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

TL;DR

The paper tackles the challenge of efficiently simulating molecular Hamiltonians on quantum hardware by improving the Generalized Superfast Encoding (GSE) for general fermionic systems. It combines path optimization, multi-edge stabilizers, and a Clifford-simulation–based approach that rotates stabilizers and logical terms into the $Z$-basis, yielding a $[[2N,N,2]]$ code and higher-distance variants compatible with square-lattice hardware. Empirical results show reduced circuit depth and enhanced absolute and correlation energies under realistic noise for systems like $$(H_2)_2$$ and $$(H_2)_3$$, with further gains as code distance increases; a distance-2 code can deliver substantial improvements on IBM Kingston, and a square-lattice compatible variant enables quasi-linear hardware implementations using Fermionic Gaussian unitaries. The work demonstrates that GSE can outperform Jordan–Wigner and prior encodings for realistic molecular Hamiltonians, offering a practical, hardware-aware path toward scalable quantum chemistry simulations and paving the way for fault-tolerant integrations in the future.

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.

Figures (11)

• Figure 1: An example of a distance-2 graph for 7 modes where each excitation is a maximum of 2-hops away.
• Figure 2: The simplest interaction graph that retains the spin-parity symmetry with single and multi-edges
• Figure 3: The Trotter-Suzuki circuit for the Hamiltonian $a_0^{\dagger}a_2+a_1^{\dagger}a_3+h.c.$ mapped using both GSE distance-3 with multi-edges and Jordan-Wigner. The resulting circuit depth for the distance-3 GSE is 21 while the Jordan-Wigner circuit depth is 27. By carefully choosing which path to define an excitation, it is possible to reduce the circuit depth.
• Figure 4: The spin-separated rotation circuit that changes the canonical stabilizers $XIXIII$, $-ZIZIII$, $IZIIII$, $IIIXIX$, $-IIIZIZ$, and $IIIIZI$ to all $Z$ operators.
• Figure 5: The circuit that rotates the same operators such that the stabilizers are changed to $Z_1,\, Z_4$.