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• W3097716063 abstract "We propose a tomographic protocol for estimating any $k$-body reduced density matrix ($k$-RDM) of an $n$-mode fermionic state, a ubiquitous step in near-term quantum algorithms for simulating many-body physics, chemistry, and materials. Our approach extends the framework of classical shadows, a randomized approach to learning a collection of quantum-state properties, to the fermionic setting. Our sampling protocol uses randomized measurement settings generated by a discrete group of fermionic Gaussian unitaries, implementable with linear-depth circuits. We prove that estimating all $k$-RDM elements to additive precision $ϵ$ requires on the order of $(genfrac{}{}{0ex}{}{n}{k}){k}^{3/2}mathrm{log}(n)/{ϵ}^{2}$ repeated state preparations, which is optimal up to the logarithmic factor. Furthermore, numerical calculations show that our protocol offers a substantial improvement in constant overheads for $kensuremath{ge}2$, as compared to prior deterministic strategies. We also adapt our method to particle-number symmetry, wherein the additional circuit depth may be halved at the cost of roughly 2--5 times more repetitions." @default.
• W3097716063 created "2020-11-09" @default.
• W3097716063 creator A5049281132 @default.
• W3097716063 creator A5052764149 @default.
• W3097716063 creator A5085372862 @default.
• W3097716063 date "2021-09-09" @default.
• W3097716063 modified "2023-10-13" @default.
• W3097716063 title "Fermionic Partial Tomography via Classical Shadows" @default.
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• W3097716063 doi "https://doi.org/10.1103/physrevlett.127.110504" @default.
• W3097716063 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/34558940" @default.
• W3097716063 hasPublicationYear "2021" @default.
• W3097716063 type Work @default.
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