Low-overhead surface code logical Hadamard

TL;DR

This paper details a low-overhead implementation of the logical Hadamard operation within the surface code, demonstrating that the entire Clifford group can be efficiently realized in this framework.

Contribution

It provides a comprehensive, detailed method for implementing logical Hadamard in surface codes, highlighting low overhead for the entire Clifford group.

Findings

Logical Hadamard can be implemented with low overhead in surface codes.

The method applies to a distance 7 double-defect logical qubit.

Surface code supports efficient Clifford group operations.

Abstract

We present an improved low-overhead implementation of surface code logical H. We describe in full detail logical H applied to a single distance 7 double-defect logical qubit in an otherwise idle scalable array such qubits. Our goal is to provide a clear description of logical H and to emphasize that the surface code possesses low-overhead implementations of the entire Clifford group.