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arXiv:2602.10435

Multiconfiguration Pair-Density Functional Theory Calculations of Low-lying States of Complex Chemical Systems with Quantum Computers

Zhanou Liu, Yuhao Chen, Yingjin Ma, Xiao He, Yuxin Deng

Published Feb 11, 2026• 0 citations
arXivHTMLPDF

Abstract

Accurately describing strong electron correlation in complex systems remains a prominent challenge in computational chemistry as near-term quantum algorithms treating total correlation often require prohibitively deep circuits. Here we present a hybrid strategy combining the Variational Quantum Eigensolver with Multiconfiguration Pair-Density Functional Theory to efficiently decouple correlation effects. This approach confines static correlation to a compact multireference quantum state while recovering dynamic correlation through a classical on-top density functional using reduced-density information. By enabling self-consistent orbital optimization, the method significantly reduces quantum resource overheads without sacrificing physical rigor. We demonstrate chemical accuracy on standard benchmarks by reproducing C$_2$ equilibrium bond lengths and benzene excitation energies with mean absolute errors of 0.006 Å and 0.048 eV respectively. Most notably, for the strongly correlated Cr$_2$ dimer requiring a large complete active space (48e, 42o), the framework yields a bound potential-energy curve and recovers qualitative dissociation behavior despite realistic hardware noise. These results establish that separating correlation types provides a practical route to reliable predictions on near-term quantum hardware.

