Simulation and performance analysis of quantum error correction with a rotated surface code under a realistic noise model

Abstract

The demonstration of quantum error correction (QEC) is one of the most important milestones in the realization of fully-fledged quantum computers. Toward this, QEC experiments using the surface codes have recently been actively conducted. However, it has not yet been realized to protect logical quantum information beyond the physical coherence time. In this work, we performed a full simulation of QEC for the rotated surface codes with a code distance 5, which employs 49 qubits and is within reach of the current state-of-the-art quantum computers. In particular, we evaluate the logical error probability in a realistic noise model that incorporates not only stochastic Pauli errors but also coherent errors due to a systematic control error or unintended interactions. While a straightforward simulation of 49 qubits is not tractable within a reasonable computational time, we reduced the number of qubits required to 26 qubits by delaying the syndrome measurement in simulation. This and a fast quantum computer simulator, Qulacs, implemented on GPU allows us to simulate full QEC with an arbitrary local noise within reasonable simulation time. Based on the numerical results, we also construct and verify an effective model to incorporate the effect of the coherent error into a stochastic noise model. This allows us to understand what the effect coherent error has on the logical error probability on a large scale without full simulation based on the detailed full simulation of a small scale. The present simulation framework and effective model, which can handle arbitrary local noise, will play a vital role in clarifying the physical parameters that future experimental QEC should target.

9 pages, 7 figures, 2 tables

References in corpus (4)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Strong quantum computational advantage using a superconducting quantum processor
• Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
• Low-distance Surface Codes under Realistic Quantum Noise

Cited by in corpus (7)

• Efficient Magic State Distillation by Zero-Level Distillation
• On the Efficacy of Surface Codes in Compensating for Radiation Events in Superconducting Devices
• Logical Error Rates for the Surface Code Under a Mixed Coherent and Stochastic Circuit-Level Noise Model Inspired by Trapped Ions
• Leakage Mobility in Superconducting Qubits as a Leakage Reduction Unit
• Symmetry in Multi-Qubit Correlated Noise Errors Enhances Surface Code Thresholds
• Generalized Code Distance through Rotated Logical States in Quantum Error Correction
• Exact and Efficient Stabilizer Simulation of Thermal-Relaxation Noise for Quantum Error Correction