Optimized Compilation of Logical Clifford Circuits

TL;DR

This paper presents a novel compilation approach for logical Clifford circuits that improves depth and error rates by using primitive blocks from quantum simulation, especially for the [[n,n-2,2]] code family.

Contribution

It introduces a size-invariant, depth-efficient compilation methodology based on quantum simulation primitives, enhancing fault-tolerant circuit realization.

Findings

Significant error-rate reductions in simulated circuits

Improved compilation strategies for sparse and dense placements

Method is flexible and extensible to other codes

Abstract

Fault-tolerant quantum computing hinges on efficient logical compilation, in particular, translating high-level circuits into code-compatible implementations. Gate-by-gate compilation often yields deep circuits, requiring significant overhead to ensure fault-tolerance. As an alternative, we investigate the compilation of primitives from quantum simulation as single blocks. We focus our study on the [[n,n-2,2]] code family, which allows for the exhaustive comparison of potential compilation primitives on small circuit instances. Based upon that, we then introduce a methodology that lifts these primitives into size-invariant, depth-efficient compilation strategies. This recovers known methods for circuits with moderate Hadamard counts and yields improved realizations for sparse and dense placements. Simulations show significant error-rate reductions in the compiled circuits. We envision the approach as a core component of peephole-based compilers. Its flexibility and low hand-crafting burden make it readily extensible to other circuit structures and code families.