Lattice QED Algorithm Advances Real-Time Simulations of Quantum Electrodynamics

Research demonstrates a real-time simulation algorithm for Quantum Electrodynamics (QED) on a lattice, utilising a field basis in position space. Equivalence between the Coulomb and temporal gauge Hamiltonians is established for physical states, ensuring unphysical field suppression. Computational cost, measured in qubit requirements and gate depth, scales polynomially with system parameters.

Quantum electrodynamics, the highly successful theory describing the interaction of light and matter, presents significant computational challenges when modelling dynamic, real-time phenomena. Traditional approaches often struggle with the complexities arising from gauge degrees of freedom, necessitating intricate constraint mechanisms. New research, detailed in a paper by Xiaojun Yao, and colleagues, addresses this issue by presenting an algorithm for simulating quantum electrodynamics in the Coulomb gauge, representing gauge fields directly in position space. The work, entitled ‘On Quantum Simulation of QED in Coulomb Gauge’, demonstrates equivalence to a temporal gauge Hamiltonian and proves a polynomial scaling of qubit cost and gate depth with system size, offering a potentially more efficient pathway for modelling complex quantum systems. The research originates from the InQubator for Quantum Simulation, within the Department of Physics at the University of Washington.

Quantum computation is rapidly enhancing the capacity to simulate intricate physical systems, notably lattice gauge theories, and thereby opening new possibilities for investigating fundamental particle interactions. Researchers are actively devising algorithms and techniques to map these theories onto quantum circuits, with a primary focus on Quantum Chromodynamics (QCD), the theory describing the strong force, and increasingly, Quantum Electrodynamics (QED), the quantum theory of electromagnetism.

Current efforts concentrate on calculating observables, measurable physical quantities, pertinent to understanding the strong force and the structure of matter. These include shear viscosity, a measure of a fluid’s resistance to flow, energy correlators, which describe the relationship between energy fluctuations at different points in space-time, and entanglement properties, quantifying the quantum correlation between particles. Simulations of parton distributions, describing the composition of hadrons like protons and neutrons, and emergent hydrodynamic modes, collective behaviours arising in strongly interacting systems, are also central to this work. This necessitates continuous development of error mitigation techniques, methods to reduce the impact of errors inherent in quantum computers, and novel quantum algorithms, procedures designed to solve specific computational problems on quantum hardware. Lattice theory, a discrete approximation to the continuous quantum field theory, forms the basis of these simulations, although future work must address the continuum limit, refining the approximation, and ultraviolet completion of QED, a process of resolving issues at very high energies.

A crucial aspect of this research involves utilising algorithms that employ techniques such as Trotterization, a method for approximating the time evolution operator, essential for simulating the dynamics of quantum systems. Initial investigations frequently target SU(2) gauge theory, a simplified model, before addressing the greater complexity of SU(3) QCD, which more accurately reflects the observed strong force. Furthermore, researchers are exploring different basis choices, such as momentum and coordinate representations, to optimise computational efficiency and accuracy, tailoring the mathematical framework to the specific quantum hardware and algorithms employed.

Recent progress includes demonstrating a scalable algorithm for simulating real-time dynamics in lattice gauge theories, a significant challenge due to the inherent complexity of time evolution, and establishing a connection between the spectral properties of the Hamiltonian, the operator representing the total energy of the system, and the transport coefficients, parameters describing the flow of energy and momentum, of the corresponding quantum field theory. These advancements suggest the potential for utilising quantum computers to resolve long-standing problems in high-energy physics and nuclear physics, offering a computational approach to questions previously inaccessible to classical methods.