Compactifying the Electronic Wavefunction II: Quantum Estimators for Spin-Coupled Generalized Valence Bond Wavefunctions Applied to H4

TL;DR

This paper introduces a shallow, ancilla-free quantum measurement framework for evaluating overlap and Hamiltonian matrix elements in spin-coupled valence bond wavefunctions, suitable for NISQ devices.

Contribution

It develops a measurement-driven quantum approach that avoids controlled operations, enabling efficient evaluation of SCGVB wavefunctions on near-term quantum hardware.

Findings

Framework accurately computes overlap and Hamiltonian matrices for H4.

Method produces results consistent with classical reference calculations.

Approach is robust and suitable for implementation on NISQ devices.

Abstract

Valence-bond-based wavefunctions, such as the spin-coupled generalized valence bond (SCGVB) ansatz, provide compact and chemically interpretable descriptions of strong correlation. However, their non-orthogonal determinant structure poses a major challenge for quantum computing implementations. Although recent fermion-qubit mappings allow non-orthogonal orbitals to be encoded on qubit registers, the evaluation of overlap and Hamiltonian matrix elements remains a bottleneck on NISQ devices due to the need for ancilla qubits, controlled operations, and deep circuits. We present a measurement-driven quantum framework for evaluating these quantities in SCGVB wavefunctions. Instead of preparing the full wavefunction, we reformulate the problem in terms of vacuum expectation values of Pauli-string operators, enabling evaluation with shallow, ancilla-free circuits based on local Clifford rotations and computational-basis measurements. Unlike Hadamard-test-based approaches, this method avoids controlled operations by reducing the task to local Pauli measurements, yielding a low-depth strategy suitable for near-term devices. We demonstrate the framework on the H4 cluster along a dissociation pathway from square geometry to the separated-fragment limit, considering five nuclear configurations via quantum-circuit emulation. The overlap and Hamiltonian matrices agree well with classical Lowdin-based references, and Chirgwin-Coulson weights remain chemically consistent. These results highlight the robustness of the approach and its suitability as a NISQ-compatible building block for SCGVB-based quantum algorithms.