Abstract
We present calculations of both the ground- and excited-state energies of spin defects in solids carried out on a quantum computer, using a hybrid classical-quantum protocol. We focus on the negatively charged nitrogen-vacancy center in diamond and on the double vacancy in 4H SiC, which are of interest for the realization of quantum technologies. We employ a recently developed first-principles quantum embedding theory to describe point defects embedded in a periodic crystal and to derive an effective Hamiltonian, which is then transformed to a qubit Hamiltonian by means of a parity transformation. We use the variational quantum eigensolver (VQE) and quantum subspace expansion methods to obtain the ground and excited states of spin qubits, respectively, and we propose a promising strategy for noise mitigation. We show that by combining zero-noise extrapolation techniques and constraints on electron occupation to overcome the unphysical-state problem of the VQE algorithm, one can obtain reasonably accurate results on near-term-noisy architectures for ground- and excited-state properties of spin defects.1 MoreReceived 7 December 2021Revised 27 January 2022Accepted 8 February 2022DOI:https://doi.org/10.1103/PRXQuantum.3.010339Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum algorithmsQuantum computationQuantum simulationPhysical SystemsNitrogen vacancy centers in diamondQuantum InformationCondensed Matter, Materials & Applied Physics
Highlights
Quantum simulations of the physical and chemical properties of molecules and solids [1–5] are crucial to gain insight into a wide range of complex problems, for example, catalytic reactions [6–8] and the search for optimal materials for sustainable energy sources [9] and quantum technologies [10,11]
The effective Hamiltonian is diagonalized with the FCI using the PySCF code [108] on a classical hardware and the eigenvalues obtained in this way are considered as reference results for our calculations on a quantum computer
ALinear extrapolation of both diagonal and off-diagonal elements of the quantum subspace expansion (QSE) matrix [Eq (8) in the text]. bQuadratic extrapolation of the diagonal, and linear of the off-diagonal, elements of the QSE matrix. cExponential extrapolation of the diagonal, and linear of the off-diagonal elements, of the QSE matrix. dThe energy of the degenerate states is computed as the average of the two energies obtained on quantum hardware. eThe energy gap between two states, which should be degenerate, due to the presence of noise
Summary
Quantum simulations of the physical and chemical properties of molecules and solids [1–5] are crucial to gain insight into a wide range of complex problems, for example, catalytic reactions [6–8] and the search for optimal materials for sustainable energy sources [9] and quantum technologies [10,11]. One of the essential ingredients of quantum simulations is the solution of the electronic structure problem for molecules and solids, namely the timeindependent Schrödinger equation of interacting electrons in the field of atomic nuclei. Such a solution provides the basis for the evaluation of numerous ground- and excitedstate properties of matter.
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