Limitations of optimization algorithms on noisy quantum devices

TL;DR

This paper analyzes how noise in near-term quantum devices limits their ability to outperform classical algorithms in optimization and Hamiltonian problems, suggesting significant noise reduction is needed for quantum advantage.

Contribution

It introduces a versatile framework combining entropic inequalities and classical Gibbs sampling to compare quantum and classical algorithms under noise.

Findings

Quantum advantage is unlikely with current noise levels.

Reducing noise rates by orders of magnitude could enable quantum benefits.

Problem topology matching quantum device architecture is crucial for advantage.

Abstract

Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is whether their noise can be overcome or it fundamentally restricts any potential quantum advantage. We present a transparent way of comparing classical algorithms to quantum ones running on near-term quantum devices for a large family of problems that include optimization problems and approximations to the ground state energy of Hamiltonians. Our approach is based on the combination of entropic inequalities that determine how fast the quantum computation state converges to the fixed point of the noise model, together with established classical methods of Gibbs state sampling. The approach is extremely versatile and allows for its application to a large variety of problems, noise models and quantum computing architectures. We use our result to provide estimates for a variety of problems and architectures that have been the focus of recent experiments, such as quantum annealers, variational quantum eigensolvers, and quantum approximate optimization. The bounds we obtain indicate that substantial quantum advantages are unlikely for classical optimization unless the current noise rates are decreased by orders of magnitude or the topology of the problem matches that of the device. This is the case even if the number of qubits increases substantially. We reach similar but less stringent conclusions for quantum Hamiltonian problems.