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  • Open Access

Symmetric Channel Verification for Purifying Noisy Quantum Channels

Kento Tsubouchi1,*, Yosuke Mitsuhashi2, Ryuji Takagi2, and Nobuyuki Yoshioka3,†

  • *Contact author: tsubouchi@noneq.t.u-tokyo.ac.jp
  • †Contact author: ny.nobuyoshioka@gmail.com
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PRX Quantum 6, 040310 – Published 15 October, 2025

DOI: https://doi.org/10.1103/jcd6-lft3

Abstract

Symmetry inherent in quantum states has been widely used to reduce the effect of noise in quantum error correction and a quantum error-mitigation technique known as symmetry verification. However, these symmetry-based techniques exploit symmetry in quantum states rather than quantum channels, limiting their application to cases where the entire circuit shares the same symmetry. In this work, we propose symmetric channel verification (SCV), a channel purification protocol that leverages the symmetry inherent in quantum channels. By introducing different phases to each symmetric subspace and employing a quantum phase estimation-like circuit, SCV can detect and correct symmetry-breaking noise in quantum channels. We further propose a hardware-efficient implementation of SCV at the virtual level, which requires only a single-qubit ancilla and is robust against the noise in the ancilla qubit. Our protocol is applied to various Hamiltonian simulation circuits and phase estimation circuits, resulting in a significant reduction of errors. Furthermore, in setups where only Clifford unitaries can be used for noise purification, which is relevant in the early fault-tolerant regime, we show that SCV under Pauli symmetry represents the optimal purification method.

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Popular Summary

Understanding and controlling noise is one of the central challenges for building reliable quantum computers. In particular, various problems in quantum many-body systems require simulating systems with intrinsic symmetries. Harnessing these symmetries provides an attractive way to counteract errors without relying on fully error-corrected hardware. However, previous symmetry-based approaches have been restricted to quantum states alone. This limitation means that they could only be applied under narrow conditions and could not fully detect errors occurring during the dynamical processes of a quantum computation.

In this work, we introduce a new method called symmetric channel verification (SCV), which generalizes the idea of symmetry-based error mitigation from states to channels. SCV detects and corrects noise by checking whether each channel preserves the relevant symmetry, independently of the input state. This approach enables error detection and correction even when the input state and the channel obey different symmetries, or when multiple channels with different symmetries are combined. We further show that SCV can be incorporated into existing quantum algorithms with only modest overhead, and that it is provably optimal for early fault-tolerant devices with partial error-correcting capabilities.

Our results demonstrate that SCV dramatically enhances computational accuracy compared with conventional state-based techniques. This opens up new opportunities for accurately simulating symmetric quantum systems—ubiquitous in physics and chemistry—on near-term and early fault-tolerant quantum devices, providing a practical pathway toward reliable quantum computation before the realization of fully fault-tolerant architectures.

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PRX Quantum 6, 040310– Published 15 October, 2025
  • Received 8 May 2025
  • Revised 23 August 2025
  • Accepted 16 September 2025
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