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Journal of Chemical Theory and Computation

Qubit-Adaptive Variational Quantum Imaginary Time Evolution: A Resource-Efficient Algorithm for Ground-State Preparation of Correlated Molecules on Near-Term Quantum Computers

Thitiwuth Chaiyatho, Zhenyu Li, Jin‐Shi Xu, Xiao-Ye Xu, Wiwittawin Sukmas

Published Sep 26, 2026• 0 citations
Publisher

Abstract

Preparing ground states of correlated molecules on near-term quantum computers requires algorithms that are both accurate and resource-efficient. We introduce the qubit-adaptive variational quantum imaginary time evolution (QAITE) algorithm, which synthesizes the systematic convergence of imaginary-time evolution with hardware-efficient, adaptive ansatz construction. By integrating the linear-scaling qubit operator pool into the adaptive variational quantum imaginary time evolution framework, QAITE deterministically constructs a compact ansatz without costly classical optimization loops. Numerical simulations for molecular systems (H4, LiH, H2O, BeH2), benchmarked against our own implementations of established adaptive algorithms under identical conditions, show that QAITE achieves chemical accuracy with a 15-45% reduction in CNOT gates compared to the standard adaptive variational quantum imaginary time evolution (AVQITE) method. For hydrogen chains (RHH = 1.5 Å, N = 6-16 qubits), QAITE's circuit complexity grows approximately quadratically and remains the lowest of the four methods at every system size, reaching 31% fewer CNOT gates than AVQITE at 16 qubits─a saving of 1322 gates. This efficiency extends to heterogeneous (LiH)n and (HBe)n chains, where QAITE maintains a CNOT gate ratio below 1 for all sizes studied (e.g., 0.81 for (LiH)2). We further show that the deterministic parameter update is numerically robust: the results are insensitive to the regularization of the quantum geometric tensor over at least 4 orders of magnitude, and chemical accuracy is retained under realistic shot noise applied to both the quantum geometric tensor and the force vector. By outperforming established adaptive algorithms in both absolute gate count and scaling, QAITE establishes a promising, scalable pathway for quantum molecular simulations on noisy intermediate-scale quantum devices.

