Direct estimation of minimum gate fidelity

Abstract

With the current interest in building quantum computers, there is a strong need for accurate and efficient characterization of the noise in quantum gate implementations. A key measure of the performance of a quantum gate is the minimum gate fidelity, i.e., the fidelity of the gate, minimized over all input states. Conventionally, the minimum fidelity is estimated by first accurately reconstructing the full gate process matrix using the experimental procedure of quantum process tomography (QPT). Then, a numerical minimization is carried out to find the minimum fidelity. QPT is, however, well known to be costly, and it might appear that we can do better, if the goal is only to estimate one single number. In this work, we propose a hybrid numerical-experimental scheme that employs a numerical gradient-free minimization (GFM) and an experimental target-fidelity estimation procedure to directly estimate the minimum fidelity without reconstructing the process matrix. We compare this to an alternative scheme, referred to as QPT fidelity estimation, that does use QPT, but directly employs the minimum gate fidelity as the termination criterion. Both approaches can thus be considered as direct estimation schemes. General theoretical bounds suggest a significant resource savings for the GFM scheme over QPT fidelity estimation; numerical simulations for specific classes of noise, however, show that both schemes have similar performance, reminding us of the need for caution when using general bounds for specific examples. The GFM scheme, however, presents potential for future improvements in resource cost, with the development of even more efficient GFM algorithms.

References in corpus (18)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Randomized Benchmarking of Quantum Gates
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Unknown Quantum States and Operations, a Bayesian View
• Robust randomized benchmarking of quantum processes
• The CMA Evolution Strategy: A Tutorial
• Benchmarking an 11-qubit quantum computer
• Direct Fidelity Estimation from Few Pauli Measurements
• Practical characterization of quantum devices without tomography
• Symmetrised Characterisation of Noisy Quantum Processes
• Minimal qubit tomography
• Sample-optimal tomography of quantum states
• Superfast maximum likelihood reconstruction for quantum tomography
• A quantum-classical cloud platform optimized for variational hybrid algorithms
• Random Quantum Operations
• Quantum process tomography via completely positive and trace-preserving projection
• User-specified random sampling of quantum channels and its applications

Cited by in corpus (7)

• Query-optimal estimation of unitary channels in diamond distance
• A Practical Introduction to Benchmarking and Characterization of Quantum Computers
• Benchmarking quantum gates and circuits
• Variational certification of quantum devices
• Augmented fidelities for single qubit gates
• Benchmarking quantum tomography completeness and fidelity with machine learning
• Uncorrelated problem-specific samples of quantum states from zero-mean Wishart distributions