Quantum error mitigation in early fault-tolerant quantum computing regime

Despite significant experimental advancements in quantum error correction and fault-tolerant quantum computing (FTQC), early generations of FTQC are still expected to experience substantial residual noise due to the high hardware overhead. Consequently, leveraging quantum error mitigation (QEM) techniques to suppress the remaining errors in logical qubits is crucial. In this talk, we introduce two QEM protocols specifically designed for the early FTQC regime. First, we propose symmetric Clifford twirling [1], a twirling technique that utilizes only symmetric Clifford operators that commute with certain Pauli subgroups. Symmetric Clifford twirling effectively transforms local biased noise into a global noise that is exponentially close to a global depolarizing noise, enabling cost-optimal QEM through simple rescaling of measurement results. Next, we present symmetric channel verification [2], a channel purification protocol that exploits the symmetry inherent in quantum channels. By introducing distinct phases to each symmetric subspace and employing a quantum phase estimation-like circuit, symmetric channel verification can detect and suppress symmetry-breaking noise in quantum channels. Furthermore, we demonstrate that symmetric channel verification under Pauli symmetry provides the optimal QEM strategy for noise purification when the available control is restricted to Clifford unitaries.

[1] K. Tsubouchi, Y. Mitsuhashi, K. Sharma, and N. Yoshioka, Symmetric Clifford twirling for cost-optimal quantum error mitigation in early FTQC regime, arXiv:2405.07720 (2024).

[2] K. Tsubouchi, Y. Mitsuhashi, R. Takagi, T. Sagawa, and N. Yoshioka, Symmetric channel verification for purifying noisy quantum channels, in preparation