Logical qubit implementation for quantum annealing: augmented Lagrangian approach

TL;DR

This paper introduces an optimization-based method using the augmented Lagrangian approach to determine effective chain weights for logical qubit representations in quantum annealing, improving problem-solving performance.

Contribution

It presents a novel optimization framework for logical qubit chain-weight assignment that outperforms existing methods on quantum annealing hardware.

Findings

Outperforms D-Wave's default chain-strength method

Produces smaller, more effective chain weights

Enhances solution quality for maximum clique problems

Abstract

Solving optimization problems on quantum annealers usually requires each variable of the problem to be represented by a connected set of qubits called a logical qubit or a chain. Chain weights, in the form of ferromagnetic coupling between the chain qubits, are applied so that the physical qubits in a chain favor taking the same value in low energy samples. Assigning a good chain-strength value is crucial for the ability of quantum annealing to solve hard problems, but there are no general methods for computing such a value and, even if an optimal value is found, it may still not be suitable by being too large for accurate annealing results. In this paper, we propose an optimization-based approach for producing suitable logical qubits representations that results in smaller chain weights and show that the resulting optimization problem can be successfully solved using the augmented Lagrangian method. Experiments on the D-Wave Advantage system and the maximum clique problem on random graphs show that our approach outperforms both the default D-Wave method for chain-strength assignment as well as the quadratic penalty method.