Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 50, Issue 30, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/aa77b8
Keywords
quantum computing; Hamiltonian simulation; quantum algorithms; many-body physics
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Funding
- Army Research Office [W911NF-15-1-0256]
- Office of Naval Research [N00014-16-1-2008]
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We present a quantum algorithm for simulating the dynamics of a first-quantized Hamiltonian in real space based on the truncated Taylor series algorithm. We avoid the possibility of singularities by applying various cutoffs to the system and using a high-order finite difference approximation to the kinetic energy operator. We find that our algorithm can simulate. interacting particles using a number of calculations of the pairwise interactions that scales, for a fixed spatial grid spacing, as < (O)over tilde>(eta(2)), versus the < (O)over tilde>(eta(5)) time required by previous methods (assuming the number of orbitals is proportional to.), and scales super-polynomially better with the error tolerance than algorithms based on the Lie-Trotter-Suzuki product formula. Finally, we analyze discretization errors that arise from the spatial grid and show that under some circumstances these errors can remove the exponential speedups typically afforded by quantum simulation.
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