Half The Qubits, Same Accuracy: Quantum Chemistry Leaps Forward

Scientists are tackling the challenge of performing accurate quantum chemistry calculations on today’s limited quantum computers. Shane McFarthing, Aidan Pellow-Jarman, and Francesco Petruccione, from Qunova Computing Inc and Stellenbosch University, present a new method called HSQD that significantly reduces the number of qubits needed for these simulations. Their research introduces a half-qubit approach to sample-based quantum diagonalization, halving qubit requirements and circuit complexity, thereby mitigating the impact of hardware noise. Demonstrating this on systems like nitrogen molecules and iron-sulfur clusters, reaching active spaces of up to (54e, 36o) , the team shows HSQD not only matches the accuracy of existing methods but also substantially reduces errors and measurement demands, paving the way for more efficient and practical quantum simulations of complex chemical systems.

This breakthrough, termed half-qubit Sampled Quantum Diagonalization (HSQD), tackles a fundamental challenge in the field: the exponential scaling of computational cost with molecular complexity.

By combining quantum sampling with classical diagonalization, HSQD offers a pathway to accurate simulations of strongly correlated chemical systems on noisy intermediate-scale quantum (NISQ) devices. The research introduces a novel technique that not only reduces qubit requirements but also drastically decreases circuit depth and gate counts, thereby suppressing the impact of hardware noise.
When applied to the dissociation of the nitrogen molecule with a (10e, 26o) active space, HSQD achieved accuracy comparable to standard SQD methods, but using half the number of qubits and requiring 40% fewer measurements. Researchers further refined HSQD with a heat-bath configuration interaction (HCI)-inspired sample selection process, resulting in HCI-HSQD, which delivers sub-millihartree accuracy across the N2 potential energy surface.

Notably, this enhanced method generates subspaces up to 39% smaller than those obtained from classical HCI, demonstrating a marked improvement in the compactness of the ground-state representation. The scalability of HCI-HSQD was then demonstrated using iron-sulfur clusters, successfully reaching active spaces of up to (54e, 36o) while maintaining the half-qubit advantage over the original SQD.

For these complex systems, HCI-HSQD reduced SQD energy errors by up to 76% for [2Fe-2S] and 26% for [4Fe-4S], alongside reductions in subspace sizes and a halving of measurement requirements. Expensive post-processing steps were also eliminated, streamlining the computational process. These results firmly establish half-qubit SQD as a resource-efficient and noise-resilient strategy for achieving practical quantum advantage in strongly correlated chemistry.

Half-qubit simulation and heat-bath configuration interaction for efficient nitrogen dissociation modelling offer promising results

A 72-qubit superconducting processor was not used; instead, the research introduced half-qubit SQD, or HSQD, a novel approach that reduces the qubit requirement for simulating chemical systems and circuit depth. HSQD was implemented by modelling the dissociation of the nitrogen molecule using a (10e, 26o) active space, achieving accuracy comparable to standard SQD but with half the qubits and a 40% reduction in measurements.

This reduction in qubit count and measurements directly addresses the limitations of noisy intermediate-scale quantum devices. Further refinement came with HCI-HSQD, which incorporates a heat-bath configuration interaction inspired selection of samples. This selection process yielded sub-millihartree accuracy across the N2 potential energy surface, demonstrating improved precision in ground-state representation.

Crucially, HCI-HSQD generated subspaces up to 39% smaller than those obtained using classical HCI, indicating a more compact and efficient representation of the quantum state. Scalability was then demonstrated using iron-sulfur clusters, extending the active spaces to (54e, 36o) while maintaining the halved qubit requirement compared to original SQD.

For [2Fe-2S] and [4Fe-4S] systems, HCI-HSQD reduced SQD energy errors by up to 76% and 26% respectively, alongside further reductions in subspace sizes and measurement counts. The team remapped opposite-spin cluster operators in the LUCJ circuit to same-spin operators, represented as exp(i Jμ(αβ→αα)), using parameterized single-qubit and controlled gates to achieve this half-qubit representation. This innovative circuit remapping is central to the resource efficiency of the HSQD method.

Half-qubit simulation achieves chemical accuracy and scalability with compact state representations for relevant molecular systems

Researchers present a novel half-qubit SQD (HSQD) approach that halves the qubit requirement for simulating chemical systems and significantly reduces circuit depth and gate counts. When modeling the dissociation of the nitrogen molecule with a (10e, 26o) active space, HSQD achieved accuracy matching standard SQD, but using half the number of qubits and requiring 40% fewer measurements.

Further enhancement with a heat-bath configuration interaction (HCI) inspired sample selection, termed HCI-HSQD, yielded sub-millihartree accuracy across the N2 potential energy surface. Specifically, HCI-HSQD produced subspaces up to 39% smaller than those obtained from classical HCI, demonstrating a marked improvement in the compactness of the ground-state representation.

The scalability of HCI-HSQD was then demonstrated using iron-sulfur clusters, reaching active spaces of up to (54e, 36o) while maintaining the half-qubit advantage over the original SQD method. For these systems, HCI-HSQD reduced SQD energy errors by up to 76% for [2Fe-2S] and 26% for [4Fe-4S]. Moreover, HCI-HSQD not only decreased energy errors but also reduced subspace sizes and halved measurement requirements, simultaneously eliminating expensive post-processing steps.

These results establish half-qubit SQD as a noise-resilient and resource-efficient pathway for achieving practical quantum advantage in strongly correlated chemistry. The work details a modified LUCJ circuit, remapping opposite-spin cluster operators to same-spin operators, enabling the reduction in qubit count.

Compact quantum simulations via half-qubit sample-based diagonalization and heat-bath selection offer a promising pathway forward

Researchers have developed a half-qubit sample-based quantum diagonalization (HSQD) approach that significantly reduces the computational resources needed for accurate quantum chemistry simulations on noisy intermediate-scale quantum (NISQ) devices. This novel method halves the qubit requirement and circuit depth compared to conventional SQD, thereby suppressing hardware noise and improving simulation accuracy.

Further enhancement with a heat-bath configuration interaction (HCI) inspired sample selection, termed HCI-HSQD, yields even more compact and accurate ground-state representations. Demonstrating the effectiveness of HCI-HSQD, the team achieved sub-millihartree accuracy across the nitrogen molecule potential energy surface, with subspaces up to 39% smaller than those obtained using classical HCI.

Scalability was further validated through simulations of iron-sulfur clusters, reaching active spaces of up to (54e, 36o) while maintaining a reduced qubit count. Notably, HCI-HSQD reduced energy errors in [2Fe-2S] and [4Fe-4S] systems by up to 76% and 26% respectively, alongside halving measurement requirements and minimising post-processing demands.

The authors acknowledge that achieving quantum advantage relies heavily on efficient sampling of the ground-state electronic wave function, a process hindered by qubit decoherence and gate noise. While configuration recovery methods offer partial mitigation, they cannot fully address sampling inefficiencies.

The current work directly tackles this issue by reducing circuit depth and qubit count, leading to more valid configurations within the sampled subspace. Future research may focus on extending this framework to even larger basis sets and more strongly correlated systems, pushing the boundaries of what is achievable with NISQ hardware. These findings establish half-qubit SQD as a promising pathway towards practical quantum advantage in strongly correlated chemistry, offering a resource-efficient and noise-resilient approach to electronic structure simulations.