computers because quantum information is vulnerable to environmental noise [1,2]
This reveals that the proposed method allows us to simulate the planar surface code with relatively large code distances, which are intractable for full statevector simulations, with a reasonable computational overhead
We have proposed a sampling-based method to estimate the logical error rate of QEC codes under coherent noise such as an over-rotation error

Summary

INTRODUCTION

Quantum error correction (QEC) is an essential ingredient for developing scalable fault-tolerant quantum computers because quantum information is vulnerable to environmental noise [1,2]. We propose a sampling-based simulation method widely applicable for fault-tolerant QEC circuits under a mixture of coherent and incoherent noise with multiple rounds of faulty syndrome measurements. This reveals that we can perform an efficient simulation in the presence of coherent errors without any additional overhead for a wide range of practically interesting parameter regions Even outside this region, the proposed quasiprobability method enables us to simulate a surface code of distance 5 with 81 qubits on a single workstation within a reasonable computational time. We evaluated how many samples are required to simulate the logical error rate reliably as a function of the noise parameters and the code distance This reveals that the proposed method allows us to simulate the planar surface code with relatively large code distances, which are intractable for full statevector simulations, with a reasonable computational overhead. This decomposition can alternatively be written as p(ki)R∗(E (i) )sgn ck(i) Sk(i),

SIMULATION OF QEC CIRCUITS UNDER COHERENT NOISE

PLANAR SURFACE CODES UNDER

Findings

CONCLUSION