DOI
10.1021/acs.jctc.6c01171

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Preparing ground states of correlated molecules on near-term quantum computers requires algorithms that are both accurate and resource-efficient. We introduce the qubit-adaptive variational quantum imaginary time evolution (QAITE) algorithm, which synthesizes the systematic convergence of imaginary-time evolution with hardware-efficient, adaptive ansatz construction. By integrating the linear-scaling qubit operator pool into the adaptive variational quantum imaginary time evolution framework, QAITE deterministically constructs a compact ansatz without costly classical optimization loops. Numerical simulations for molecular systems (H4, LiH, H2O, BeH2), benchmarked against our own implementations of established adaptive algorithms under identical conditions, show that QAITE achieves chemical accuracy with a 15-45% reduction in CNOT gates compared to the standard adaptive variational quantum imaginary time evolution (AVQITE) method. For hydrogen chains (RHH = 1.5 Å, N = 6-16 qubits), QAITE's circuit complexity grows approximately quadratically and remains the lowest of the four methods at every system size, reaching 31% fewer CNOT gates than AVQITE at 16 qubits─a saving of 1322 gates. This efficiency extends to heterogeneous (LiH)n and (HBe)n chains, where QAITE maintains a CNOT gate ratio below 1 for all sizes studied (e.g., 0.81 for (LiH)2). We further show that the deterministic parameter update is numerically robust: the results are insensitive to the regularization of the quantum geometric tensor over at least 4 orders of magnitude, and chemical accuracy is retained under realistic shot noise applied to both the quantum geometric tensor and the force vector. By outperforming established adaptive algorithms in both absolute gate count and scaling, QAITE establishes a promising, scalable pathway for quantum molecular simulations on noisy intermediate-scale quantum devices.
Abstract An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near‐term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan distance is constrained by the quality of the ansatz, the AVQITE method iteratively expands the ansatz along the dynamical path to keep the McLachlan distance below a chosen threshold. This ensures the state is able to follow the quantum imaginary time evolution path in the system Hilbert space rather than in a restricted variational manifold set by a predefined fixed ansatz. AVQITE is used to prepare ground states of H 4 , H 2 O, and BeH 2 molecules, where it yields compact variational ansätze and ground state energies within chemical accuracy. Polynomial scaling of circuit depth with system size is shown through a set of AVQITE calculations of quantum spin models. Finally, quantum Lanczos calculations are demonstrated alongside AVQITE without additional quantum resource costs.
An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near-term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions, and avoids difficult nonconvex high-dimensional optimization that plagues other variational approaches such as the variational quantum eigensolver. The variational parameters evolve according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the minimal McLachlan distance is constrained by the quality of the ansatz, the adaptive method iteratively expands the ansatz along the dynamical path to ensure the McLachlan distance remains below a chosen threshold. AVQITE is used to prepare ground states of H4_44​, H2_22​O and BeH2_22​ molecules and yields compact variational ansatze and ground state energies beyond chemical accuracy. Finally, quantum Lanczos calculations can also be naturally performed alongside AVQITE without additional quantum resource costs.
Compact ground-state preparation circuits are essential for early fault-tolerant quantum chemistry. We introduce Variational Imaginary-time Majorana Evolution (VIME), a classical pre-training algorithm that extends operator-projected variational quantum imaginary-time evolution (OVQITE) to molecular electronic structure using a single compiled Majorana-propagation (MP) surrogate graph. We pair VIME with a compressed tiled Unitary Product State (c-tUPS) ansatz that we develop to reduce both classical simulation and quantum state-preparation costs. In the strongly correlated ruthenium complex TLD-1411, active-space calculations requiring up to 52 qubits achieve chemical precision against DMRG reference energies, with energy errors approximately 400×400\times400× smaller than those from ADAPT-VQE-based variational Majorana-propagation (ADAPT-VMPE). Across the strongly multireference acene series up to heptacene (60 qubits), VIME matches or improves on the MP-reported energy accuracy of the ADAPT-VMPE comparison points with up to 26×26\times26× fewer CNOTs and 167×167\times167× lower two-qubit depth. These results establish imaginary-time classical pre-training of compressed variational ansätze as a promising route to resource-efficient molecular ground-state preparation.
Quantum imaginary time evolution (QITE) is one of the promising candidates for finding the eigenvalues and eigenstates of a Hamiltonian on a quantum computer. However, the original proposal suffers from large circuit depth and measurements due to the size of the Pauli operator pool and Trotterization. To alleviate the requirement for deep circuits, we propose a time-dependent drifting scheme inspired by the qDRIFT algorithm [Campbell, E. Phys. Rev. Lett. 2019, 123, 070503]. We show that this drifting scheme removes the depth dependency on the size of the operator pool and converges inversely with respect to the number of steps. We further propose a deterministic algorithm that selects the dominant Pauli term to reduce the fluctuation for the ground state preparation. We also introduce an efficient measurement reduction scheme across Trotter steps that removes its cost dependence on the number of iterations. We analyze the main source of error for our scheme both theoretically and numerically. We numerically test the validity of depth reduction, convergence performance of our algorithms, and the faithfulness of the approximation for our measurement reduction scheme on several benchmark molecules. In particular, the results on the LiH molecule give circuit depths comparable to that of the advanced adaptive variational quantum eigensolver (VQE) methods while requiring much fewer measurements.
The matrix product state (MPS) Ansatz offers a promising approach for finding the ground state of molecular Hamiltonians and solving quantum chemistry problems. Building on this concept, the proposed technique of quantum circuit MPS (QCMPS) enables the simulation of chemical systems using a relatively small number of qubits. In this study, we enhance the optimization performance of the QCMPS Ansatz by employing the variational quantum imaginary time evolution (VarQITE) approach. Guided by McLachlan's variational principle, the VarQITE method provides analytical metrics and gradients, resulting in improved convergence efficiency and robustness of the QCMPS. We validate these improvements numerically through simulations of H2, H4, and LiH molecules. In addition, given that VarQITE is applicable to non-Hermitian Hamiltonians, we evaluate its effectiveness in preparing the ground state of transcorrelated Hamiltonians. This approach yields energy estimates comparable to the complete basis set (CBS) limit while using even fewer qubits. In particular, we perform simulations of the beryllium atom and LiH molecule using only three qubits, maintaining high fidelity with the CBS ground state energy of these systems. This qubit reduction is achieved through the combined advantages of both the QCMPS Ansatz and transcorrelation. Our findings demonstrate the potential practicality of this quantum chemistry algorithm on near-term quantum devices.
Quantum imaginary-time evolution (QITE) provides a systematic route to ground-state preparation, but its cost grows rapidly with the locality DDD of the unitary approximation, for which the local Pauli basis scales as 4D4^D4D. We introduce Sparse-QITE, a regularized formulation that promotes compact generators, reducing the number of quantum operations and yielding circuits with fewer gates and lower depth. We derive rigorous bounds on the sparsification error and benchmark the method in one-dimensional transverse-field Ising and antiferromagnetic Heisenberg models. Sparse-QITE exhibits a controllable sparsity--accuracy trade-off while retaining strong compression even in the high-accuracy regime. In scalability experiments with respect to DDD, the active support grows much more slowly than in standard QITE and, in several regimes, approximately saturates over the domain sizes studied. After circuit construction and transpilation, some of the largest-domain cases require only about 1%1\%1% of the standard-QITE gate count while maintaining high accuracy. We further introduce adaptive and active-discovery variants: the former selects the regularization strength dynamically during the evolution, while the latter reduces the number of Pauli expectation values that need to be evaluated and, consequently, the measurement requirements. These results establish sparsity-promoting regularization as a route toward more resource-efficient QITE. More broadly, these results suggest that sparsity-promoting regularization may also benefit variational quantum algorithms.