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.
The flow matching has rapidly become a dominant paradigm in classical generative modeling, offering an efficient way to interpolate between two complex distributions. We extend this idea to the quantum realm and introduce the Quantum Flow Matching (QFM), a quantum-circuit realization that offers efficient interpolation between two density matrices. QFM offers systematic preparation of density matrices and generation of samples for accurately estimating observables, and can be realized on quantum computers without the need for costly circuit redesigns. We validate its versatility on a set of applications: (i) generating target states with prescribed magnetization and entanglement entropy, (ii) estimating nonequilibrium free-energy differences to test the quantum Jarzynski equality, and (iii) expediting the study on superdiffusion. These results position QFM as a unifying and promising framework for generative modeling across quantum systems.
Reinforcement learning (RL) can automate quantum architecture search, but its scalability is limited when useful circuit trajectories become rare in the rapidly expanding search space. Existing replay mechanisms reuse observed transitions; the proposed learned model produces additional predicted one step transitions from real state-action seeds. Here we introduce GenQAS, a tensor network-guided RL framework that combines a fixed matrix product state warm-start with prioritized generative replay. A learned local transition model generates synthetic circuit transitions on demand and mixes them with real experience during Double Deep Q-Network updates. Under a random exploration analysis, near ground state circuits occupy a rapidly shrinking region of the accessible state space. We investigate whether real data anchored synthetic replay can improve the effective training signal in this regime. Across chemical Hamiltonian benchmarks from 6 to 12 qubits, GenQAS improves fixed-budget success probability and identifies compact circuits at competitive energy error. At 12 qubits, it improves final success probability by up to 7.0× over passive replay. On a 15-qubit transverse field Ising model, GenQAS increases success probability from 12% to 21%. In a noisy 6-qubit BeH2 transfer experiment, generative replay reduces the steps to chemical accuracy by 92.7%. These results show that generative replay can mitigate sample starvation in quantum architecture search and support more resource efficient circuit discovery.
Akash Kundu, Amit Kumar Jaiswal, Sebastian Feld +1
Communication complexity provides a natural framework for quantifying the classical resources required to reproduce quantum statistics. In the qubit prepare-and-measure scenario, two classical bits have been shown to be necessary and sufficient to simulate arbitrary qubit states and arbi- trary quantum measurements exactly. However, this result does not exclude the possibility that restricted families of measurements may admit accurate 1-bit classical approximations. We use a neural network procedure to demonstrate that a single bit can achieve high average accuracy for specific measurement families. A performance analysis of our neural network reveals that symmet- ric measurements with uniformly weighted elements, such as those forming regular polyhedra, are particularly amenable to this restricted communication. By analyzing the patterns learned by the neural network, we derive an analytical protocol that is extremely accurate for finite information- ally complete symmetric configurations and becomes exact in the limit of a continuous isotropic measurement.