Noise-Resilient Quantum Chemistry with Half the Qubits

TL;DR

This work addresses the challenge of simulating strongly correlated chemistry on NISQ devices by integrating sampled-based quantum diagonalization (SQD) with a half-qubit approach (HSQD) that halves the qubit requirement via a modified LUCJ ansatz. The authors further enhance sampling quality with a deterministic, HCI-inspired subspace selection (HCI-HSQD), yielding compact subspaces and accurate ground-state energies while dramatically reducing circuit depth and measurement counts. They demonstrate state-of-the-art performance on nitrogen dissociation and iron–sulfur clusters, achieving comparable or better accuracy than full-qubit SQD with half the qubits, up to 40% fewer measurements, and no expensive post-processing. Overall, HSQD and HCI-HSQD establish a noise-resilient, resource-efficient path toward practical quantum advantage in strongly correlated chemistry on near-term devices.

Abstract

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.

Figures (7)

• Figure 1: Half-qubit LUCJ circuit.(a) Original $M$-qubit truncated LUCJ circuit used in SQD Robledo2025, comprising orbital rotation unitaries $\exp(-\hat{K}_{\mu\sigma})$, same-spin cluster operators $\exp(i(\hat{J}_{\mu\alpha\alpha} + \hat{J}_{\mu\beta\beta}))$, and opposite-spin cluster operators $\exp(i\hat{J}_{\mu\alpha\beta})$, where $\mu$ is the layer index, $\sigma \in \{\alpha,\beta\}$ denotes spin, $\alpha$ refers to spin-up orbitals, and $\beta$ to spin-down orbitals. (b) Modified $M/2$-qubit LUCJ circuit, in which opposite-spin cluster operators $\exp(i\hat{J}_{\mu\alpha\beta})$ are remapped to same-spin operators $\exp(i\hat{J}_{\mu\alpha\alpha})$, represented as $\exp(i\hat{J}_{\mu(\alpha\beta\rightarrow\alpha\alpha)})$, with $\alpha_i$ and $\beta_i$ denoting the spin-up and spin-down orbitals of spatial orbital $i$. (c) The circuit remapping used to obtain $\exp(i\hat{J}_{\mu(\alpha\beta\rightarrow\alpha\alpha)})$, showing parameterized single-qubit gates $U(\theta)_{\sigma_i}$ on qubit $\sigma_i$ and controlled gates $CU(\theta)_{\sigma_i\gamma_j}$ with control qubit $\sigma_i$ and target qubit $\gamma_j$, where $\sigma, \gamma \in \{\alpha,\beta\}$ and $\sigma_i, \gamma_j$ are the qubits of the corresponding spin-orbitals for spatial orbitals $i$ and $j$, respectively.
• Figure 2: Workflow of the HCI-HSQD method.Left: A noisy subspace $\tilde{S}$ is sampled from a variational state $\lvert\Psi(\boldsymbol\theta)\rangle$ prepared on a quantum processor via a $M/2$-qubit circuit, reducing the qubit requirement by half. A classical recovery step produces the corrected subspace $S$, which is passed to an HCI-inspired selection to yield a compact subspace $S'$ and its ground state $\lvert\Psi^{S'}\rangle$ with energy $E^{S'}$. Right: Construction of $S'$ from $S$ without explicit formation of the full tensor-product space $S_{\text{tensor}}=S\otimes S$, by dynamically combining half-configurations and filtering them with the standard HCI criterion Holmes2016.
• Figure 3: Chemical systems can be modeled accurately with half-qubit circuits.(a) Energies from the modified half-qubit LUCJ ansatz on a noiseless simulator for N$_2$ in the $6$-$31$G basis with a (10e, 12o) active space. The remapped LUCJ circuit yields lower energies than CCSD, indicating that the remapped cluster operators $\exp(i\hat{J}{\mu(\alpha\beta\rightarrow\alpha\alpha)})$ can accurately capture correlations within the HSQD framework. (b) Potential energy surface of N$_2$ in the cc-pVDZ basis with a (10e, 26o) active space, comparing HSQD to classical HCI. HSQD reproduces the dissociation curve with accuracy comparable to the original SQD Robledo2025 while using half the qubits and 40% fewer quantum measurements.
• Figure 4: Improved selection of sampled configurations with HCI-HSQD yields chemical accuracy.(a) Energy errors across the N$_2$ (cc-pVDZ, 10e, 26o) potential energy surface. Replacing the stochastic subspace selection Robledo2025 in HSQD with the HCI-inspired selection developed in this work reduces the energy error of half-qubit samples to below 1 mHa across all geometries. (b) Comparison of subspace sizes returned by classical HCI and HCI-HSQD. HCI-HSQD produces subspaces that are up to 39% more compact, demonstrating that half-qubit sampled configurations accurately capture the ground-state support and can accelerate selected CI expansions.
• Figure 5: Cost to correct noisy samples can be reduced with HCI-HSQD(a) Energies along the N$_2$ (cc-pVDZ, 10e, 26o) potential energy surface using HCI-HSQD with different configuration recovery procedures applied to the noisy samples $\tilde{S}$. Labels (0C), (1C), (5C), and (9C) indicate corrections using the occupation vector n from a single diagonalization of valid configurations in $\tilde{S}$, 1 cycle of SCCR, 5 cycles of SCCR, and 9 cycles of SCCR, respectively. SCCR slightly lowers the energies, but all corrections yield errors below 1 mHa relative to classical HCI. (b) Wallclock runtimes with each correction method in (a), with classical HCI included as a reference. SCCR significantly increases runtime, so the modest energy improvement must be weighed against computational cost.