Lowering qubit requirements for quantum simulations of fermionic systems

TL;DR

This paper introduces methods to reduce qubit requirements for quantum simulations of fermionic systems by trading qubit count for circuit complexity, leveraging classical codes and symmetry considerations.

Contribution

It develops a framework connecting classical error-correcting codes to fermionic-to-qubit mappings, enabling qubit savings at the cost of additional gates.

Findings

Significant qubit savings achieved with non-linear classical codes.

New mappings that balance qubit reduction and gate complexity.

Potential for further savings using symmetries and multi-controlled gates.

Abstract

The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in chemistry and physics, quantum simulation is one of the great promises of the coming age of quantum computers. One challenge in realizing simulations on near-term quantum devices is the large number of qubits required by such mappings. In this work, we develop methods that allow us to trade-off qubit requirements against the complexity of the resulting quantum circuit. We first show that any classical code used to map the state of a fermionic Fock space to qubits gives rise to a mapping of fermionic models to quantum gates. As an illustrative example, we present a mapping based on a non-linear classical error correcting code, which leads to significant qubit savings albeit at the expense of additional quantum gates. We proceed to use this framework to present a number of simpler mappings that lead to qubit savings with only a very modest increase in gate difficulty. We discuss the role of symmetries such as particle conservation, and savings that could be obtained if an experimental platform could easily realize multi-controlled gates.