Simulating Hadronic Physics on NISQ devices using Basis Light-Front Quantization

Abstract

The analogy between quantum chemistry and light-front quantum field theory, first noted by Kenneth G. Wilson, serves as motivation to develop light-front quantum simulation of quantum field theory. We demonstrate how calculations of hadron structure can be performed on Noisy Intermediate-Scale Quantum devices within the Basis Light-Front Quantization framework. We calculate the light-front wave functions of pions using an effective light-front Hamiltonian in a basis representation on a current quantum processor. We use the Variational Quantum Eigensolver to find the ground state energy and wave function, which is subsequently used to calculate pion mass radius, decay constant, elastic form factor, and charge radius.

Variational quantum eigensolvers for sparse Hamiltonians

“…For sparse Hamiltonians, we have demonstrated how VQE can be implemented via a decomposition into one-sparse, self-inverse Hermitian terms. Simulation of second-quantized Hamiltonians in compact representations in quantum chemistry, condensed matter, high energy and nuclear physics are natural candidates for this sparse VQE method [15,28,29,36].…”

“…However, many other quantities are of interest given an ansatz state that is a good approximation to the ground state or other energy eigenstate. For example, [15,28,29] study various properties of composite particles in interacting quantum field theory. Properties such as the invariant mass, mass radius, parton distribution function, and form factor are expectation values of corresponding operators, whereas quantities such as the decay constant are matrix elements between different states [29].…”

“…For example, [15,28,29] study various properties of composite particles in interacting quantum field theory. Properties such as the invariant mass, mass radius, parton distribution function, and form factor are expectation values of corresponding operators, whereas quantities such as the decay constant are matrix elements between different states [29]. We will therefore consider estimation of quantities φ| Ô |ψ for sparse operators Ô between ansatz functions |φ = V |0 and |ψ = U |0 prepared by quantum circuits U and V .…”

Quantum Simulation of Second-Quantized Hamiltonians in Compact Encoding

“…But to reiterate, either of these approaches is efficient; choosing whether or not to exploit a conserved quantity simply changes the details of the scaling. Hence, although our main presentation focused on the planewave momentum basis, we can apply our methods to a wide variety of theories expressed in other bases, in quantum chemistry, condensed matter physics, and quantum field theory, including basis light-front quantization [36][37][38].…”

“…However, the methods we will present extend straightforwardly to cases where the sums within interactions run over quantum numbers other than plane wave momenta, as long as the number of distinct interactions in such a Hamiltonian is constant, and the total number of terms is polynomial in the system parameters (such as momentum cutoffs). These cases include a wide range of theories in quantum chemistry, condensed matter physics, and quantum field theory, including basis light-front quantization [36][37][38].…”