Measurement-Efficient Differentiable Quantum Architecture Search for Combinatorial Optimization

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.

Deep reinforcement learning for quantum circuit optimization faces three bottlenecks: replay buffers that overlook temporal difference (TD) target reliability, curriculum-based architecture search requiring a full quantum-classical evaluation after every edit, and the discard of noiseless trajectories when retraining under hardware noise. We address these limitations by treating replay as a central algorithmic lever. We introduce ReaPER+, an annealed replay rule that transitions from TD-error prioritization to reliability-aware sampling as value estimates mature. ReaPER+ achieves up to 4x higher sample efficiency than fixed PER, ReaPER, and uniform replay, while matching prior on-policy solution quality with up to 32x fewer interactions At 12 qubits, fixed ReaPER reaches the lowest energy error in the fewest steps, while PER and uniform replay find more compact circuits at higher error. On tasks scaling to 20 qubits, ReaPER+ retains its advantage, demonstrating that reliability-aware annealing extends beyond small-system benchmarks. LunarLander-v3 confirms that the ReaPER+ is domain-agnostic, it improves success rates by up to 26.8% over PER and 21.8% over fixed ReaPER, with a 3% AUC gain over both. We further introduce OptCRLQAS, which amortizes quantum-classical evaluations across multiple architectural edits, reducing training wall-clock time by up to 67.5% on 12-qubit without degrading solution quality. Finally, lightweight replay-buffer transfer warm-starts noisy optimization from noiseless trajectories, without weight transfer or $ε$-greedy pretraining, reducing steps to chemical accuracy by 85-90% and final energy error by up to 90% relative to from-scratch learning. Transfer gains increase with system size. Together, these results establish experience storage, sampling, and transfer as decisive levers for sample efficient, noise-aware quantum circuit optimization.

Extracting quantum information from a quantum state is a fundamental task of quantum computation, often requiring the estimation of many non-commuting observables under a finite measurement budget. For both near-term and early fault-tolerant settings, the measurement protocol must balance statistical efficiency against implementation resources such as circuit depth, connectivity, and entangling-gate count. Many existing strategies focus on two extremes: hardware-friendly product measurements with high sampling cost, and fully commuting measurements with deep circuits. Here we recast resource-constrained measurement design as a generative learning problem. We introduce FlowMeas, which uses a generative flow network to directly sample finite ensembles of shallow Clifford measurement circuits subject to a prescribed shot budget and hardware constraints. At zero entangling depth, FlowMeas learns qubit-wise commuting measurement schedules and already matches or improves leading product-measurement methods on nearly all molecular benchmarks. Allowing one or two entangling gate layers yields further reductions in energy estimation error of up to $27\%$ relative to the strongest state-independent product-measurement baseline. The learned policy can also be reused across related Hamiltonians, substantially accelerating retraining along a molecular potential-energy surface. We further obtain results for molecular Hamiltonians with up to 20 qubits and apply the framework to a compactly encoded 54-qubit interacting fermionic model, extending the demonstrated scale beyond prior molecular benchmarks. These results establish generative learning as a flexible and unified framework for quantum measurement design under practical resource constraints.