Comparison of encoding schemes for quantum computing of $S > 1/2$ spin chains

TL;DR

This paper compares four encoding schemes for quantum computing of higher-spin chains, finding the Dicke mapping most efficient and analyzing how simulation accuracy depends on spin size and time step length.

Contribution

It introduces and evaluates four encoding schemes for higher-spin quantum chains, highlighting the efficiency of the Dicke mapping and the inverse relationship between time step size and spin quantum number.

Findings

Dicke mapping is the most efficient encoding scheme.

The time step length should be inversely proportional to the spin quantum number for consistent accuracy.

Simulations demonstrate the effectiveness of different encodings on a trapped-ion quantum computer.

Abstract

We compare four different encoding schemes for the quantum computing of spin chains with a spin quantum number $S>1/2$: a compact mapping, a direct (or one-hot) mapping, a Dicke mapping, and a qudit mapping. The three different qubit encoding schemes are assessed by conducting Hamiltonian simulation for $1/2 \le S \le 5/2$ using a trapped-ion quantum computer. The qudit mapping is tested by running simulations with a simple noise model. The Dicke mapping, in which the spin states are encoded as superpositions of multi-qubit states, is found to be the most efficient because of the small number of terms in the qubit Hamiltonian. We also investigate the $S$-dependence of the time step length $\Delta\tau$ in the Suzuki-Trotter approximation and find that, in order to obtain the same accuracy for all $S$, $\Delta\tau$ should be inversely proportional to $S$.