# Analog Errors in Quantum Annealing: Doom and Hope

## TL;DR

This paper investigates how analog control errors, causing $J$-chaos, severely impair quantum annealing performance, but demonstrates that quantum annealing correction can mitigate these effects and restore potential quantum speedups.

## Contribution

It provides empirical evidence of $J$-chaos causing catastrophic failure in quantum annealing and shows that quantum annealing correction can effectively mitigate this issue.

## Key findings

- $J$-chaos leads to worse-than-classical scaling in quantum annealing.
- Quantum annealing correction improves scaling to outperform classical methods.
- Empirical validation on D-Wave quantum annealers confirms the mitigation strategy's effectiveness.

## Abstract

Quantum annealing has the potential to provide a speedup over classical algorithms in solving optimization problems. Just as for any other quantum device, suppressing Hamiltonian control errors will be necessary before quantum annealers can achieve speedups. Such analog control errors are known to lead to $J$-chaos, wherein the probability of obtaining the optimal solution, encoded as the ground state of the intended Hamiltonian, varies widely depending on the control error. Here, we show that $J$-chaos causes a catastrophic failure of quantum annealing, in that the scaling of the time-to-solution metric becomes worse than that of a deterministic (exhaustive) classical solver. We demonstrate this empirically using random Ising spin glass problems run on the two latest generations of the D-Wave quantum annealers. We then proceed to show that this doomsday scenario can be mitigated using a simple error suppression and correction scheme known as quantum annealing correction (QAC). By using QAC, the time-to-solution scaling of the same D-Wave devices is improved to below that of the classical upper bound, thus restoring hope in the speedup prospects of quantum annealing.