Abstract
We present a quantum algorithm for simulation of quantum field theory in the light-front formulation and demonstrate how existing quantum devices can be used to study the structure of bound states in relativistic nuclear physics. Specifically, we apply the Variational Quantum Eigensolver algorithm to find the ground state of the light-front Hamiltonian obtained within the Basis Light-Front Quantization (BLFQ) framework. The BLFQ formulation of quantum field theory allows one to readily import techniques developed for digital quantum simulation of quantum chemistry. This provides a method that can be scaled up to simulation of full, relativistic quantum field theories in the quantum advantage regime. As an illustration, we calculate the mass, mass radius, decay constant, electromagnetic form factor, and charge radius of the pion on the IBM Vigo chip. This is the first time that the light-front approach to quantum field theory has been used to enable simulation of a real physical system on a quantum computer.
Highlights
We present a quantum algorithm for simulation of quantum field theory in the light-front formulation and demonstrate how existing quantum devices can be used to study the structure of bound states in relativistic nuclear physics
To simulate the Basis Light-Front Quantization (BLFQ) Hamiltonian described above, we will use the variational quantum eigensolver (VQE) algorithm, which can be implemented on existing quantum computers
Written as an operator acting on valence sector Fock states, the Hamiltonian (4) is a fourth-order polynomial in quark and antiquark creation and annihilation operators. It resembles the general form of Hamiltonians in quantum chemistry, H = ∑i,j hij ai† a j + ∑i,j,k,l hijkl ai† a†j ak al, where a† is a fermionic operator, which in our case could create either a quark or antiquark. This remains true as one extends the problem to multi-particle Fock states, and enables us to use methods developed for digital quantum simulation of quantum chemistry [4]
Summary
While the Hamiltonian (2) is only designed to act on the meson valence sector wave function (7) to be introduced below, by using the single-particle basis [23], BLFQ allows one to extend the AdS/QCD LFWFs and effective interactions to the multi-particle Fock sectors [23,37,38,39]. This is crucial for quantum-computing applications, since we only expect to attain quantum advantage in the multi-particle regime. The matrix elements of the full Hamiltonian (4) in this representation can be calculated analytically [32]
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