Quantum generative models offer a promising framework for exploring whether quantum computation can enhance generative machine learning. Flow matching is a generative method in which samples are generated by transporting a simple, known distribution to the target data distribution with a learned velocity field. Its quantum counterpart, known as quantum flow matching (QFM), was introduced recently, and, like its classical counterpart, requires integrating an ordinary differential equation over many time steps during inference. As each step requires the output from the previous step, the circuit submission is sequential and a drawback on quantum computers as they have high input/output costs. To alleviate this problem, we introduce Quantum MeanFlow (QMF), the quantum analogue of the MeanFlow formulation, which allows single-step sample generation. While the QFM learns an instantaneous velocity field at each time step, QMF learns the average velocity over a time interval. We use a parameterized quantum circuit to learn these velocity fields and benchmark the two methods on the MNIST dataset. We show that while single-step QMF has lower image quality compared to multi-step QFM, it performs better than the single-step QFM sampling at every shot count. Both of our models are executed on IBM quantum computers and best-of-N rejection sampling recovers most of the accuracy lost to device noise without modifying the circuit. This is especially advantageous for QMF which has only one circuit evaluation per image. Here, We establish QMF as a viable method for single-step quantum generative sampling, saving on quantum circuit evaluations per generated sample.
The NISQ era places stringent constraints on quantum computation, where noise and decoherence fundamentally limit performance. In classical deep learning, model robustness and resilience to perturbations are well studied: deep neural networks (DNNs) maintain high performance despite pruning, noise injection, and structural perturbations due to inherent redundancy in their representations. A central challenge in quantum machine learning is to transfer this notion of robustness to quantum neural networks (QNNs) under realistic NISQ noise. While classical deep learning exhibits robustness through structural redundancy, analogous principles for QNNs remain underdeveloped. We propose JGRA: a framework for assessing robustness in noise-aware QNNs via Jacobian geometry, capturing model sensitivity to parameter perturbations induced by noise. Our method includes entropy-matched noise calibration, noise-aware training, and noise-conditioned Jacobian extraction, yielding geometric descriptors that link clean-regime structure to noisy inference behaviour. We also empirically demonstrate that these descriptors encode predictive information about robustness under unseen noise.
Noisy intermediate-scale quantum (NISQ) processors are entering an early fault-tolerance regime where full quantum error correction carries prohibitive resource costs, yet lightweight error detection can meaningfully improve algorithmic success rates. Existing compilation and error-detection toolchains treat these concerns in isolation, with no principled way to balance detection overhead against success probability under latency constraints. We present an integrated hardware-aware compilation and data-driven quantum error-detection (QED) framework that jointly optimises qubit mapping, SWAP insertion, and syndrome-schedule placement via a noise-weighted cost function and a learned multi-objective scheduler. Simulation experiments on an HPC cluster using GPU-accelerated density-matrix simulation (NVIDIA cuQuantum SDK) across VQE, phase-estimation, and Grover benchmarks, three noise profiles, and circuit sizes of 6-20 qubits (depths 10-160), show that joint co-design raises algorithmic success probability by up to 68 percent (95 percent CI: 60 percent to 76 percent) over SABRE on an 8-qubit VQE instance with post-selection.