Optimal Particle-Conserved Linear Encoding for Practical Fermionic Simulation

TL;DR

This paper introduces an optimal fermionic encoding scheme that reduces quantum resource requirements for simulating fermionic systems, with scalable complexity bounds and practical decoding methods tested on molecular simulations.

Contribution

It develops a new fermionic encoding framework with optimal resource bounds and proposes the Fermionic Expectation Decoder for scalable quantum simulations.

Findings

Achieved $ ext{O}(N ext{log} M)$ qubit encoding bounds.

Demonstrated the decoder's effectiveness on molecular energy calculations.

Validated the approach with variational quantum eigensolver experiments.

Abstract

Number-conserved subspace encoding reduces resources needed for quantum simulations, but scalable complexity trade-off bounds for $M$ modes and $N$ particles with $\mathcal{O}(N\log M)$ qubits have remained unknown. We study qubit-gate-measurement trade-offs through the lens of classical/quantum error correction complexity, and develop a framework of fermionic gate and measurement complexity based on encoder and decoder complexities appeared in error correction framework. We demonstrate optimal encoding with random classical parity check code and propose the Fermionic Expectation Decoder for scalable probability decoding in $\mathcal{O}(M^4)$ bases. The protocol is tested with variational quantum eigensolver on LiH in the STO-3G and 6-31G basis, and $\text{H}_2$ potential energy curve in the 6-311G* basis.