Symmetric Clifford twirling for cost-optimal quantum error mitigation in early FTQC regime (2405.07720v4)

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.

• The paper proposes symmetric Clifford twirling, a technique using Clifford operations to transform Pauli noise into global white noise for cost-optimal quantum error mitigation.
• It characterizes how this twirling scrambles Pauli-X and Y noise close to global white noise, while Pauli-Z noise is largely unaffected.
• The technique is practical for early FTQC systems, requiring minimal CNOT gates for efficient noise approximation and showing significant bias reduction numerically.

An Overview of Symmetric Clifford Twirling for Quantum Error Mitigation

The paper "Symmetric Clifford twirling for cost-optimal quantum error mitigation in the early FTQC regime" by Tsubouchi et al. addresses a pivotal challenge in the domain of quantum error mitigation, particularly in the nascent stages of fault-tolerant quantum computing (FTQC). The paper focuses on symmetric Clifford twirling, aiming to transform Pauli noise in quantum circuits into global white noise, thereby enabling cost-optimal quantum error mitigation (QEM).

Key Contributions

1. Symmetric Clifford Twirling: The authors propose a symmetric Clifford twirling technique, which employs Clifford operations that commute with given non-Clifford gates, thus allowing for effective noise scrambling without affecting the target operations. This method targets Pauli noise associated with non-Clifford gates, providing a systematic way to convert it into global white noise—a state where errors are uniformly distributed across the Hilbert space.
2. Characterization of Noise Scrambling: The paper provides a rigorous characterization of how symmetric Clifford twirling transforms different types of Pauli noise. Notably, it demonstrates that Pauli-X and Y noise can be scrambled to a noise exponentially close to global white noise, whereas Pauli-Z noise remains largely unaffected by the twirling process.
3. Practical Implementation: The paper emphasizes the practical applicability of their method in early FTQC systems by showing that even a minimal application of CNOT gates (termed as "2-sparse symmetric Clifford twirling") can efficiently approximate the target noise transformations. This approach ensures that the overhead in terms of additional gate usage is minimized, which is crucial given the error sensitivity of quantum hardware.
4. Numerical Demonstrations: Tsubouchi et al. provide numerical evidence supporting the efficacy of symmetric Clifford twirling in complex circuit architectures such as Trotterized Hamiltonian simulation circuits. Their results indicate a significant reduction in bias between the ideal and error-mitigated expectation values, with the noise effect on typical observables described well by global white noise.

Implications and Future Directions

The implications of this work are profound for both theoretical and practical quantum computing. By achieving close-to-optimal error mitigation with minimal resource overhead, this technique aids in bridging the gap between near-term quantum systems and fault-tolerant quantum computation. Cost-optimal mitigation has the potential to significantly reduce hardware requirements, particularly in scenarios where physical error rates approach the thresholds critical for error-correcting codes.

Looking forward, several avenues warrant exploration. The development of methods to systematically introduce noise in non-Clifford operations that can be efficiently twirled could enhance the practicality of the symmetric Clifford twirling technique. Furthermore, extending the applications of symmetric Clifford twirling beyond QEM, such as in fidelity estimation and the assessment of information loss in quantum systems, could uncover additional utility in broader quantum information science contexts.

In conclusion, this paper presents a comprehensive exploration of symmetric Clifford twirling, offering a significant advancement in quantum error mitigation strategies. Its combination of theoretical insights, practical considerations, and numerical validations positions it as an essential contribution to the evolving landscape of quantum computing technologies.