Neural Information Processing Systems http://nips.cc/

Quantum computing promises a revolution in information processing, with significant potential for machine learning and classification tasks. However, achieving this potential requires overcoming several fundamental challenges. One key limitation arises at the prediction stage, where the intrinsic randomness of quantum model outputs necessitates repeated executions, resulting in substantial overhead. To overcome this, we propose a novel measurement strategy for a variational quantum classifier that allows us to define the unambiguous quantum classifier. This strategy achieves near-deterministic predictions while maintaining competitive classification accuracy in noisy environments, all with significantly fewer quantum circuit executions. Although this approach entails a slight reduction in performance, it represents a favorable trade-off for improved resource efficiency. We further validate our theoretical model with supporting experimental results.

We propose and evaluate a quantum-inspired algorithm for solving Quadratic Unconstrained Binary Optimization (QUBO) problems, which are mathematically equivalent to finding ground states of Ising spin-glass Hamiltonians. The algorithm employs Matrix Product States (MPS) to compactly represent large superpositions of spin configurations and utilizes a discrete driving schedule to guide the MPS toward the ground state. At each step, a driver Hamiltonian -- incorporating a transverse magnetic field -- is combined with the problem Hamiltonian to enable spin flips and facilitate quantum tunneling. The MPS is updated using the standard Density Matrix Renormalization Group (DMRG) method, which iteratively minimizes the system's energy via multiple sweeps across the spin chain. Despite its heuristic nature, the algorithm reliably identifies global minima, not merely near-optimal solutions, across diverse QUBO instances. We first demonstrate its effectiveness on intermediate-level Sudoku puzzles from publicly available sources, involving over $200$ Ising spins with long-range couplings dictated by constraint satisfaction. We then apply the algorithm to MaxCut problems from the Biq Mac library, successfully solving instances with up to $251$ nodes and $3,265$ edges. We discuss the advantages of this quantum-inspired approach, including its scalability, generalizability, and suitability for industrial-scale QUBO applications.

Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of the Hilbert space, QML faces practical limits in classical simulations with the state-vector representation of quantum system. On the other hand, phase-space methods offer an alternative by encoding quantum states as quasi-probability functions. Building on prior work in qubit phase-space and the Stratonovich-Weyl (SW) correspondence, we construct a closed, composable dynamical formalism for one- and many-qubit systems in phase-space. This formalism replaces the operator algebra of the Pauli group with function dynamics on symplectic manifolds, and recasts the curse of dimensionality in terms of harmonic support on a domain that scales linearly with the number of qubits. It opens a new route for QML based on variational modelling over phase-space.

Ensembles of neural network weight matrices are studied through the training process for the MNIST classification problem, testing the efficacy of matrix models for representing their distributions, under assumptions of Gaussianity and permutation-symmetry. The general 13-parameter permutation invariant Gaussian matrix models are found to be effective models for the correlated Gaussianity in the weight matrices, beyond the range of applicability of the simple Gaussian with independent identically distributed matrix variables, and notably well beyond the initialisation step. The representation theoretic model parameters, and the graph-theoretic characterisation of the permutation invariant matrix observables give an interpretable framework for the best-fit model and for small departures from Gaussianity. Additionally, the Wasserstein distance is calculated for this class of models and used to quantify the movement of the distributions over training. Throughout the work, the effects of varied initialisation regimes, regularisation, layer depth, and layer width are tested for this formalism, identifying limits where particular departures from Gaussianity are enhanced and how more general, yet still highly-interpretable, models can be developed.

Designing and optimizing task-specific quantum circuits are crucial to leverage the advantage of quantum computing. Recent large language model (LLM)-based quantum circuit generation has emerged as a promising automatic solution. However, the fundamental challenges remain unaddressed: (i) parameterized quantum gates require precise numerical values for optimal performance, which also depend on multiple aspects, including the number of quantum gates, their parameters, and the layout/depth of the circuits. Extensive evaluation shows improvements in both syntax and semantic performance of the generated quantum circuits. We release our model at HuggingFace and provide the training code at GitHub. Quantum hardware has improved remarkably in recent years (AI & Collaborators, 2025; Bravyi et al., 2024; Bluvstein et al., 2024) and this rapid hardware development creates demand for improved quantum software and algorithms. Quantum software and algorithms can be categorized into classical platforms that support quantum computers themselves, including quantum error mitigation software and quantum compilers. The second category comprises domain-specific quantum algorithms, including examples like Shor's algorithm and Grover's algorithm. At the core of quantum software and algorithms is the quantum circuit model (Nielsen & Chuang, 2010), which is an assembly-level abstraction for operating gate-based quantum computers. Most of the quantum algorithms can be expressed as quantum circuits (Jordan, 2025). The design of quantum circuits is the foundation in quantum compilers and quantum algorithm development.

Quantum machine learning (QML) models conventionally rely on repeated measurements (shots) of observables to obtain reliable predictions. This dependence on large shot budgets leads to high inference cost and time overhead, which is particularly problematic as quantum hardware access is typically priced proportionally to the number of shots. In this work we propose Y ou Only Measure Once (Y omo), a simple yet effective design that achieves accurate inference with dramatically fewer measurements, down to the single-shot regime. Y omo replaces Pauli expectation-value outputs with a probability aggregation mechanism and introduces loss functions that encourage sharp predictions. Our theoretical analysis shows that Y omo avoids the shot-scaling limitations inherent to expectation-based models, and our experiments on MNIST and CIFAR-10 confirm that Y omo consistently outperforms baselines across different shot budgets and under simulations with depolarizing channels. By enabling accurate single-shot inference, Y omo substantially reduces the financial and computational costs of deploying QML, thereby lowering the barrier to practical adoption of QML. Quantum computing (Nielsen & Chuang, 2010) has emerged as a promising paradigm for advancing computational capabilities beyond the classical regime. Unlike classical machine learning, however, QML inherently involves probabilistic measurement outcomes. To obtain reliable outputs, QML models typically require repeated circuit executions, aggregating many measurement shots to estimate expectation values of observables. This reliance on repeated measurements constitutes one of the fundamental distinctions between classical and quantum machine learning.

Quantum noise fundamentally limits the utility of near-term quantum devices, making error mitigation essential for practical quantum computation. While traditional quantum error correction codes require substantial qubit overhead and complex syndrome decoding, we propose a machine learning approach that directly reconstructs clean quantum states from noisy density matrices without additional qubits. We formulate quantum noise reduction as a supervised learning problem using a convolutional neural network (CNN) autoencoder architecture with a novel fidelity-aware composite loss function. Our method is trained and evaluated on a comprehensive synthetic dataset of 10,000 density matrices derived from random 5-qubit quantum circuits, encompassing five noise types (depolarizing, amplitude damping, phase damping, bit-flip, and mixed noise) across four intensity levels (0.05-0.20). The CNN successfully reconstructs quantum states across all noise conditions, achieving an average fidelity improvement from 0.298 to 0.774 (Δ = 0.476). Notably, the model demonstrates superior performance on complex mixed noise scenarios and higher noise intensities, with mixed noise showing the highest corrected fidelity (0.807) and improvement (0.567). The approach effectively preserves both diagonal elements (populations) and off-diagonal elements (quantum coherences), making it suitable for entanglement-dependent quantum algorithms. While phase damping presents fundamental information-theoretic limitations, our results suggest that CNN-based density matrix reconstruction offers a promising, resource-efficient alternative to traditional quantum error correction for NISQ-era devices. This data-driven approach could enable practical quantum advantage with fewer physical qubits than conventional error correction schemes require.