Optimized Measurement Schedules for the Surface Code with Dropout

TL;DR

This paper introduces optimized measurement schedules for the surface code that improve error correction performance by leveraging gauge operator choices, qubit excision, and ILP-based circuit design, especially under dropout conditions.

Contribution

It presents novel optimization techniques for surface code measurement schedules, including gauge operator selection, qubit excision, and ILP-based circuit synthesis, enhancing error correction at dropout rates.

Findings

Achieves up to 23.6% improvement in error correction performance.

Demonstrates effectiveness at 1% dropout rate with significant noise resilience.

Provides a framework for optimizing surface code measurement circuits.

Abstract

Recent work has shown that fabrication defects can be well-handled using a strategy relying on the mid-error-correction-cycle state. In this work we present two improvements to the original prescription. First, we quantify the impact of the choice of a more complete set of gauge operators originally proposed for the hex-grid surface code on the standard square-grid surface code, as well as a new method for excising effectively unused qubits. Second, we leverage the expressivity of the LUCI framework as an intermediate representation, using integer linear programming to find performant physical circuits from the large space of valid LUCI circuits. We show that on the $d = 11$ surface code at $1\%(3\%)$ dropout rate for qubits and couplers, these optimizations allow for a total improvement of $14.5\%(23.6\%)$ over $4d$ round of syndrome extraction using the SI1000 noise model at $0.1\%$ noise.