Scalable effective temperature reduction for quantum annealers via nested quantum annealing correction

TL;DR

Nested quantum annealing correction (NQAC) is an error correction method that encodes logical qubits into larger physical qubit graphs, effectively reducing the temperature and errors in quantum annealing, scalable to thousands of qubits.

Contribution

This paper demonstrates that NQAC achieves scalable temperature reduction in quantum annealers, confirmed on D-Wave devices up to 2048 qubits, and extends its application to sampling problems.

Findings

NQAC achieves effective temperature reduction scaling as C^{-ta} with ta  2.

Empirical validation on D-Wave 2000Q supports theoretical predictions.

NQAC improves performance in sampling applications relevant to machine learning.

Abstract

Nested quantum annealing correction (NQAC) is an error correcting scheme for quantum annealing that allows for the encoding of a logical qubit into an arbitrarily large number of physical qubits. The encoding replaces each logical qubit by a complete graph of degree $C$. The nesting level $C$ represents the distance of the error-correcting code and controls the amount of protection against thermal and control errors. Theoretical mean-field analyses and empirical data obtained with a D-Wave Two quantum annealer (supporting up to $512$ qubits) showed that NQAC has the potential to achieve a scalable effective temperature reduction, $T_{\rm eff} \sim C^{-\eta}$, with $\eta \leq 2$. We confirm that this scaling is preserved when NQAC is tested on a D-Wave 2000Q device (supporting up to $2048$ qubits). In addition, we show that NQAC can be also used in sampling problems to lower the effective temperature of a quantum annealer. Such effective temperature reduction is relevant for machine-learning applications. Since we demonstrate that NQAC achieves error correction via an effective reduction of the temperature of the quantum annealing device, our results address the problem of the "temperature scaling law for quantum annealers", which requires the temperature of quantum annealers to be reduced as problems of larger sizes are attempted to be solved.