Abstract Non-orthogonal quantum state discrimination (QSD) is a fundamental task in quantum information processing, yet conventional methods face critical limitations in the noisy intermediate-scale quantum (NISQ) era: high circuit complexity, ambiguous cost-function interpretability, and training issues such as barren plateaus. This work proposes a variational QSD (VQSD) framework with three systematic improvements. First, we design a compact, hardware-efficient quantum circuit that approximates ideal positive-operator-valued measures without resource-intensive tomography. Second, we provide a rigorous physical interpretation of classical cost functions revealing how asymmetric weighting and L 2 -norm regularization explicitly widen the confidence gap between non-orthogonal states and suppress parameter fluctuations. Third, we introduce a random-sample preloading mechanism on ancillary qubits, which can empirically reduce error rates by two orders of magnitude. Built upon quantum decision theory, our framework establishes a direct mapping between network optimization and Bayesian risk, enabling both minimum-error discrimination (MED) and unambiguous discrimination (UD) within the same architecture. Numerical simulations achieve an ultra-low error rate of 0.0004 in UD tasks. Experiments on a real superconducting quantum processor (‘Wuyuan’) demonstrate strong noise robustness, reaching 96% discrimination accuracy in MED tasks. This work provides not only a practical and interpretable tool for QSD in the NISQ era but also a design blueprint for quantum neural networks that balance physical clarity with high trainability.
Abstract Non-orthogonal quantum state discrimination (QSD) is a fundamental task in quantum information processing, yet conventional methods face critical limitations in the noisy intermediate-scale quantum (NISQ) era: high circuit complexity, ambiguous cost-function interpretability, and training issues such as barren plateaus. This work proposes a variational QSD (VQSD) framework with three systematic improvements. First, we design a compact, hardware-efficient quantum circuit that approximates ideal positive-operator-valued measures without resource-intensive tomography. Second, we provide a rigorous physical interpretation of classical cost functions revealing how asymmetric weighting and L 2 -norm regularization explicitly widen the confidence gap between non-orthogonal states and suppress parameter fluctuations. Third, we introduce a random-sample preloading mechanism on ancillary qubits, which can empirically reduce error rates by two orders of magnitude. Built upon quantum decision theory, our framework establishes a direct mapping between network optimization and Bayesian risk, enabling both minimum-error discrimination (MED) and unambiguous discrimination (UD) within the same architecture. Numerical simulations achieve an ultra-low error rate of 0.0004 in UD tasks. Experiments on a real superconducting quantum processor (‘Wuyuan’) demonstrate strong noise robustness, reaching 96% discrimination accuracy in MED tasks. This work provides not only a practical and interpretable tool for QSD in the NISQ era but also a design blueprint for quantum neural networks that balance physical clarity with high trainability.
Abstract Quantum state discrimination (QSD) is a fundamental task in quantum information processing with numerous applications. We present a variational quantum algorithm that performs the minimum-error QSD, called the variational quantum state discriminator (VQSD). The VQSD uses a parameterized quantum circuit that is trained by minimizing a cost function derived from the QSD, and finds the optimal positive-operator valued measure (POVM) for distinguishing target quantum states. The VQSD is capable of discriminating even unknown states, eliminating the need for expensive quantum state tomography. Our numerical simulations and comparisons with semidefinite programming demonstrate the effectiveness of the VQSD in finding optimal POVMs for minimum-error QSD of both pure and mixed states. In addition, the VQSD can be utilized as a supervised machine learning algorithm for multi-class classification. The area under the receiver operating characteristic curve obtained in numerical simulations with the Iris flower dataset ranges from 0.97 to 1 with an average of 0.985, demonstrating excellent performance of the VQSD classifier.
We develop error-tolerant quantum state discrimination(QSD) strategies that maintain reliable performance under moderate noise. Two complementary approaches are proposed: CrossQSD, which generalizes unambiguous discrimination with tunable confidence bounds to balance accuracy and efficiency, and FitQSD, which optimizes the measurement outcome distribution to approximate that of the ideal noiseless case. Furthermore, we provide a unified hybrid-objective QSD framework that continuously interpolates between minimum-error discrimination (MED) and FitQSD, allowing flexible trade-offs among competing objectives. The associated optimization problems are formulated as convex programs and efficiently solved via disciplined convex programming or, in many cases, semidefinite programming. Additionally, a circuit synthesis framework based on a modified Naimark dilation and isometry synthesis enables hardware-efficient implementations with substantially reduced qubit and gate resources. An open-source toolkit automates the full optimization and synthesis workflow, providing a practical route to QSD on current quantum devices.
Variational quantum algorithms (VQAs) represent the most promising approach for achieving quantum advantage in near-term supervised learning, yet they face two fundamental challenges that severely limit their practical deployment: device noise degrades classification performance, and barren plateaus render gradient-based training ineffective. We address both challenges simultaneously through a novel hybrid architecture that selectively applies stabilizer quantum error correction only to the most noise-sensitive circuit components while preserving the variational structure essential for NISQ-era feasibility. Our approach combines Steane [7, 1, 3] encoding around entangling layers with a learned variational recovery mechanism (VarQEC). We establish rigorous theoretical foundations through two main contributions: First, we prove an explicit error-suppression theorem showing that selective protection reduces logical error scaling from O(p) to O(p 2) in the physical depolarizing rate p, with the exact leading constant p L ≤ 147 9 p 2 + O(p 3) derived through deterministic combinatorial enumeration of harmful Pauli patterns. Second, we demonstrate enhanced trainability by proving that selective encoding mitigates barren plateaus (reducing exponential suppression from physical to logical qubit scaling) while simultaneously improving noise-induced gradient attenuation from O(p) to O(p 2) through rigorous Weingarten calculus analysis. The manuscript provides complete implementation details including gate-level circuits, unambiguous training algorithms, and reproducible numerical experiments, positioning this work as both a theoretical advance and a practical framework for noise-resilient quantum machine learning.
