Symmetric Clifford twirling for cost-optimal quantum error mitigation in early FTQC regime

Abstract

Twirling noise affecting quantum gates is essential in understanding and controlling errors, but applicable operations to noise are usually restricted by symmetries inherent in quantum gates. In this work, we propose symmetric Clifford twirling, a Clifford twirling utilizing only symmetric Clifford operators that commute with certain Pauli subgroups. We fully characterize how each Pauli noise is converted through the twirling and show that certain Pauli noise can be scrambled to a noise exponentially close to the global white noise. Moreover, we provide numerical demonstrations for highly structured circuits, such as Trotterized Hamiltonian simulation circuits, that noise effect on typical observables can be described by the global white noise. We further demonstrate that symmetric Clifford twirling and its hardware-efficient variant using only local symmetric Clifford operators can significantly accelerate the scrambling. These findings enable us to mitigate errors in non-Clifford operations with minimal sampling overhead in the early fault-tolerant regime.

11 + 15 pages, 9 figures

References in corpus (27)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Teleportation is a Universal Computational Primitive
• Black holes as mirrors: quantum information in random subsystems
• Error mitigation for short-depth quantum circuits
• Logical quantum processor based on reconfigurable atom arrays
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• Quantum Error Mitigation
• Toward the first quantum simulation with quantum speedup
• Noise tailoring for scalable quantum computation via randomized compiling
• Hybrid quantum-classical algorithms and quantum error mitigation
• Scalable Noise Estimation with Random Unitary Operators
• Characterizing Quantum Gates via Randomized Benchmarking
• Real-time quantum error correction beyond break-even
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
• Scalable error mitigation for noisy quantum circuits produces competitive expectation values
• Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
• Phase transition in Random Circuit Sampling
• Early Fault-Tolerant Quantum Computing
• The cost of universality: A comparative study of the overhead of state distillation and code switching with color codes
• Universal Sampling Lower Bounds for Quantum Error Mitigation
• Universal cost bound of quantum error mitigation based on quantum estimation theory
• Tight bounds on the convergence of noisy random circuits to the uniform distribution
• Clifford Group and Unitary Designs under Symmetry
• Practical quantum advantage on partially fault-tolerant quantum computer

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