Noise-Resilient Quantum Chemistry with Half the Qubits

Sample-based quantum diagonalization (SQD) offers a powerful route to accurate quantum chemistry on noisy intermediate-scale quantum (NISQ) devices by combining quantum sampling with classical diagonalization. Here we introduce HSQD, a novel half-qubit SQD approach that halves the qubit requirement for simulating a chemical system and drastically reduces overall circuit depth and gate counts, suppressing hardware noise. When modeling the dissociation of the nitrogen molecule with a (10e, 26o) active space, HSQD matches the accuracy of SQD on IBM quantum hardware using only half the number of qubits and 40% fewer measurements. We further enhance HSQD with a heat-bath configuration interaction (HCI) inspired selection of the samples, forming HCI-HSQD. This yields sub-millihartree accuracy across the N2 potential energy surface and produces subspaces up to 39% smaller than those from classical HCI, showing a significant improvement in the compactness of the ground-state representation. Finally, we demonstrate the scalability of HCI-HSQD using iron-sulfur clusters, reaching active spaces of up to (54e, 36o) while using only half as many qubits as the original SQD. For these systems, HCI-HSQD reduces SQD energy errors by up to 76% for [2Fe-2S] and 26% for [4Fe-4S], while also reducing subspace sizes, halving measurement requirements, and eliminating expensive post-processing. Together, these results establish half-qubit SQD as a noise-resilient and resource-efficient pathway toward practical quantum advantage in strongly correlated chemistry.

💡 Research Summary

The paper introduces a novel “half‑qubit” variant of Sample‑Based Quantum Diagonalization (SQD), called HSQD, which reduces the qubit count required for quantum chemistry simulations by a factor of two while simultaneously cutting circuit depth and gate count roughly in half. The key insight is to compress each spatial orbital’s two spin‑orbitals (α and β) into a single qubit using a modified Jordan–Wigner mapping and a remapped Local Unitary Cluster Jastrow (LUCJ) ansatz. In the original LUCJ circuit, opposite‑spin cluster operators exp(i Jαβ) are replaced by same‑spin operators exp(i Jαα) that can be implemented with controlled‑U and single‑qubit rotation gates on the reduced qubit register. This structural change halves the number of CNOTs and parameterized gates, dramatically lowering the exposure to decoherence and gate errors on noisy intermediate‑scale quantum (NISQ) hardware.

HSQD proceeds by preparing a variational state |Ψ(θ)⟩ on the M/2‑qubit circuit, measuring it repeatedly in the computational basis, and collecting a set of binary strings ˜S that represent sampled electron configurations. Because hardware noise can corrupt the sampled strings (e.g., violating particle‑number or spin symmetry), previous SQD implementations relied on Self‑Consistent Configuration Recovery (SCCR), an iterative post‑processing step that repeatedly corrects occupations and re‑diagonalizes sub‑spaces. SCCR, however, incurs substantial classical overhead and many additional quantum measurements.

To replace SCCR, the authors embed a Heat‑Bath Configuration Interaction (HCI)‑inspired deterministic selection into the workflow, yielding the combined method HCI‑HSQD. After obtaining ˜S, a lightweight classical recovery step removes obviously invalid configurations, producing a corrected sub‑space S. Rather than using a stochastic Monte‑Carlo estimator to choose determinants, HCI‑HSQD evaluates the Hamiltonian matrix elements of candidate determinants generated by tensor‑product combinations of half‑configurations and retains only those that satisfy the HCI selection criterion (|ΔE| < ε). This deterministic pruning dramatically reduces the final sub‑space dimension while preserving the most energetically relevant determinants.

The authors benchmark HSQD and HCI‑HSQD on three chemically challenging systems:

1. Nitrogen dissociation (N₂) in a (10 e, 26 o) active space – HSQD reproduces the potential energy surface (PES) obtained with full‑qubit SQD, but uses 40 % fewer measurements and half the qubits. Adding the HCI‑inspired selection (HCI‑HSQD) brings the energy error below 1 mHa across the entire PES and yields sub‑spaces that are 18–39 % smaller than those generated by classical HCI.

2. **