DOI
10.48550/arxiv.2602.10435

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Accurately describing strong electron correlation in complex systems remains a prominent challenge in computational chemistry as near-term quantum algorithms treating total correlation often require prohibitively deep circuits. Here we present a hybrid strategy combining the Variational Quantum Eigensolver with Multiconfiguration Pair-Density Functional Theory to efficiently decouple correlation effects. This approach confines static correlation to a compact multireference quantum state while recovering dynamic correlation through a classical on-top density functional using reduced-density information. By enabling self-consistent orbital optimization, the method significantly reduces quantum resource overheads without sacrificing physical rigor. We demonstrate chemical accuracy on standard benchmarks by reproducing C2_22​ equilibrium bond lengths and benzene excitation energies with mean absolute errors of 0.006 Å and 0.048 eV respectively. Most notably, for the strongly correlated Cr2_22​ dimer requiring a large complete active space (48e, 42o), the framework yields a bound potential-energy curve and recovers qualitative dissociation behavior despite realistic hardware noise. These results establish that separating correlation types provides a practical route to reliable predictions on near-term quantum hardware.
Understanding strongly correlated systems is essential for advancing quantum chemistry and materials science, yet conventional methods like Density Functional Theory (DFT) often fail to capture their complex electronic behavior. To address these limitations, we develop a hybrid quantum-classical framework that integrates Multiconfigurational Self-Consistent Field (MCSCF) with the Variational Quantum Eigensolver (VQE). Our initial benchmarks on water dissociation enabled the systematic optimization of key computational parameters, including ansatz selection, active space construction, and error mitigation. Building on this, we extend our approach to investigate the interactions between graphene analogues and water, demonstrating that our framework produces binding energies consistent with high-accuracy quantum methods. Furthermore, we apply this methodology to predict the binding energies of transition metals (Fe, Co, Ni) on both pristine and defective graphene analogues, revealing strong charge transfer effects and pronounced multireference character─phenomena often misrepresented by standard DFT. In contrast to many existing quantum algorithms that are constrained to small molecular systems, our framework achieves chemically accurate predictions for larger, strongly correlated systems such as metal-graphene complexes. This advancement highlights the capacity of hybrid quantum-classical approaches to address complex electronic interactions and demonstrates a practical route toward realizing quantum advantage for real-world materials applications in the Noisy Intermediate-Scale Quantum (NISQ) era.
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While chemical systems containing hundreds to thousands of electrons remain beyond the reach of quantum devices, hybrid quantum-classical algorithms present a promising pathway toward a quantum advantage. Hybrid algorithms treat the exponentially scaling part of the calculation-the static correlation-on the quantum computer and the non-exponentially scaling part-the dynamic correlation-on the classical computer. While a variety of algorithms have been proposed, the dependence of many methods on the total wave function limits the development of easy-to-use classical post-processing implementations. Here, we present a novel combination of quantum and classical algorithms, which computes the all-electron energy of a strongly correlated molecular system on the classical computer from the 2-electron reduced density matrix (2-RDM) evaluated on the quantum device. Significantly, we circumvent the wave function in the all-electron calculations by using density matrix methods that only require input of the statically correlated 2-RDM. Although the algorithm is completely general, we test it with two classical density matrix methods, the anti-Hermitian contracted Schrödinger equation (ACSE) and multiconfiguration pair-density functional theories, using the recently developed quantum ACSE method for simulating the statically correlated 2-RDM. We obtain experimental accuracy for the relative energies of all three benzyne isomers and thereby demonstrate the ability of the developed algorithm to achieve chemically relevant and accurate results on noisy intermediate-scale quantum devices.
Quantum embedding methods offer a promising route to extend quantum chemical calculations to large multiscale systems by treating a chemically important subsystem at a high level of theory while describing its surrounding environment at an affordable level. The methods are also quite relevant for quantum computing approaches based on hardware with limited resources. Here, we present an iterative projection-based embedding framework combined with VQE, in which the environment density is allowed to respond self-consistently to the refined electronic structure of the embedded subsystem described by VQE. Unlike conventional one-shot approaches where the environment remains frozen after the initial orbital optimization, the proposed iterative scheme alternates between the VQE-level treatment of the subsystem and a mean-field-level refinement of the environment until mutual self-consistency is achieved. The convergence behavior of the scheme is first examined using several small test systems. Its practical applicability is then demonstrated with a composite system with a CH2NH molecule sandwiched by two benzene rings, with the C=N dihedral angle rotating from 0 to 90 deg. The iterative procedure consistently converges within ~10 iteration steps across all tested geometries, yielding energies below the conventional one-shot embedding results. The converged results well reproduce the fully correlated reference energy employing the same active space, and the resulting potential energy surface with respect to the dihedral rotation is also in good agreement with the reference one. These results demonstrate that our iterative embedding framework is numerically robust and physically sound, yielding a self-consistent and reliable treatment of inter-subsystem correlation. We expect that its formulation will be particularly compatible with the emerging paradigm of quantum-classical hybrid computing.
Abstract Variational quantum eigensolvers (VQE) are among the most promising approaches for solving electronic structure problems on near-term quantum computers. A critical challenge for VQE in practice is that one needs to strike a balance between the expressivity of the VQE ansatz versus the number of quantum gates required to implement the ansatz, given the reality of noisy quantum operations on near-term quantum computers. In this work, we consider an orbital-optimized pair-correlated approximation to the unitary coupled cluster with singles and doubles (uCCSD) ansatz and report a highly efficient quantum circuit implementation for trapped-ion architectures. We show that orbital optimization can recover significant additional electron correlation energy without sacrificing efficiency through measurements of low-order reduced density matrices (RDMs). In the dissociation of small molecules, the method gives qualitatively accurate predictions in the strongly-correlated regime when running on noise-free quantum simulators. On IonQ’s Harmony and Aria trapped-ion quantum computers, we run end-to-end VQE algorithms with up to 12 qubits and 72 variational parameters—the largest full VQE simulation with a correlated wave function on quantum hardware. We find that even without error mitigation techniques, the predicted relative energies across different molecular geometries are in excellent agreement with noise-free simulators.
The multiconfigurational self-consistent field theory is considered the standard starting point for almost all multireference approaches required for strongly correlated molecular problems. The limitation of the approach is generally given by the number of strongly correlated orbitals in the molecule, since its cost will grow exponentially with this number. We present a new multiconfigurational self-consistent field approach, wherein linear determinant coefficients of a multiconfigurational wave function are optimized via the stochastic full configuration interaction quantum Monte Carlo technique at greatly reduced computational cost, with nonlinear orbital rotation parameters updated variationally based on this sampled wave function. This extends this approach to strongly correlated systems with far larger active spaces than it is possible to treat via conventional means. By comparison with this traditional approach, we demonstrate that the introduction of stochastic noise in both the determinant amplitudes and the gradient and Hessian of the orbital rotations does not preclude robust and reliable convergence of the orbital optimization. It can even improve the ability to avoid convergence to local minima in the orbital space, and therefore aid in finding variationally lower-energy solutions. We consider the effect on the convergence of the orbitals as the number of walkers and the sampling time within the active space increases, as well as the effect on the final energy and error. The scope of the new protocol is demonstrated with a study of the increasingly strongly correlated electronic structure in a series of polycyclic aromatic hydrocarbons, up to the large coronene molecule in a complete active space of 24 π electrons in 24 orbitals, requiring only modest computational resources