Basic Energy Sciences Roundtable: Opportunities for Quantum Computing in Chemical and Materials Sciences

Moore, Joel E.; Aspuru‐Guzik, Alán; Bauer, Bela; Coppersmith, Sue; Jong, Wibe De; Devereaux, T. P.; Fernández-Serra, Mariví; Galli, Giulia; Harrison, Robert J.; Love, Peter J.; Maier, Thomas; Mezzacapo, Antonio; McClean, Jarrod R.; Monroe, C.; Preskill, John; Scuseria, Gus; Whaley, Birgitta; Whitfield, James D.; Yao, Norman Y.; Zgid, Dominika; Garrett, Bruce C.; Horton, Linda; Murphy, Jim; Davenport, J. M.; Graf, Matthias J.; Krause, Jeff; Maracas, G. N.; Russell, Tom; Susut-Bennett, Ceren; Runkles, Katie; Wyatt, Brenda; Counce, Deborah; Jones, Kathy

doi:10.2172/1616253

Cited by 1 publication

(1 citation statement)

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“…A decade later the first general quantum algorithms appeared [2][3][4][5][6], with applications to quantum chemistry [7], condensed matter [8], and high energy physics [9]. Quantum simulation is now recognized as a significant future application of quantum computation [10][11][12], especially in the context of near-term devices. Quantum algorithms for quantum simulation have improved over the last decade [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Quantum Simulation of Quantum Field Theory in the Light-Front Formulation

Kreshchuk,

Kirby,

Goldstein

et al. 2020

Preprint

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We develop quantum simulation algorithms based on the light-front formulation of relativistic quantum field theories. We analyze a simple theory in 1 + 1D and show how to compute the analogues of parton distribution functions of composite particles in this theory. Upon quantizing the system in light-front coordinates, the Hamiltonian becomes block diagonal. Each block approximates the Fock space with a certain harmonic resolution K, where the light-front momentum is discretized in K steps. The lower bound on the number of qubits required is O( √ K), and we give a complete description of the algorithm in a mapping that requires O( √ K) qubits. The cost of simulation of time evolution within a block of fixed K is O(tK 4 ) gates. The cost of time-dependent simulation of adiabatic evolution for time T along a Hamiltonian path with max norm bounded by final harmonic resolution K is O(T K 4 ) gates. In higher dimensions, the qubit requirements scale as O(K). This is an advantage of the light-front formulation; in equal-time the qubit count will increase as the product of the momentum cutoffs over all dimensions. We provide qubit estimates for QCD in 3 + 1D, and discuss measurements of form-factors and decay constants.

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