Simulating lattice quantum electrodynamics on a quantum computer
Angus Kan, Yunseong Nam
Abstract
Abstract U(1) lattice gauge theories (LGTs) offer a way to simulate quantum electrodynamics, one of the three forces unified by the Standard Model of particles physics. Here we provide complete, quantum-gate-by-quantum-gate algorithms to simulate U(1) LGTs on a fault-tolerant quantum computer. We further perform rigorous error analysis in order to derive concrete estimates of the quantum computational resources required for an accurate simulation of U(1) LGTs using a second-order product formula. We show that U(1) LGTs in any spatial dimension can be simulated using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover> <mml:mi>O</mml:mi> <mml:mo stretchy="false">˜</mml:mo> </mml:mover> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mrow> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:msup> <mml:msup> <mml:mi>N</mml:mi> <mml:mrow> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:msup> <mml:mi mathvariant="normal">Λ</mml:mi> <mml:msup> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> non-Clifford T gates, where T is the simulation time, N is the number of lattice sites, Λ is the truncation parameter for the bosonic gauge fields, and ε is the simulation error. This work paves the way towards fault-tolerant quantum simulations of physical models closely related to the Standard Model of particle physics.