Exploiting Locality in Quantum Computation for Quantum Chemistry

Abstract

Accurate prediction of chemical and material properties from first principles quantum chemistry is a challenging task on traditional computers. Recent developments in quantum computation offer a route towards highly accurate solutions with polynomial cost, however this solution still carries a large overhead. In this perspective, we aim to bring together known results about the locality of physical interactions from quantum chemistry with ideas from quantum computation. We show that the utilization of spatial locality combined with the Bravyi-Kitaev transformation offers an improvement in the scaling of known quantum algorithms for quantum chemistry and provide numerical examples to help illustrate this point. We combine these developments to improve the outlook for the future of quantum chemistry on quantum computers.

Chemical basis of Trotter-Suzuki errors in quantum chemistry simulation

“…Since then, a great deal of work has focused on specific strategies for the quantum simulation of quantum chemistry. While most of these approaches are based on a second quantized representation of the problem making use of both phase estimation and Trotterization [3][4][5][6][7][8][9][10][11][12][13], recently some have proposed alternative schemes such as the quantum variational eigensolver [14], an adiabiatic algorithm [15] and an oracular approach based on a 1-sparse decomposition of the configuration interaction Hamiltonian [16]. In fact, quantum chemistry is such a popular application that toy problems in chemistry have been solved on a variety of experimental quantum information processors which include quantum optical systems [14,17], nuclear magnetic resonance [18,19] and solid-state Nitrogen-vacancy center systems [20].…”

“…Recently, a series of papers [10][11][12][13] has provided improved analytical and empirical bounds on the resources required to simulate classically intractable benchmarks using a quantum computer. While the initial findings in [10] were pessimistic, improvements in both bounds and algorithms introduced in [11] and [12] have reduced these estimates by more than thirteen orders of magnitude for simulations of Ferredoxin.…”

“…While the initial findings in [10] were pessimistic, improvements in both bounds and algorithms introduced in [11] and [12] have reduced these estimates by more than thirteen orders of magnitude for simulations of Ferredoxin. The primary contribution of [13] was to point out that in the limit of large molecules, the use of a local basis can substantially reduce asymptotic complexity of these algorithms. In this paper we build on the findings of [10][11][12][13] to offer new perspectives regarding the scaling of the second quantized, Trotterized, phase estimation algorithm for quantum chemistry.…”

“…The primary contribution of [13] was to point out that in the limit of large molecules, the use of a local basis can substantially reduce asymptotic complexity of these algorithms. In this paper we build on the findings of [10][11][12][13] to offer new perspectives regarding the scaling of the second quantized, Trotterized, phase estimation algorithm for quantum chemistry. In particular, we question a basic assumption implicit in all of these works: that the Trotter error explicitly depends on the number of spin orbitals being simulated.…”

Simulating Hamiltonian Dynamics with a Truncated Taylor Series

“…DOI: 10.1103/PhysRevLett.114.090502 PACS numbers: 03.67.Ac, 89.70.Eg One of the main motivations for quantum computers is their ability to efficiently simulate the dynamics of quantum systems [1], a problem that is apparently hard for classical computers. Since the mid-1990s, many algorithms have been developed to simulate Hamiltonian dynamics on a quantum computer [2][3][4][5][6][7][8][9][10][11][12], with applications to problems such as simulating spin models [13] and quantum chemistry [14][15][16][17]. While it is now well known that quantum computers can efficiently simulate Hamiltonian dynamics, ongoing work has improved the performance and expanded the scope of such simulations.…”