Hardware-tailored logical Clifford circuits for stabilizer codes

TL;DR

This paper presents a new mathematical framework and open-source software for designing hardware-efficient logical Clifford circuits for stabilizer codes, optimizing for hardware constraints and gauge choices.

Contribution

It introduces a discrete optimization approach for compiling logical Clifford circuits tailored to specific hardware, incorporating gauge optimization and holistic circuit compilation.

Findings

Designed fault-tolerant logical Hadamard circuits for the [[8,3,2]] code

Framework explicitly integrates hardware connectivity constraints

Achieves practical savings over standard generator decomposition methods

Abstract

Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to measuring stabilizers, decoding syndromes, and applying an appropriate correction. Although quantum information can be protected in this way, it is notoriously difficult to manipulate encoded quantum data without introducing uncorrectable errors. Here, we introduce a mathematical framework for constructing hardware-tailored quantum circuits that implement any desired Clifford unitary on the logical level of any given stabilizer code. Our main contribution is the formulation of this task as a discrete optimization problem. We can explicitly integrate arbitrary hardware connectivity constraints. As a key feature, our framework naturally incorporates an optimization over all Clifford gauges (differing only in their action outside the code space) of a desired logical circuit. In this way, we find, for example, fault-tolerant and teleportation-free logical Hadamard circuits for the $[[8,3,2]]$ code. From a broader perspective, we turn away from the standard generator decomposition approach and instead focus on the holistic compilation of entire logical circuits, leading to significant savings in practice. Our work introduces both the necessary mathematics and open-source software to compile hardware-tailored logical Clifford circuits for stabilizer codes.