Estimating properties of a quantum state by importance-sampled operator shadows

2023/05/16 by Naixu Guo, Guo, Naixu, Pan, Feng +1
Physics and Astronomy · Computer Science · #Quantum Mechanics and Applications #Quantum Information and Cryptography #Advanced Thermodynamics and Statistical Mechanics

paper · pdf · doi:10.48550/arxiv.2305.09374

Abstract

Measuring properties of quantum systems is a fundamental problem in quantum mechanics. We provide a simple method for estimating the expectation value of observables with an unknown quantum state. The idea is to use a data structure to sample the terms of observables based on the Pauli decomposition proportionally to their importance. We call this technique operator shadow as a shorthand for the procedure of preparing a sketch of an operator to estimate properties. Only when the numbers of observables are small for multiple local observables, the sample complexity of this method is better than the classical shadow technique. However, if we want to estimate the expectation value of a linear combination of local observables, for example the energy of a local Hamiltonian, the sample complexity is better on all parameters. The time complexity to construct the data structure is 2^O(k) for k-local observables, similar to the post-processing time of classical shadows.

Related

• Predicting Features of Quantum Systems from Very Few Measurements
• Measurements of Quantum Hamiltonians with Locally-Biased Classical Shadows
• Real classical shadows
• Operator-aware shadow importance sampling for accurate fidelity estimation
• Expectation value estimation with parametrized quantum circuits