Variational circuit compiler for quantum error correction

TL;DR

This paper presents a variational compiler that efficiently constructs quantum error correction encoding circuits optimized for specific hardware, reducing noise and improving fidelity in the noisy intermediate scale quantum regime.

Contribution

It introduces a novel variational method for compiling quantum error correction circuits tailored to hardware constraints, including noise minimization and fidelity maximization.

Findings

Derived new encoders for five-qubit and Steane codes.

Demonstrated circuit optimization for noise reduction.

Showed applicability to general quantum error correction codes.

Abstract

Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are typically not 'optimal' either in terms of the circuit depth (and therefore the error burden) or the specifics of the target platform, i.e. the native gates and topology of a system. This work introduces a variational compiler for efficiently finding the encoding circuit of general quantum error correcting codes with given quantum hardware. Focusing on the noisy intermediate scale quantum regime, we show how to systematically compile the circuit following an optimising process seeking to minimise the number of noisy operations that are allowed by the noisy quantum hardware or to obtain the highest fidelity of the encoded state with noisy gates. We demonstrate our method by deriving novel encoders for logic states of the five qubit code and the seven qubit Steane code. We describe ways to augment the discovered circuits with error detection. Our method is applicable quite generally for compiling the encoding circuits of quantum error correcting codes.