Efficient and Noise-Resilient Molecular Quantum Simulation with the Generalized Superfast Encoding

TL;DR

This paper introduces an advanced Fermion-to-qubit encoding method, the Generalized Superfast Encoding (GSE), which improves accuracy and hardware efficiency for molecular quantum simulations, especially under realistic noise conditions.

Contribution

It develops a suite of techniques to enhance GSE, making it more compact, noise-resilient, and suitable for general molecular Hamiltonians, outperforming prior encodings.

Findings

GSE outperforms previous encodings in accuracy and efficiency.

Significant energy estimation improvements under hardware noise.

Twofold reduction in RMSE for orbital rotations on IBM hardware.

Abstract

Simulating molecular systems on quantum computers requires efficient mappings from Fermionic operators to qubit operators. Traditional mappings such as Jordan-Wigner or Bravyi-Kitaev often produce high-weight Pauli terms, increasing circuit depth and measurement complexity. Although several local qubit mappings have been proposed to address this challenge, most are specialized for structured models like the Hubbard Hamiltonian and perform poorly for realistic chemical systems with dense two-body interactions. In this work, we utilize a suite of techniques to construct compact and noise-resilient Fermion-to-qubit mappings suitable for general molecular Hamiltonians. Building on the Generalized Superfast Encoding (GSE) and other similar works, we demonstrate that it outperforms prior encodings in both accuracy and hardware efficiency for molecular simulations. Our improvements include path optimization within the Hamiltonian's interaction graph to minimize operator weight, introduction of multi-edge graph structures for enhanced error detection without added circuit depth, and a stabilizer measurement framework that directly maps logical terms and stabilizers to the Z-basis using Clifford simulation. Applying these methods to simulations of $(H_2)_2$ and $(H_2)_3$ systems yields significantly improved absolute and correlation energy estimates under realistic hardware noise, with further accuracy gains achieved by increasing code distance. We also propose a [[2N, N, 2]] variant of GSE compatible with square-lattice and (quasi-)linear hardware topologies, demonstrating a twofold reduction in RMSE for orbital rotations on IBM Kingston hardware. These results establish GSE as a very attractive mapping for molecular quantum simulations.