Protection of Exponential Operation using Stabilizer Codes in the Early Fault Tolerance Era

TL;DR

This paper presents a systematic method to encode exponential quantum operations using stabilizer codes, reducing noise and resource overhead in early fault-tolerant quantum computing.

Contribution

It introduces a new encoding scheme for exponential maps into stabilizer codes with simple circuits and low qubit overhead, improving error suppression.

Findings

Encoded circuits achieve small logical error rates after postselection.

The scheme is 4-7 times less noisy than unencoded operations under current device noise levels.

At most 3% of runs need to be discarded to maintain low error rates.

Abstract

Quantum error correction offers a promising path to suppress errors in quantum processors, but the resources required to protect logical operations from noise, especially non-Clifford operations, pose a substantial challenge to achieve practical quantum advantage in the early fault-tolerant quantum computing (EFTQC) era. In this work, we develop a systematic scheme to encode exponential maps of the form $\exp(-i\theta P)$ into stabilizer codes with simple circuit structures and low qubit overhead. We provide encoded circuits with small first-order logical error rate after postselection for the [[n, n-2, 2]] quantum error-detecting codes and the [[5, 1, 3]], [[7, 1, 3]], and [[15, 7, 3]] quantum error-correcting codes. Detailed analysis shows that under the level of physical noise of current devices, our encoding scheme is 4--7 times less noisy than the unencoded operation, while at most 3% of runs need to be discarded.