Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use a smaller, fixed number of qubits at the cost of systematic errors. We systematize this approach by deriving the single plaquette action through matching the continuous group action to that of a discrete one via group character expansions modulo the field fluctuation contributions. We accompany this scheme by simulations of pure gauge over the largest discrete crystal-like subgroup of $SU(3)$ up to the fifth order in the coupling constant.Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use a smaller, fixed number of qubits at the cost of systematic errors. We systematize this approach by deriving the single plaquette action through matching the continuous group action to that of a discrete one via group character expansions modulo the field fluctuation contributions. We accompany this scheme by simulations of pure gauge over the largest discrete crystal-like subgroup of $SU(3)$ up to the fifth order in the coupling constant.

arXiv:2203.02330Physical review. D/Physical review. D.Jun 8, 202318 citations

Qubit-based Model for Simulation of Discrete Quantum Systems

Steven Peil

Bulletin of the American Physical SocietyMay 21, 20090 citations

Semiclassical dynamics of nonadiabatic transitions in discrete-state systems using spin coherent-state path integrals

A. Lücke, Chi H. Mak, Jürgen T. Stockburger

We present a semiclassical method for simulating the dynamics of nonadiabatic transitions in a discrete-state quantum system coupled to a bath of explicit continuous coordinates. This method employs a coherent-state formulation of the path integrals for the discrete system whose dynamics is described by spin operators. This spin coherent-state formulation allows the discrete system to be mapped onto a continuous coordinate. Stationary approximations of the resulting coherent-state path integrals of the system plus bath lead to quasiclassical equations of motion which can be solved numerically by direct integration. This algorithm reduces the problem to a number of simple classical trajectory calculations and does not require calculating any fluctuation determinants.We present a semiclassical method for simulating the dynamics of nonadiabatic transitions in a discrete-state quantum system coupled to a bath of explicit continuous coordinates. This method employs a coherent-state formulation of the path integrals for the discrete system whose dynamics is described by spin operators. This spin coherent-state formulation allows the discrete system to be mapped onto a continuous coordinate. Stationary approximations of the resulting coherent-state path integrals of the system plus bath lead to quasiclassical equations of motion which can be solved numerically by direct integration. This algorithm reduces the problem to a number of simple classical trajectory calculations and does not require calculating any fluctuation determinants.

The Journal of Chemical PhysicsDec 22, 199913 citations

Continuous quantum systems in a fluctuating environment

Kamel Ourabah

The European Physical Journal PlusJan 28, 20200 citations

SU(3)

up to the fifth order in the coupling constant.