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arXiv:2201.00805

Superconformal Quantum Mechanics on a Quantum Computer

Feng, Yuan, McGuigan, Michael, Tristen White

Published Jan 3, 2022• 0 citations
arXivHTMLPDF

Abstract

We investigate superconformal quantum mechanics (SCQM) on a quantum computer. We study the ground state of the mass deformed SCQM on a quantum computed using the Variational Quantum Eigensolver (VQE) using a one boson and one boson - one fermion Hilbert space with and without noise and compare the accuracy of the results. We study the Feynman path integral for SCQM using the Evolution of Hamiltonian (EOH) algorithm on the quantum computer using the Trotter-Suzuki approximation and compare with the exact result. We consider an N boson and N fermion version of SCQM given be the Supersymmetric Calogero-Moser-Sutherland (SCMS) model. We compare the ground state of SCMS theory obtained using the VQE computation with the exact solution. Finally we discuss the implications of the the numerical simulation of SCQM on a quantum computer for the simulation of quantum gravity in light of the Anti-de Sitter/Superconformal field theory (AdS/CFT) correspondence.

DOI
10.48550/arxiv.2201.00805

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Cosmology is in an era of rapid discovery especially in areas related to dark energy, dark matter and inflation. Quantum cosmology treats the cosmology quantum mechanically and is important when quantum effects need to be accounted for, especially in the very early Universe. Quantum computing is an emerging new method of computing which excels in simulating quantum systems. Quantum computing may have some advantages when simulating quantum cosmology, especially because the Euclidean action of gravity is unbounded from below, making the implementation of Monte Carlo simulation problematic. In this paper we present several examples of the application of quantum computing to cosmology. These include a dark energy model that is related to Kaluza-Klein theory, dark matter models where the dark sector is described by a self interacting gauge field or a conformal scalar field and an inflationary model with a slow roll potential. We implement quantum computations in the IBM QISKit software framework and show how to apply the Variational Quantum Eigensolver (VQE) and Evolution of Hamiltonian (EOH) algorithms to solve the Wheeler-DeWitt equation that can be used to describe the cosmology in the mini-superspace approximation. We find excellent agreement with classical computing results and describe the accuracy of the different quantum algorithms. Finally we discuss how these methods can be scaled to larger problems going beyond the mini-superspace approximation where the quantum computer may exceed the performance of classical computation.
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In this paper we discuss the Morse potential on a quantum computer. The Morse potential is useful to describe diatomic molecules and has a finite number of bound states which can be measured through spectroscopy. It is also a example of an exactly soluble potential using supersymmetric quantum mechanics. Using the the supersymmetric quantum mechanics formalism one can derive a heirachy of Hamiltonians such that the ground state of the next rung on the heirarchy yeids the first excited state of the hamiltonian below it. Using this method one can determine all the states of the Morse potential by calculating all the ground states of the sequence of Hamiltonians in the heirarchy. We use the IBM QISKit software together with the Variational Quantum Eiegensolver (VQE) algorithm to calculate the ground state and first excited state energy of the Morse potential and find agreement with the exact expression for the bound state energies of the Morse Potential. We analyze different optimizers to study the numerical effect on the calculations. Finally we perform quantum computations for diatomic and triatomic molecules to illustrate the application of these techniques on near term quantum computers and find excellent agreement with experimental data.
In this paper we discuss the computation of Casimir energy on a quantum computer. The Casimir energy is an ideal quantity to calculate on a quantum computer as near term hybrid classical quantum algorithms exist to calculate the ground state energy and the Casimir energy gives physical implications for this quantity in a variety of settings. Depending on boundary conditions and whether the field is bosonic or fermionic we illustrate how the Casimir energy calculation can be set up on a quantum computer and calculated using the Variational Quantum Eigensolver algorithm with IBM QISKit. We compare the results based on a lattice regularization with a finite number of qubits with the continuum calculation for free boson fields, free fermion fields and chiral fermion fields. We use a regularization method introduced by Bergman and Thorn to compute the Casimir energy of a chiral fermion. We show how the accuracy of the calculation varies with the number of qubits. We show how the number of Pauli terms which are used to represent the Hamiltonian on a quantum computer scales with the number of qubits. We discuss the application of the Casimir calculations on quantum computers to cosmology, nanomaterials, string models, Kaluza Klein models and dark energy.