Simulating Effective QED on Quantum Computers

Abstract

In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly correlated electronic systems. To date, most treatments have ignored the question of whether relativistic effects, which are described most generally by quantum electrodynamics (QED), can also be simulated on a quantum computer in polynomial time. Here we show that effective QED, which is equivalent to QED to second order in perturbation theory, can be simulated in polynomial time under reasonable assumptions while properly treating all four components of the wavefunction of the fermionic field. In particular, we provide a detailed analysis of such simulations in position and momentum basis using Trotter-Suzuki formulas. We find that the number of T-gates needed to perform such simulations on a 3D lattice of ns sites scales at worst as O(ns3/ϵ)1+o(1) in the thermodynamic limit for position basis simulations and O(ns4+2/3/ϵ)1+o(1) in momentum basis. We also find that qubitization scales slightly better with a worst case scaling of O~(ns2+2/3/ϵ) for lattice eQED and complications in the prepare circuit leads to a slightly worse scaling in momentum basis of O~(ns5+2/3/ϵ). We further provide concrete gate counts for simulating a relativistic version of the uniform electron gas that show challenging problems can be simulated using fewer than 1013 non-Clifford operations and also provide a detailed discussion of how to prepare multi-reference configuration interaction states in effective QED which can provide a reasonable initial guess for the ground state. Finally, we estimate the planewave cutoffs needed to accurately simulate heavy elements such as gold.

Quantum information scrambling: from holography to quantum simulators

“…Apart from the SYK model, there are some recent works on Hamiltonian simulation of certain gauge theories, which are also based on Trotterization of the Hamiltonian [215][216][217][218][219][220][221][222][223][224]. It is possible to construct the ground state for these systems, and measure some observables, via a mapping to a qubit system [215].…”

Snowmass White Paper: Quantum Computing Systems and Software for High-energy Physics Research

“…In most of these applications, the limited number of qubits and gate fidelities available in QC hardware implementations represent bottlenecks for a proper comparison with classical algorithms and, therefore, any assessment of quantum advantage. On the other hand, the application of QCD with the lattice gauge model [37,38] represents an exciting challenge on the real-device implementation that requires a novel design following quantum device limitations, state-of-the-art classical simula-tors handling a decent number of qubits to benchmark the quantum computation algorithms with existing classical approaches, and the exploration of gravity/QFT duality [26].…”

Medium induced jet broadening in a quantum computer

“…Results at finite (blue triangles) and infinite (red circles) jet energy are compared to the analytical result given in Eq. (19). Parameters used in the simulations: L ⊥ = 4.8 GeV −1 , mg = 0.8 GeV, and N ⊥ = 16.…”

“…Some of these novel proposals to use quantum technologies have ranged from the simulation of scalar [2][3][4][5][6][7][8][9][10][11], fermionic [12][13][14] and gauge field theories [15][16][17][18][19][20][21][22][23][24][25][26][27] to thermal systems [28] and the thermalization of nonequilibrium systems [29][30][31]. Beside field theory based simulations, they have also been applied to specific topics such as nuclear structure [32][33][34][35][36][37], neutrino oscillation [38] and string theory [39].…”