Prospects for Simulating a Qudit Based Model of (1+1)d Scalar QED

Abstract

We present a gauge invariant digitization of (1 + 1)d scalar quantum electrodynamics for an arbitrary spin truncation for qudit-based quantum computers. We provide a construction of the Trotter operator in terms of a universal qudit-gate set. The cost savings of using a qutrit based spin-1 encoding versus a qubit encoding are illustrated. We show that a simple initial state could be simulated on current qutrit based hardware using noisy simulations for two different native gate set.

Lattice Lindblad simulation

“…Theoretical physicists have proposed many candidates for the solution, e.g., the complex Langevin method [1][2][3], the Lefschetz thimble method [4][5][6], and the tensor network approach [7][8][9]. Algorithms on quantum computers are also being discussed [10][11][12][13][14][15][16]. Although these proposals are hopeful, their applications are currently limited to systems with small numbers of degrees of freedom.…”