Quantum Simulation of Electronic Structure with Linear Depth and Connectivity

As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the fermionic swap network, we can simulate a Trotter step of the elect...

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Published inPhysical review letters Vol. 120; no. 11; p. 110501
Main Authors Kivlichan, Ian D, McClean, Jarrod, Wiebe, Nathan, Gidney, Craig, Aspuru-Guzik, Alán, Chan, Garnet Kin-Lic, Babbush, Ryan
Format Journal Article
LanguageEnglish
Published United States 16.03.2018
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Summary:As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the fermionic swap network, we can simulate a Trotter step of the electronic structure Hamiltonian in exactly N depth and with N^{2}/2 two-qubit entangling gates, and prepare arbitrary Slater determinants in at most N/2 depth, all assuming only a minimal, linearly connected architecture. We conjecture that no explicit Trotter step of the electronic structure Hamiltonian is possible with fewer entangling gates, even with arbitrary connectivities. These results represent significant practical improvements on the cost of most Trotter-based algorithms for both variational and phase-estimation-based simulation of quantum chemistry.
ISSN:1079-7114
DOI:10.1103/PhysRevLett.120.110501