Quantum architecture search for molecular ground-state estimation is commonly evaluated through energy accuracy, which does not describe circuit cost or the physical properties of the prepared state. We introduce HamQASBench, a structure-aware benchmark comprising eleven molecular Hamiltonians of up to fourteen qubits, selected using Hamiltonian and target-state properties and supplied with exact references. Its evaluation protocol combines energy accuracy and success rates with reference-relative circuit cost, local entropy profiles for non-degenerate targets, and state identification within degenerate ground subspaces. Experiments with five methods spanning four search paradigms reveal differences hidden by energy-only comparisons. On a near-product instance under the shallow search budget, the best outputs of all five methods reach chemical accuracy while using between two and sixty-two gates. Equal-energy outputs on a degenerate instance occupy distinct spin components. Local entropy profiles distinguish inaccurate outputs and show that entangling-gate counts need not reflect realized entanglement. Across the molecular instance ladder, product-state outputs can meet or miss chemical accuracy, motivating interpretation of success alongside target-state properties. These results support retaining energy as the task-success criterion while using circuit-cost and state diagnostics for more informative comparisons. The benchmark instances, references, evaluation implementation, and per-run data are released for reuse.
Quantum architecture search for molecular ground-state estimation is commonly evaluated through energy accuracy, which does not describe circuit cost or the physical properties of the prepared state. We introduce HamQASBench, a structure-aware benchmark comprising eleven molecular Hamiltonians of up to fourteen qubits, selected using Hamiltonian and target-state properties and supplied with exact references. Its evaluation protocol combines energy accuracy and success rates with reference-relative circuit cost, local entropy profiles for non-degenerate targets, and state identification within degenerate ground subspaces. Experiments with five methods spanning four search paradigms reveal differences hidden by energy-only comparisons. On a near-product instance under the shallow search budget, the best outputs of all five methods reach chemical accuracy while using between two and sixty-two gates. Equal-energy outputs on a degenerate instance occupy distinct spin components. Local entropy profiles distinguish inaccurate outputs and show that entangling-gate counts need not reflect realized entanglement. Across the molecular instance ladder, product-state outputs can meet or miss chemical accuracy, motivating interpretation of success alongside target-state properties. These results support retaining energy as the task-success criterion while using circuit-cost and state diagnostics for more informative comparisons. The benchmark instances, references, evaluation implementation, and per-run data are released for reuse.
We evaluate deterministic higher-order product formulae for molecular ground-state energy estimation. Motivated by recent fault-tolerant architectures in which non-Clifford operations may be generated more locally and cheaply than in conventional assumptions, we re-examine such formulae as practical candidates for quantum chemistry. Using one-dimensional hydrogen chains from H2 to H15 as benchmarks, we estimate both the total gate count and the depth of RZ-rotation layers required to reach a target energy error. To make this comparison feasible at larger system sizes, we use a perturbative method to estimate the eigenvalue error induced by each product formula and thereby evaluate the cost of the corresponding phase-estimation procedure. Among the previously considered formulae, the eighth-order construction introduced by Morales et al. [M. E. S. Morales et al., "Greatly improved higher-order product formulae for quantum simulation," arXiv:2210.15817v2 (2024)] minimizes both cost metrics in the benchmark at a chemically relevant target error. We also find that increasing the formal order does not automatically reduce the total cost: near chemical accuracy, the tenth-order formula introduced in the same work can be less efficient than the eighth-order one. Motivated by this observation, we construct a new fourth-order formula; it achieves the lowest total gate count among the formulae considered for all H-chain instances near chemical accuracy and over much of the 0.1-10 mHa target-error window for most instances, while also reducing the RZ-layer depth. These results clarify how deterministic higher-order product formulae should be selected for molecular ground-state energy estimation.
Reinforcement-learning-based quantum architecture search (RL-QAS) repeatedly invokes a variational quantum eigensolver (VQE) after each gate addition even though circuit transitions and action legality are known. DreamQAS preserves these exact dynamics and learns only expensive post-VQE feedback through a recurrent ensemble that predicts a frontier-relative feedback score without requiring the exact ground-state energy, enabling uncertainty-controlled multi-step imagination. Under a common 15,000-episode budget and frozen evaluation, DreamQAS has the lowest reported mean error among RL methods on all five main molecular tasks. At fine-error targets reached by all seeds of DreamQAS and a matched non-imaginative control, it uses 1.6-2.0 times fewer real VQE calls on four tasks. Holding LiH-4q feedback-model weights fixed, its imagined-policy actor attains 0.073 mHa, versus 4.280 mHa and 4.434 mHa for greedy and beam deployment. Learned-transition and end-to-end predictor controls further show that preserving exact circuit structure and using feedback through policy learning are both important. Counterfactual action-ranking improves throughout training on all five probed tasks, while ensemble disagreement improves risk-coverage over random rejection on three tasks. DreamQAS therefore learns decision-useful feedback for QAS without modeling already-known circuit dynamics or requiring the exact ground-state energy.
