Minimal qubit representations of Hamiltonians via conserved charges

TL;DR

This paper introduces a universal, efficient method to reduce qubit requirements for simulating Hamiltonians by removing irrelevant qubits and exploiting conserved charges, thereby simplifying complex quantum systems.

Contribution

The authors present a systematic, classically efficient approach to minimize qubit representations of Hamiltonians using symmetry and conservation laws, applicable to various models.

Findings

Successfully simplified chemical molecules and lattice gauge theories

Reduced qubit counts in Hubbard and Kitaev models

Demonstrated efficiency and optimality of the method

Abstract

In the last years, we have been witnessing a tremendous push to demonstrate that quantum computers can solve classically intractable problems. This effort, initially focused on the hardware, progressively included the simplification of the models to be simulated. We consider Hamiltonians written in terms of Pauli operators and systematically cut all qubits that are not essential to simulate the system. Our approach is universally applicable and lowers the complexity by first ensuring that the largest possible portion of the Hilbert space becomes irrelevant, and then by finding and exploiting all conserved charges of the system, i.e., symmetries that can be expressed as Pauli operators. Remarkably, both processes are classically efficient and optimal. To showcase our algorithm, we simplify chemical molecules, lattice gauge theories, the Hubbard and the Kitaev models.