Quantum Architecture Search (QAS) automates the design of parameterized quantum circuits for variational quantum algorithms, yet existing benchmarks organize instances by molecular identity or qubit count -- criteria agnostic to Hamiltonian structure -- and rely solely on energy accuracy, which cannot detect structural failures such as over-parameterization on near-product ground states. We introduce HamQASBench, a Hamiltonian-informed diagnostic benchmark organizing 11 molecules into five structural tiers via fingerprints derived from the Pauli operator basis, computational basis representation, and ground-state entanglement. A post-hoc critical-structure extraction procedure identifies minimal circuits consistent with each tier's requirements, complementing energy-based evaluation with per-qubit entanglement analysis and pairwise state fidelity. Benchmarking five QAS methods across four paradigms reveals failure modes invisible to conventional metrics: over-parameterization in the minimalism regime, eigenstate commitment under degeneracy, a representation bottleneck in strongly correlated systems, topology-induced routing failure, and circuit search space growth as a scalability bottleneck.
Quantum Architecture Search (QAS) automates the design of parameterized quantum circuits for variational quantum algorithms, yet existing benchmarks organize instances by molecular identity or qubit count -- criteria agnostic to Hamiltonian structure -- and rely solely on energy accuracy, which cannot detect structural failures such as over-parameterization on near-product ground states. We introduce HamQASBench, a Hamiltonian-informed diagnostic benchmark organizing 11 molecules into five structural tiers via fingerprints derived from the Pauli operator basis, computational basis representation, and ground-state entanglement. A post-hoc critical-structure extraction procedure identifies minimal circuits consistent with each tier's requirements, complementing energy-based evaluation with per-qubit entanglement analysis and pairwise state fidelity. Benchmarking five QAS methods across four paradigms reveals failure modes invisible to conventional metrics: over-parameterization in the minimalism regime, eigenstate commitment under degeneracy, a representation bottleneck in strongly correlated systems, topology-induced routing failure, and circuit search space growth as a scalability bottleneck.
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.
Designing quantum neural networks (QNNs) that are both accurate and deployable on NISQ hardware is challenging. Handcrafted ansatze must balance expressivity, trainability, and resource use, while limited qubits often necessitate circuit cutting. Existing quantum architecture search methods primarily optimize accuracy while only heuristically controlling quantum and mostly ignore the exponential overhead of circuit cutting. We introduce QNAS, a neural architecture search framework that unifies hardware aware evaluation, multi objective optimization, and cutting overhead awareness for hybrid quantum classical neural networks (HQNNs). QNAS trains a shared parameter SuperCircuit and uses NSGA-II to optimize three objectives jointly: (i) validation error, (ii) a runtime cost proxy measuring wall clock evaluation time, and (iii) the estimated number of subcircuits under a target qubit budget. QNAS evaluates candidate HQNNs under a few epochs of training and discovers clear Pareto fronts that reveal tradeoffs between accuracy, efficiency, and cutting overhead. Across MNIST, Fashion-MNIST, and Iris benchmarks, we observe that embedding type and CNOT mode selection significantly impact both accuracy and efficiency, with angle-y embedding and sparse entangling patterns outperforming other configurations on image datasets, and amplitude embedding excelling on tabular data (Iris). On MNIST, the best architecture achieves 97.16% test accuracy with a compact 8 qubit, 2 layer circuit; on the more challenging Fashion-MNIST, 87.38% with a 5 qubit, 2 layer circuit; and on Iris, 100% validation accuracy with a 4 qubit, 2 layer circuit. QNAS surfaces these design insights automatically during search, guiding practitioners toward architectures that balance accuracy, resource efficiency, and practical deployability on current hardware.
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.
Abstract Quantum computers promise to solve electronic structure, lattice dynamics, and strongly correlated problems beyond classical reach. However, near-term noisy intermediate scale quantum (NISQ) processors require systematic benchmarking to establish where variational algorithms with error mitigation can achieve chemical accuracy and cor rectly predict physical phenomena. Here we present 28 quantum material simula tions implemented with Qiskit, spanning molecular hydrogen (H 2 ) through the iron molybdenum cofactor (FeMoco), one-dimensional Hubbard chains, Kitaev honeycomb spin liquids, topological insulators (SSH model), BCS superconductors, and disordered Anderson insulators. Using the variational quantum eigensolver (VQE) with UCCSD ansatz, we achieve chemical accuracy (±1.6 mHa) for H 2 across the full dissociation curve and recover exact ground-state energies for H4 within 9 mHa after zero-noise extrapolation (ZNE) — reducing raw VQE errors from 152 mHa to 9 mHa. We accu rately identify the transverse-field Ising quantum critical point (h c = J) with 4 qubits, resolve Majorana Dirac dispersions in the Kitaev spin liquid, and reproduce the Mott transition in the Fermi-Hubbard model at U c = 6t. Resource estimation for FeMoco reveals O(N 2.5 ) scaling, projecting chemical accuracy with ∼200 logical qubits. Across all benchmarks, we quantify the accuracy-circuit depth tradeoff, demonstrating that depth-6 VQE ans¨atze achieve chemical accuracy for small molecules while depth-10 is required for correlated lattices. These results establish a comprehensive benchmark suite for evaluating quantum hardware, error mitigation protocols, and variational al gorithms for materials science on NISQ processors.
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.