Molecular ground-state energies help determine conformer rankings, reaction energetics, and electronic effects in computational drug discovery, but accurate calculations become difficult when strong correlation or large active spaces are important. Variational quantum eigensolvers estimate these energies by optimizing a parameterized quantum state, making ansatz design central to both accuracy and cost. We study a fixed-topology Givens-exchange ansatz that avoids architecture search. The circuit starts from the computational-basis state with the lowest diagonal Hamiltonian expectation and applies local RY rotations with two ordered all-pair Givens exchange blocks. Parameters are optimized using Hamiltonian expectation values, while exact diagonalization is used only after optimization to compute errors and fidelities. Across six fixed seeds, coefficient-verified LiH-6 and H2O-8 Hamiltonians, together with a BeH2-6 public-specification candidate, are chemically accurate in every run. The corresponding six-seed mean errors are 0.000000124 Hartree, equivalent to 0.000124 milli-Hartree; 0.000128558 Hartree, equivalent to 0.128558 milli-Hartree; and 0.000002152 Hartree, equivalent to 0.002152 milli-Hartree, respectively. On LiH-6 and H2O-8, these mean errors are lower than the published point errors of the compared quantum-architecture-search methods, while the ansatz uses a larger pre-compilation macro budget. The method is therefore an accurate, reproducible, and search-free reference template for molecular variational eigensolvers.
Subspace eigenvalue problems arise ubiquitously in quantum chemistry and condensed-matter physics, where the relevant object is often a low-energy manifold rather than a single ground-state wavefunction. In this work, we propose a fault-tolerant quantum algorithm for this subspace-level task based on the Feshbach effective-Hamiltonian formalism. Given block-encoding access to the full Hamiltonian and a chosen d-dimensional reference subspace, the algorithm estimates eigenvalues of states with nonzero overlap with the reference subspace through a local secant fixed-point search. It then implements the associated wave operator and prepares an orthonormal basis whose span approximates the target invariant subspace. The construction combines projected block encodings with quantum singular value transformation (QSVT), which approximates the complementary-space resolvent and thereby provides both the self-energy used for eigenvalue estimation and the wave operator used for eigenstate reconstruction. For target accuracy ε, a single evaluation of the effective Hamiltonian has query complexity O(d3/(g2ε)), up to block-encoding normalization factors, where g is the distance between the target eigenvalue and the nearest pole of the effective Hamiltonian. Under the stated local regularity conditions, the secant search requires only O(loglog(1/ε)) effective-Hamiltonian evaluations to reach the working precision. Classical numerical emulations for an open 4×2 Fermi--Hubbard cluster, all-electron LiH bond stretching, and [Ru(bpy)3]2+ demonstrate the resolution and reconstruction of low-energy states and manifolds across spin-sector crossings, near-degeneracies, and dense excited-state spectra.
Variational quantum algorithm is a leading approach for quantum chemistry and many-body physics on noisy intermediate-scale quantum devices. The performance depends strongly on the structure of the parameterized quantum circuits. Quantum architecture search (QAS) can automate ansatz design. However, it requires repeated training and evaluation of many candidate circuits, leading to high evaluation cost. In this work, we propose a noise-aware quantum architecture search framework based on ZX-calculus topological reuse (ZX-QAS). The framework encodes the search space with a ternary Gray-code mapping and integrates a noise-aware quantum neural network with a ZX-calculus topological reuse mechanism. The effectiveness of the framework is validated through ground-state energy estimation tasks and one-dimensional transverse-field Ising model tasks under noisy conditions. The results show that the ZX-QAS exhibits stable convergence and remarkably reduces the cost of expensive evaluations under noisy conditions.
Quantum error mitigation (QEM) is essential for extracting chemically accurate results from near-term quantum hardware. Many widely used QEM methods rely on uncontrolled heuristics whose bias depends on the specific circuit and noise realization. In this work, we employ QESEM---a characterization-based, unbiased quasi-probabilistic mitigation method---on IBM's Aachen quantum processor to compute the ground-state potential energy surface (PES) of the symmetrically-stretched water molecule. We consider a classically-optimized, single-layer perfect-pairing tiled unitary product state ansatz. We map this ansatz to an 8-qubit register corresponding to a (4,4) active space and the STO-3G basis set. Compared to the statevector reference, we find that raw QPU results typically overestimate the ground-state energy by around 500~mHa across the scanned geometries. On the other hand, QESEM-mitigated results fall approximately within 100~mHa, 30~mHa, or ``chemical accuracy'' ($\sim$1.5~mHa), depending on the target precision. We benchmark QESEM at both loose (0.1~Ha) and tight (0.01~Ha) precision targets, evaluating both individual and merged batches of runs. As the precision target is tightened, the accuracy improves systematically, matching or exceeding results reported in the literature. We further quantify the sampling cost of these results, reporting the number of shots required at each precision level. Our results show how, with the current levels of hardware error, reaching the highest accuracies demands substantial QPU time. The results demonstrate that the characterization-based, unbiased error mitigation provided by QESEM allows to measure quantitatively meaningful potential energy surfaces on current quantum hardware. Concurrently, they highlight the sampling overhead associated with QEM, which remains a central bottleneck en route to larger chemical problems and higher precision.