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

• URL: http://arxiv.org/abs/2305.09374v2
• Date: Fri, 22 Mar 2024 07:20:38 GMT
• Title: Estimating properties of a quantum state by importance-sampled operator shadows
• Authors: Naixu Guo, Feng Pan, Patrick Rebentrost,
• Abstract summary: We provide a simple method for estimating the expectation value of observables with an unknown quantum state. The time complexity to construct the data structure is $2O(k)$ for $k$-local observables, similar to the post-processing time of classical shadows.
• Score: 1.3854792306663213
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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