Optimizing Unitary Compilations for Noise Resilience

Until the advent of fault-tolerant quantum computers, it remains an important task to mitigate or avoid the effects of noise in near-term quantum algorithms. We consider a setting where certain circuit patches of limited width and depth are known a priori to suffer from increased noise rates. Relying on the notion of "fragility" introduced in [1], we consider to what extent variational quantum compiling (VQC [2]) can discover sets of angles which recompile these patches into ansatze which are more resilient to certain coherent noise models. We aim to bias VQC towards those solutions which minimize the amount of curvature induced by the coherent noise as quantified by the quantum Fisher information, and we study to what extent we can optimize objectives which incorporate functions of this curvature. We find in some cases that overparameterized ansatze yield a wider "curvature disparity" amongst good-enough solutions. Those solutions of lower curvature can have average fidelities on par with shallower versions of the ansatz, potentially allowing for the benefit of increased solution quality that comes with deeper ansatze while sidestepping increased levels of noise.

[1] Garcia-Pintos et al. "Resilience-Runtime Tradeoff Relations for Quantum Algorithms"

[2] Kunal Sharma et al. "Noise resilience of variational quantum compiling" 2020 New J. Phys. 22 043006