Minimizing the Number of Code Switching Operations in Fault-Tolerant Quantum Circuits

TL;DR

This paper presents a polynomial-time method to minimize code switching operations in fault-tolerant quantum circuits, improving efficiency and reducing errors in quantum computations that use multiple error-correcting codes.

Contribution

It introduces the first automated, logical-level optimization approach for code switching in quantum circuits, formulated as a minimum-cut problem on a derived graph.

Findings

Efficient polynomial-time algorithm for minimizing code switches.

Flexible formulation incorporating depth and code bias considerations.

First automated approach for logical-level code-switching optimization.

Abstract

Fault-tolerant quantum computers rely on Quantum Error-Correcting Codes (QECCs) to protect information from noise. However, no single error-correcting code supports a fully transversal and therefore fault-tolerant implementation of all gates required for universal quantum computation. Code switching addresses this limitation by moving quantum information between different codes that, together, support a universal gate set. Unfortunately, each switch is costly-adding time and space overhead and increasing the logical error rate. Minimizing the number of switching operations is, therefore, essential for quantum computations using code switching. In this work, we study the problem of minimizing the number of code switches required to run a given quantum circuit. We show that this problem can be solved efficiently in polynomial time by reducing it to a minimum-cut instance on a graph derived from the circuit. Our formulation is flexible and can incorporate additional considerations, such as reducing depth overhead by preferring switches during idle periods or biasing the compilation to favor one code over another. To the best of our knowledge, this is the first automated approach for compiling and optimizing code-switching-based quantum computations at the logical level.