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arXiv:2601.05973 · Journal of Chemical Theory and Computation

Counterdiabatic ADAPT-VQE for molecular simulation

Diego Tancara, Herbert Díaz-Moraga, Dardo Goyeneche

quant-phSubmitted Jan 9, 2026• Announced Jan 12, 2026• 1 citation
arXivHTMLPDF

Abstract

Among variational quantum algorithms designed for NISQ devices, ADAPT-VQE stands out for its robustness against barren plateaus, particularly in estimating molecular ground states. On the other hand, counterdiabatic algorithms have shown advantages in both performance and circuit depth when compared to standard adiabatic approaches. In this work, we propose a hybrid method that integrates the ADAPT-VQE framework with counterdiabatic driving within an adiabatic evolution scheme. Specifically, we map the molecular Hamiltonian to a qubit representation and construct an adiabatic Hamiltonian, from which an approximate adiabatic gauge potential is computed using nested commutators. The resulting operator terms define the operator pool, and the ADAPT-VQE algorithm is applied to iteratively select the most relevant elements for the ansatz. Our results demonstrate improvements in performance and reductions in circuit depth compared to using either counterdiabatic algorithms or ADAPT-VQE with fermionic excitation operators, thus supporting the effectiveness of combining both paradigms in molecular simulations.

DOI
10.1021/acs.jctc.6c00197
Comments
10 pages, 5 figures, 4 tables

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Among variational quantum algorithms designed for NISQ devices, ADAPT-VQE stands out for its robustness against barren plateaus, particularly in estimating molecular ground states. On the other hand, counterdiabatic algorithms have shown advantages in both performance and circuit depth when compared to standard adiabatic approaches. In this work, we propose a hybrid method that integrates the ADAPT-VQE framework with counterdiabatic driving within an adiabatic evolution scheme. Specifically, we map the molecular Hamiltonian to a qubit representation and construct an adiabatic Hamiltonian, from which an approximate adiabatic gauge potential is computed using nested commutators. The resulting operator terms define the operator pool, and the ADAPT-VQE algorithm is applied to iteratively select the most relevant elements for the ansatz. Our results demonstrate improvements in performance and reductions in circuit depth compared to using either counterdiabatic algorithms or ADAPT-VQE with fermionic excitation operators, thus supporting the effectiveness of combining both paradigms in molecular simulations.
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Quantum algorithms offer a promising route toward computational advantage, but current implementations remain constrained by limited coherence and gate errors, making circuit complexity and noise sensitivity critical considerations. Here, we develop a shortcuts-to-adiabaticity strategy for molecular ground-state preparation and apply it to both digitized adiabatic quantum computing and the variational quantum eigensolver. In the adiabatic framework, we construct an approximate counterdiabatic (CD) Hamiltonian using a nested-commutator expansion. For the molecular systems considered, the CD correction accelerates state preparation and improves energy convergence in the fast-evolution regime, enabling a target accuracy to be reached with a lower implemented-operator count. In the variational setting, we introduce the adiabatic gauge ansatz ($\mbox{AGA}$), obtained by promoting the Pauli-string components generated by the approximate adiabatic gauge potential (AGP) to independent variational generators. We further propose a reduced variant, $\mbox{AGAR}$, that retains only Pauli generators with weight not larger than two, substantially reducing the ansatz size while maintaining competitive accuracy over the regimes considered. Benchmarks on LiH\mathrm{LiH}LiH and BeH2\mathrm{BeH}_2BeH2​ show that the proposed ansätze achieve accuracies competitive with established approaches such as UCCSD. Experiments on the \texttt{IBM\_basquecountry} superconducting quantum processor, together with simulations under depolarizing noise, show that the reduced CD-inspired ansatz yields smaller energy discrepancies than UCCSD under the noise conditions considered. Overall, our results demonstrate how AGP-inspired operator structures can be used to balance accuracy and implementation cost in molecular simulations on current noise-limited quantum hardware.
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Designing compact ansätze in Variational Quantum Eigensolver (VQE) is crucial for solving energetic problems of practical molecules on near-term quantum devices. However, existing Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) ansätze face two challenges: improper operator selection and accumulation of degraded operators. In this paper, we propose the Hamiltonian-Aware (HA) ADAPT-VQE algorithm to address these issues. First, we establish a novel excitation operator selection criterion. It breaks the local constraint of existing criteria by incorporating Hamiltonian information, prioritizes physically meaningful excitation operators, and incurs no extra classical or quantum computational overhead. Furthermore, we develop a problem-adaptive method for discriminating and pruning redundant excitation operators stemming from improper selection and inevitable degradation. This method balances redundant operator pruning and convergence guarantee, and is applicable to ansätze with arbitrary scales. Systematic numerical experiments on typical strongly correlated molecular systems demonstrate that our HA-ADAPT-VQE avoids energy plateaus and outperforms baseline algorithms in terms of energy error, ansatz size, and measurement cost. This work offers an efficient, robust ansatz construction paradigm, facilitating the development and practical deployment of large-scale VQE in quantum chemistry.
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