Logical-qubit operations in an error-detecting surface code

TL;DR

This paper demonstrates high-fidelity logical qubit operations within an error-detecting surface code, including initialization, measurement, and universal gates, advancing quantum error correction techniques.

Contribution

It introduces a suite of logical operations on a distance-two logical qubit with repeated error detection, including process tomography of logical gates, showing improved fault-tolerant performance.

Findings

Fault-tolerant variants outperform non-fault-tolerant ones

Successful process tomography of logical gates

Integration of logical operations with scalable error detection

Abstract

We realize a suite of logical operations on a distance-two logical qubit stabilized using repeated error detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch sphere, and a universal set of single-qubit gates. For each type of operation, we observe higher performance for fault-tolerant variants over non-fault-tolerant variants, and quantify the difference through detailed characterization. In particular, we demonstrate process tomography of logical gates, using the notion of a logical Pauli transfer matrix. This integration of high-fidelity logical operations with a scalable scheme for repeated stabilization is a milestone on the road to quantum error correction with higher-distance superconducting surface codes.