Noise-tolerant quantum speedups in quantum annealing without fine tuning

TL;DR

This paper introduces RFQA, a noise-resilient quantum annealing variant that maintains quantum speedup without requiring fine-tuning, demonstrated on specific problems and resilient to realistic noise sources.

Contribution

The authors propose RFQA, a new quantum annealing approach with random oscillations that preserves quantum speedup under noise and modest control precision, with practical implementation potential.

Findings

RFQA achieves quantum speedup for Grover and quantum random energy model problems.

The method is resilient to $1/f$ noise and local heating effects.

Bath-assisted quantum phase transitions can enhance the algorithm's speedup.

Abstract

Quantum annealing is a powerful alternative model for quantum computing, which can succeed in the presence of environmental noise even without error correction. However, despite great effort, no conclusive proof of a quantum speedup (relative to state of the art classical algorithms) has been shown for these systems, and rigorous theoretical proofs of a quantum advantage generally rely on exponential precision in at least some aspects of the system, an unphysical resource guaranteed to be scrambled by random noise. In this work, we propose a new variant of quantum annealing, called RFQA, which can maintain a scalable quantum speedup in the face of noise and modest control precision. Specifically, we consider a modification of flux qubit-based quantum annealing which includes random, but coherent, low-frequency oscillations in the directions of the transverse field terms as the system evolves. We show that this method produces a quantum speedup for finding ground states in the Grover problem and quantum random energy model, and thus should be widely applicable to other hard optimization problems which can be formulated as quantum spin glasses. Further, we show that this speedup should be resilient to two realistic noise channels ($1/f$-like local potential fluctuations and local heating from interaction with a finite temperature bath), and that another noise channel, bath-assisted quantum phase transitions, actually accelerates the algorithm and may outweigh the negative effects of the others. The modifications we consider have a straightforward experimental implementation and could be explored with current technology.