Efficient Quantum Simulation of Electron-Phonon Systems by Variational Basis State Encoder

TL;DR

This paper introduces a variational basis state encoding method for quantum simulation of electron-phonon systems that significantly reduces qubit and gate requirements, enabling practical simulations on near-term quantum hardware.

Contribution

It proposes a novel variational encoding algorithm that reduces qubit and gate scaling to constant levels for certain systems, verified through simulations and hardware experiments.

Findings

One or two qubits per phonon mode suffice for accurate results.

The method reduces resource scaling from linear/logarithmic to constant.

Experimental validation demonstrates practical feasibility.

Abstract

Digital quantum simulation of electron-phonon systems requires truncating infinite phonon levels into $N$ basis states and then encoding them with qubit computational basis. Unary encoding and the more compact binary/Gray encoding are the two most representative encoding schemes, which demand $\mathcal{O}(N)$ and $\mathcal{O}(\log{N})$ qubits as well as $\mathcal{O}(N)$ and $\mathcal{O}(N\log{N})$ quantum gates respectively. In this work, we propose a variational basis state encoding algorithm that reduces the scaling of the number of qubits and quantum gates to both $\mathcal{O}(1)$ for systems obeying the area law of entanglement entropy. The cost for the scaling reduction is a constant amount of additional measurement. The accuracy and efficiency of the approach are verified by both numerical simulation and realistic quantum hardware experiments. In particular, we find using one or two qubits for each phonon mode is sufficient to produce quantitatively correct results across weak and strong coupling regimes. Our approach paves the way for practical quantum simulation of electron-phonon systems on both near-term hardware and error-corrected quantum computers.