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arXiv:2606.05968

Shattering the Symmetry Trap in Fixed-Ansatz VQE: An Accelerated ADAPT-VQE Study of Three Pillar Molecules under Bravyi-Kitaev Mapping

Hermawan Kresno Dipojono

quant-phSubmitted Jun 4, 2026• Announced Jun 5, 2026• 0 citations
arXivHTMLPDF

Abstract

Fixed-ansatz Variational Quantum Eigensolvers (VQE), such as the Unitary Coupled Cluster with Singles and Doubles (UCCSD) framework, frequently suffer from severe initialization paralyzation and zero-gradient traps when evaluated using the non-local Bravyi-Kitaev (BK) fermion-to-qubit mapping. In this work, we systematically demonstrate how the Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT-VQE) framework shatters these structural limitations across three distinct electronic and geometric molecular pillars: Lithium Hydride ($\text{LiH}$), Hydrogen Fluoride ($\text{HF}$), and Water ($\text{H}_2\text{O}$), under heavily stretched or asymmetric multi-reference configurations. While conventional UCCSD-VQE flatlines completely at a zero energy shift ($0.000000$~Ha) due to global phase cancellations inherent to the BK tree structures, our dynamic ADAPT-VQE loop successfully isolates the dominant symmetry-breaking operators using analytical commutator gradients. To bypass the severe $\mathcal{O}(N^3)$ computational bottlenecks of dense matrix exponentiation and Singular Value Decomposition on larger registers, we implement a highly optimized, vector-based Taylor series expansion state-evolution engine. Our numerical results show that the accelerated ADAPT-VQE framework achieves instant, exact Full Configuration Interaction (FCI) convergence within the very first macro-cycle across all three molecular systems, maintaining absolute numerical stability up to a 12-qubit register space. This study establishes a robust, hardware-efficient path for simulating strongly correlated, highly polarized triatomic chemical environments on near-term local architectures.

Comments
8 pages, including raw algorithmic telemetry logs

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Simulating strongly correlated molecular systems on near-term quantum hardware remains challenging because current hardware offers limited quantum volume and moderate-fidelity qubits. One way to address this challenge is through bootstrap embedding (BE). Bootstrap embedding partitions molecules into smaller fragments that are then embedded in the ``bath'' of other fragments iteratively. Bootstrap embedding is appealing for quantum simulation because fragmentation reduces the qubit requirements of each fragment problem. In this work, we develop a quantum bootstrap embedding (QBE) workflow that uses variational quantum eigensolver (VQE) fragment solvers and examines the algorithmic choices that determine the success of the overall VQE-QBE procedure. To improve efficiency, we introduce FastAdaptVQE, a sparse-matrix-accelerated form of the adaptive variational quantum eigensolver (ADAPT-VQE) that replaces symbolic commutator evaluation with direct statevector calculations, and MatrixFreeAdaptVQE, a matrix-free extension that removes the sparse-matrix memory bottleneck that arises for larger fragments. We also explore modifying the ADAPT-VQE operator-selection step by replacing the purely greedy choice with a lookahead strategy. Benchmarks on H4_44​, F2_22​, and selected geometries of H6_66​ reach chemical accuracy, within 1 kcal/mol of BE results obtained with a full configuration interaction (FCI) solver. For nnn-butane, density-matching residuals converged, but energy errors remained outside chemical accuracy. These results show that combining QBE with VQE can accurately compute molecular energies, while density convergence alone does not ensure energy accuracy. This work lays the foundation for extending these energy calculations to larger molecular systems and quantum materials on near-term quantum hardware.
While fermion-to-qubit isomorphisms are mathematically invariant under exact unitary statevector transformations, their physical implementation on noisy intermediate-scale quantum (NISQ) devices introduces severe, practical measurement bottlenecks. In this work, we systematically investigate the measurement efficiency of adaptive derivative-assembled pseudo-trotter variational quantum eigensolver (ADAPT-VQE) algorithms across three critical molecular benchmarks (LiH, BeH2, and H2O) at stretched bond lengths (2xRe) covering distinct point-group symmetries. First, we establish exact representation invariance across all target multi-reference geometries, demonstrating that operator pool gradients and statevector electronic energies remain strictly isomorphic under exact mathematical execution (E(LiH) = -7.691469 Ha, E(BeH2) = -15.110110 Ha, and E(H2O) = -74.566874 Ha). Second, we quantify the hardware measurement overhead by partitioning operator pool observables into qubit-wise commuting (QWC) tensor-product basis (TPB) cliques. We reveal that while both Jordan-Wigner (JW) and Bravyi-Kitaev (BK) encodings yield identical total Pauli term counts across the singlet excitation manifold (128 terms for H2O and BeH2), the hierarchical binary-tree layout of the BK mapping dramatically compresses the required measurement circuits---achieving up to a 45.31% reduction in total hardware execution steps compared to 12.50% under JW. Our findings demonstrate that tree-structured mappers serve as implicit, highly efficient measurement-packing engines for adaptive quantum simulations without altering the underlying variational trajectory.