High-order noise filtering in nontrivial quantum logic gates

TL;DR

This paper develops a theoretical framework to model and analyze the effects of classical noise on complex quantum logic gates, enabling improved understanding and design of error-resilient quantum operations.

Contribution

It introduces an effective Hamiltonian approach and a general method to compute ensemble-averaged fidelity for nontrivial quantum gates under classical noise.

Findings

Derived explicit filter functions for piecewise-constant control sequences.

Validated the approach with numerical simulations showing good agreement.

Provided a systematic way to assess and improve quantum gate robustness.

Abstract

Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of non-commuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics.