# Quantum Solutions Library Canonical URL: https://superpositions.studio/quantum-solutions-library Superpositions Studio publishes applied quantum use cases, algorithm explainers, and benchmark comparisons across finance, healthcare, manufacturing, chemistry, and optimization. ## Finance - [Quantum Fraud Detection with QNN and Grover](https://superpositions.studio/finance/fraud-detection-grover): Detect financial fraud with a QNN and Grover search pipeline, with reproducible benchmarks, classical baselines, and downloadable reports. - [Portfolio Knapsack Optimization with QAOA and QWM](https://superpositions.studio/finance/portfolio-knapsack-qaoa-qwm): Run constrained portfolio knapsack optimization with QAOA and a Quantum Walk Mixer, with feasibility checks, MILP benchmarks, and reproducible outputs. - [Mean-Variance Portfolio Optimization with HHL](https://superpositions.studio/finance/portfolio-optimization-hhl): Benchmark mean-variance portfolio optimization with the HHL algorithm, allocation weights, risk checks, and reproducible reports for constrained portfolios. - [Cardinality-Constrained Portfolio Optimization with Quantum Annealing](https://superpositions.studio/finance/portfolio-optimization-quantum-annealing): Solve cardinality-constrained portfolio optimization with QUBO and quantum annealing, including risk-return benchmarks, exact K-of-N selection, and reproducible outputs. - [VaR and CVaR Estimation with IQAE](https://superpositions.studio/finance/var-cvar-risk-estimation-iqae): Estimate Value at Risk and Conditional Value at Risk with Iterative Quantum Amplitude Estimation, Monte Carlo benchmarks, and reproducible reports. ## Healthcare - [Breast Cancer Classification with QSVM](https://superpositions.studio/healthcare/breast-cancer-classification-qsvm): Evaluate breast cancer classification with QSVM from FNA image features, with reproducible baselines, diagnostic metrics, and research-grade reports. - [Breast Cancer Classification with LS-QSVM and HHL](https://superpositions.studio/healthcare/breast-cancer-classification-qsvm-hhl): Benchmark breast cancer classification with LS-QSVM and HHL using reproducible workflows, classical baselines, and interpretable diagnostic metrics. ## Manufacturing - [Additive Manufacturing Anomaly Detection with QSVM](https://superpositions.studio/manufacturing/anomaly-detection-qsvm): Detect additive manufacturing anomalies with QSVM and quantum kernels, with reproducible benchmarks, baseline comparisons, and implementation notes. - [Hydraulic System Monitoring with HQNN](https://superpositions.studio/manufacturing/hydraulic-system-monitoring-qnn): Monitor hydraulic system conditions with HQNN, reproducible accuracy benchmarks, classical baselines, and predictive maintenance workflows. - [Melt Pool Shape Classification with QSVM](https://superpositions.studio/manufacturing/meltpool-shape-classification-qsvm): Classify melt-pool shapes in additive manufacturing with QSVM, reproducible multi-class benchmarks, and quality-control reports. - [Predictive Maintenance with HQNN](https://superpositions.studio/manufacturing/predictive-maintenance-hqnn): Run predictive maintenance with HQNN on production telemetry, with reproducible metrics, classical baseline comparisons, and executable code. - [Steel Plate Fault Detection with QSVM](https://superpositions.studio/manufacturing/steel-plate-fault-detection-qsvm): Detect steel plate faults with QSVM, reproducible industrial benchmarks, downloadable reports, and inspection-ready classification workflows. ## Chemistry and Materials - [Molecular Optimization with VQE Simulations](https://superpositions.studio/chemistry-materials/molecular-optimization-vqe): Optimize molecular structures with VQE simulations, ground-state energy estimation, reproducible reports, and quantum chemistry benchmarks. ## Algorithms - [Grover's Algorithm for Quantum Search](https://superpositions.studio/algorithms/grover-algorithm): Learn and benchmark Grover. - [HHL Algorithm for Quantum Linear Systems](https://superpositions.studio/algorithms/hhl-harrow-hassidim-lloyd): Explore the Harrow-Hassidim-Lloyd algorithm for quantum linear systems, portfolio optimization examples, and reproducible benchmark pipelines. - [Hybrid Quantum Neural Network](https://superpositions.studio/algorithms/hqnn-hybrid-quantum-neural-network): Benchmark hybrid quantum neural networks for classification and regression with reproducible pipelines, classical baselines, and implementation notes. - [QAOA for QUBO and Ising Optimization](https://superpositions.studio/algorithms/qaoa-quantum-approximate-optimization-algorithm): Explore the Quantum Approximate Optimization Algorithm for QUBO and Ising problems with reproducible benchmarks, parameter schedules, and hardware notes. - [Quantum Neural Networks](https://superpositions.studio/algorithms/qnn-quantum-neural-networks): Benchmark parameterized quantum neural networks for classification and regression with reproducible experiments, classical baselines, and NISQ implementation notes. - [Quantum Support Vector Machine](https://superpositions.studio/algorithms/qsvm-quantum-support-vector-machine): Build and benchmark quantum support vector machine pipelines with quantum kernels, classical SVM baselines, and reproducible machine learning workflows. - [Quantum Annealing for QUBO and Ising Problems](https://superpositions.studio/algorithms/quantum-annealing-for-qubo-optimization): Map combinatorial optimization problems to QUBO and Ising form and benchmark quantum annealing with reproducible runs, baselines, and hardware notes. - [Variational Quantum Eigensolver](https://superpositions.studio/algorithms/vqe-variational-quantum-eigensolver): Estimate ground-state energies with the Variational Quantum Eigensolver using reproducible quantum chemistry workflows, benchmarks, and implementation notes. ## Comparisons - [QAOA vs MILP for Portfolio Knapsack Optimization](https://superpositions.studio/comparisons/qaoa-vs-milp): Compare constrained QAOA with MILP on a 5-asset portfolio knapsack PoC using an 11-qubit simulator run, feasibility checks, and objective-quality audits. - [QSVM vs Classical SVM for Classification](https://superpositions.studio/comparisons/qsvm-vs-classical-svm): Compare QSVM with classical SVM on a 569-sample breast-cancer benchmark with 30 FNA features, 4 qubits, 2 layers, 96% accuracy, and 0.99 ROC-AUC.