Quantum Computation and Visualization of Hamiltonians Using Discrete Quantum Mechanics and IBM QISKit

Conference · Mon Aug 06 04:00:00 EDT 2018

DOI:https://doi.org/10.1109/NYSDS.2018.8538959· OSTI ID:1619265

Miceli, Raffaele; McGuigan, Michael

Quantum computers have the potential to transform the ways in which we tackle some important problems. The efforts by companies like Google, IBM and Microsoft to construct quantum computers have been making headlines for years. Equally important is the challenge of translating problems into a state that can be fed to these machines. Because quantum computers are in essence controllable quantum systems, the problems that most naturally map to them are those of quantum mechanics. Quantum chemistry has seen particular success in the form of the variational quantum eigensolver (VQE) algorithm, which is used to determine the ground state energy of molecular systems. The goal of our work has been to use the matrix formulation of quantum mechanics to translate other systems so that they can be run through this same algorithm. We describe two ways of accomplishing this using a position basis approach and a Gaussian basis approach. We use this translation to compute finite temperature quantities such as the average energy as a function of temperature. We do this by constructing a 0+1- dimensional thermal field theory, constructing a thermal double of the system and using tensor products to construct operators in the system coupled to a heat bath. We also discuss how to include a chemical potential in the quantum computations. We then connect the 0+1 formalism to gauge theory by using an effective matrix model description used in nuclear theory. We study effective potentials for components of the gauge field and use the VQE algorithm to calculate the ground state energies. We also visualize the wave functions from the eigensolver and make comparisons to theoretical results obtained with continuous operators.

• Research Organization: Brookhaven National Laboratory (BNL), Upton, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (SC-21); Laboratory-Directed Research and Development (LDRD)
• DOE Contract Number: SC0012704
• OSTI ID: 1619265
• Report Number(s): BNL-209527-2018-PUCP
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Hamiltonians