Variational quantum algorithms hold great promise for unlocking the power of near-term quantum processors, yet high measurement costs, barren plateaus, and challenging optimization landscapes frequently hinder them. Here, we introduce sVQNHE, a neural-guided variational quantum algorithm that decouples amplitude and sign learning across classical and quantum modules, respectively. Our approach employs shallow quantum circuits composed of commuting diagonal gates to efficiently model quantum phase information, while a classical neural network learns the amplitude distribution and guides circuit optimization in a bidirectional feedback loop. This hybrid quantum-classical synergy not only reduces measurement costs but also achieves high expressivity with limited quantum resources and improves the convergence rate of the variational optimization. We demonstrate the advancements brought by sVQNHE through extensive numerical experiments. For the 6-qubit J1-J2 model, a prototypical system with a severe sign problem for Monte Carlo-based methods, it reduces the mean absolute error by 98.9% and suppresses variance by 99.6% relative to a baseline neural network, while requiring nearly 19x fewer optimization steps than a standard hardware-efficient VQE. Furthermore, for MaxCut problems on 45-vertex Erdos-Renyi graphs, sVQNHE improves solution quality by 19% and quantum resource efficiency by 85%. Importantly, this framework is designed to be scalable and robust against hardware noise and finite-sampling uncertainty, making it well-suited for both current NISQ processors and future high-quality quantum computers. Our results highlight a promising path forward for efficiently tackling complex many-body and combinatorial optimization problems by fully exploiting the synergy between classical and quantum resources in the NISQ era and beyond.
Quantum neural networks generalize classical artificial neural networks into the quantum domain. They are formulated as parameterized quantum circuits which are optimized by measuring and minimizing a suitably chosen loss function. The core challenge in understanding, implementing and ultimately using quantum neural networks is that they represent many-body systems with an exponentially large Hilbert space, in combination with a large parameter search space. Moreover, noise -- which is inherent to any quantum measurement -- sets practical limits for the estimation of training loss. Here, we study physics-informed large-scale quantum neural networks that are trained through a finite number of noisy loss function measurements. We show that this architecture permits the construction of nontrivial decision boundaries that enable the classification of quantum states through measuring an order parameter. Our approach can directly process quantum data that is output from quantum simulators and computers and is well suited for implementation on current hardware. Moreover, owed to a close link between the neural network dynamics and the evolution of Markovian open many-body quantum systems, one may expect a certain robustness to noise, which is ubiquitous in the current NISQ era.
The convergence of quantum computing and machine learning offers significant potential for processing complex data distributions. However, the realization of this potential in the Noisy Intermediate-Scale Quantum (NISQ) era is constrained by physical hardware limitations, particularly restricted qubit counts and system noise. This thesis addresses the challenge of the ”Representation Bottleneck” by establishing a framework for resource-efficient quantum representation learning. The research demonstrates that effective learning on near-term devices can be achieved by optimizing circuit architectures and objective functions to align with hardware constraints. First, to address resource limitations in high-dimensional visual recognition, we propose the Multi-Gate Quantum Convolutional Neural Network (MG-QNN). By employing a Multi-Gate strategy, this architecture optimizes the utilization of quan tum resources within the circuit design. Empirical evaluations on face recognition benchmarks indicate that this approach maintains competitive recognition accuracy while reducing the qubit requirement compared to standard quantum convolutional methods. Second, extending the framework to non-Euclidean data, we introduce the Single-Qubit Graph Neural Network (sQGNN). Utilizing Discrete-Time Quantum Walks, this method encodes graph topologies and relational patterns onto a single qubit. This approach circumvents the need for multi-qubit entangling gates, thereby reducing the computational overhead and noise sensitivity typically associated with processing graph-structured data. Third, in the domain of generative modeling, we present the Single-Qubit Quan tum Convolutional Variational Autoencoder (QCVAE). Addressing the difficulty of generative tasks on constrained devices, this model integrates the Information Bottleneck principle with efficient data re-uploading techniques. The study demonstrates that a single qubit possesses sufficient expressivity to model and reconstruct image distributions effectively when guided by appropriate information theoretic constraints. Finally, to resolve the fundamental limitations of classical loss functions in quantum learning, we establish the Hilbert-Schmidt Information Bottleneck (HSIB). We identify that standard Euclidean metrics often fail to respect the geometric structure of the Hilbert space. The HSIB framework employs the Hilbert Schmidt distance as a tractable geometric measure, providing a learning objective that maximizes information retention while adhering to the intrinsic geometry of quantum states. Collectively, these contributions illustrate that practical quantum machine learning advantage in the NISQ era does not rely solely on scaling hardware, but on the strategic design of resource-efficient architectures and geometrically valid metrics.