Qubit encodings for lattices of dipolar planar rotors

TL;DR

This paper compares two qubit encoding schemes for simulating planar rotor lattice Hamiltonians on near-term quantum devices, analyzing their implementation and resource requirements for quantum simulations.

Contribution

It introduces and evaluates two novel qubit encoding methods for planar rotor lattices, including a binary decomposition and a unary embedding approach.

Findings

Binary decomposition encoding is effective for small chains.

Unary embedding encoding allows for larger Hilbert space representation.

Quantum phase estimation resources are analyzed for near-term device simulation.

Abstract

Near term quantum devices have recently garnered significant interest as promising candidates for investigating difficult-to-probe regimes in many-body physics. To this end, various qubit encoding schemes targeting second quantized Hamiltonians have been proposed and optimized. In this work, we investigate two qubit representations of the planar rotor lattice Hamiltonian. The first representation is realized by decomposing the rotor Hamiltonian projectors in binary and mapping them to spin-1/2 projectors. The second approach relies on embedding the planar rotor lattice Hilbert space in a larger space and recovering the relevant qubit encoded system as a quotient space projecting down to the physical degrees of freedom. This is typically called the unary mapping and is used for bosonic systems. We establish the veracity of the two encoding approaches using sparse diagonalization on small chains and discuss quantum phase estimation resource requirements to simulate small planar rotor lattices on near-term quantum devices.