Even More Efficient Quantum Computations of Chemistry Through Tensor Hypercontraction

We describe quantum circuits with only O ~ ( N ) Toffoli complexity that block encode the spectra of quantum chemistry Hamiltonians in a basis of N arbitrary (e.g., molecular) orbitals. With O ( λ/ϵ ) repetitions of these circuits one can use phase estimation to sample in the molecular eigenbasis, w...

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Vydáno v:	PRX quantum Ročník 2; číslo 3; s. 030305
Hlavní autoři:	Lee, Joonho, Berry, Dominic W., Gidney, Craig, Huggins, William J., McClean, Jarrod R., Wiebe, Nathan, Babbush, Ryan
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	United States American Physical Society (APS) 01.07.2021 American Physical Society
Témata:	CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS electronic structure electronic structure calculations quantum algorithms quantum computation quantum simulation strongly correlated systems
ISSN:	2691-3399, 2691-3399
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Popis
Shrnutí:	We describe quantum circuits with only O ~ ( N ) Toffoli complexity that block encode the spectra of quantum chemistry Hamiltonians in a basis of N arbitrary (e.g., molecular) orbitals. With O ( λ/ϵ ) repetitions of these circuits one can use phase estimation to sample in the molecular eigenbasis, where λ is the 1-norm of Hamiltonian coefficients and ϵ is the target precision. This is the lowest complexity shown for quantum computations of chemistry within an arbitrary basis. Furthermore, up to logarithmic factors, this matches the scaling of the most efficient prior block encodings that can work only with orthogonal-basis functions diagonalizing the Coloumb operator (e.g., the plane-wave dual basis). Our key insight is to factorize the Hamiltonian using a method known as tensor hypercontraction (THC) and then to transform the Coulomb operator into an isospectral diagonal form with a nonorthogonal basis defined by the THC factors. We then use qubitization to simulate the nonorthogonal THC Hamiltonian, in a fashion that avoids most complications of the nonorthogonal basis. We also reanalyze and reduce the cost of several of the best prior algorithms for these simulations in order to facilitate a clear comparison to the present work. In addition to having lower asymptotic scaling space-time volume, compilation of our algorithm for challenging finite-sized molecules such as FeMoCo reveals that our method requires the least fault-tolerant resources of any known approach. By laying out and optimizing the surface-code resources required of our approach we show that FeMoCo can be simulated using about four million physical qubits and under 4 days of runtime, assuming 1- μ s cycle times and physical gate-error rates no worse than 0.1 % .
Bibliografie:	Australian Research Council (ARC) USDOE Laboratory Directed Research and Development (LDRD) Program PNNL-SA-157861 AC05-76RL01830; DP190102633; DP21010136; SC0012704
ISSN:	2691-3399 2691-3399
DOI:	10.1103/PRXQuantum.2.030305