Estimating distinguishability measures on quantum computers

Abstract

The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result of the protocol is from the ideal case. The most prominent distinguishability measures are those based on the fidelity and trace distance, due to their physical interpretations. In this paper, we propose and review several algorithms for estimating distinguishability measures based on trace distance and fidelity. The algorithms can be used for distinguishing quantum states, channels, and strategies (the last also known in the literature as "quantum combs"). The fidelity-based algorithms offer novel physical interpretations of these distinguishability measures in terms of the maximum probability with which a single prover (or competing provers) can convince a verifier to accept the outcome of an associated computation. We simulate many of these algorithms by using a variational approach with parameterized quantum circuits. We find that the simulations converge well in both the noiseless and noisy scenarios, for all examples considered. Furthermore, the noisy simulations exhibit a parameter noise resilience. Finally, we establish a strong relationship between various quantum computational complexity classes and distance estimation problems.

v4: 45 pages, 17 figures, accepted for publication in Physical Review A

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• Subsystem distances between quasiparticle excited states
• Optimal Trace Distance and Fidelity Estimations for Pure Quantum States
• Trace distance between fermionic Gaussian states from a truncation method
• QSlack: A slack-variable approach for variational quantum semi-definite programming
• Multivariate Fidelities
• Schrödinger as a Quantum Programmer: Estimating Entanglement via Steering
• Efficient quantum algorithms for testing symmetries of open quantum systems
• Quantum Computational Complexity and Symmetry
• Quantum distinguishability measures: projectors vs. states maximization
• Quantum Lower Bounds by Sample-to-Query Lifting
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• Riemannian-geometric generalizations of quantum fidelities and Bures-Wasserstein distance