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• W3189190097 abstract "The Hamiltonian operator plays a central role in quantum theory being a generator of unitary quantum dynamics. Its expectation value describes the energy of a quantum system. Typically being a non-unitary operator, the action of the Hamiltonian is either encoded using complex ancilla-based circuits, or implemented effectively as a sum of Pauli string terms. Here, we show how to approximate the Hamiltonian operator as a sum of propagators using a differential representation. The proposed approach, named Hamiltonian operator approximation (HOA), is designed to benefit analog quantum simulators, where one has direct access to simulation of quantum dynamics, but measuring separate circuits is not possible. We describe how to use this strategy in the hybrid quantum-classical workflow for performing energy measurements. Benchmarking the measurement scheme, we discuss the relevance of the discretization step size, stencil order, number of shots, and noise. We also use HOA to prepare ground states of complex material science models with direct iteration and quantum filter diagonalization, finding the lowest energy for the 12-qubit Hamiltonian of hydrogen chain H$_6$ with $10^{-5}$ Hartree precision using $11$ time-evolved reference states. The approach is compared to the variational quantum eigensolver, proving HOA beneficial for systems at increasing size corresponding to noisy large scale quantum devices. We find that for Heisenberg model with twelve or more spins our approach may outperform variational methods, both in terms of the gate depth and the total number of measurements." @default.
• W3189190097 created "2021-08-16" @default.
• W3189190097 creator A5022170081 @default.
• W3189190097 creator A5071149447 @default.
• W3189190097 date "2021-08-02" @default.
• W3189190097 modified "2023-09-23" @default.
• W3189190097 title "Hamiltonian Operator Approximation for Energy Measurement and Ground-State Preparation" @default.
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• W3189190097 doi "https://doi.org/10.1103/prxquantum.2.030318" @default.
• W3189190097 hasPublicationYear "2021" @default.
• W3189190097 type Work @default.
• W3189190097 sameAs 3189190097 @default.

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