Spectral Minimax Direct Fidelity Estimation for Generic Target States

TL;DR

This paper introduces an exact spectral minimax approach for direct fidelity estimation that outperforms previous surrogate methods in variance reduction, using semidefinite programming and local measurements.

Contribution

It develops a novel spectral replacement method for arbitrary target states, providing an exact minimax solution and an efficient algorithm for fidelity estimation.

Findings

Outperforms OASIS surrogate in estimation variance.

Uses semidefinite programming for optimal sampling law.

Effective under depolarizing noise in simulations.

Abstract

Direct fidelity estimation benefits from tailoring measurements to a fixed target, but the operator-aware shadow importance sampling (OASIS) method optimizes an outcome-wise linear-program surrogate rather than the exact worst-case variance over physical states. We propose an exact spectral replacement for arbitrary target states under the same non-adaptive single-copy measurement model. Specifically, we characterize unbiased linear estimators by a single operator identity, determine the state-wise optimal sampling law for fixed reconstruction coefficients, and convert the exact minimax problem into a semidefinite program. The resulting offline design and online estimator are presented as an algorithm and implemented with local Pauli measurements. Numerical simulations under depolarizing noise demonstrate that our exact spectral optimization outperforms the OASIS surrogate in terms of estimation variance.