Classical supply chain risk models treat node failures as statistically independent events, systematically underestimating correlated cascade failures across multi-tier supplier networks. We present QR-SPPS (Quantum-Native Retail Shock Propagation and Policy Stress Simulator), a quantum-native framework for retail supply chain risk analysis implemented on the Qiskit ecosystem using OpenFermion-based Ising Hamiltonian encoding. A 40-node, four-tier supply network is mapped to a 40-qubit Hamiltonian with ZZ coupling terms representing correlated supplier dependencies. A hardware-efficient Variational Quantum Eigensolver (VQE) computes the stress ground state, revealing entangled cascade failures that differ substantially from classical Monte Carlo predictions. We further introduce the application of ADAPT-VQE gradient screening for counterfactual policy evaluation, enabling real-time ranking of six crisis interventions without repeated variational optimization. Finally, Density-of-States Quantum Phase Estimation (DOS-QPE) reconstructs the eigenspectrum through Trotter evolution and estimates Boltzmann-weighted catastrophe probabilities as a function of market-volatility temperature, providing a quantum-native tail-risk metric compatible with Value-at-Risk analysis. The framework demonstrates scalable quantum algorithms for correlated supply chain stress propagation, policy optimization, and systemic risk quantification while highlighting the exponential computational barriers faced by classical simulation at industrial-scale problem sizes.
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38 pages, 12 figures, 9 tables. Developed for the Fujitsu Quantum Simulator Challenge 2025-26. Source code and supplementary materials are available upon request
Classical supply chain risk models treat node failures as statistically independent events, systematically underestimating correlated cascade failures across multi-tier supplier networks. We present QR-SPPS (Quantum-Native Retail Shock Propagation and Policy Stress Simulator), a quantum-native framework for retail supply chain risk analysis implemented on the Qiskit ecosystem using OpenFermion-based Ising Hamiltonian encoding. A 40-node, four-tier supply network is mapped to a 40-qubit Hamiltonian with ZZ coupling terms representing correlated supplier dependencies. A hardware-efficient Variational Quantum Eigensolver (VQE) computes the stress ground state, revealing entangled cascade failures that differ substantially from classical Monte Carlo predictions. We further introduce the application of ADAPT-VQE gradient screening for counterfactual policy evaluation, enabling real-time ranking of six crisis interventions without repeated variational optimization. Finally, Density-of-States Quantum Phase Estimation (DOS-QPE) reconstructs the eigenspectrum through Trotter evolution and estimates Boltzmann-weighted catastrophe probabilities as a function of market-volatility temperature, providing a quantum-native tail-risk metric compatible with Value-at-Risk analysis. The framework demonstrates scalable quantum algorithms for correlated supply chain stress propagation, policy optimization, and systemic risk quantification while highlighting the exponential computational barriers faced by classical simulation at industrial-scale problem sizes.
Classical supply chain risk models treat node failures as statistically independent events, systematically underestimating cascade probabilities when supplier dependencies are strongly correlated. At n=40 nodes, the full correlated failure distribution requires O(2^n) classical samples, a regime where exact simulation demands 17.6 TB of memory and over 369,000 hours of computation on a standard workstation. We present QR-SPPS (Quantum-Native Retail Shock Propagation and Policy Stress Simulator), a three-algorithm quantum pipeline implemented using the Qiskit framework with the Aer statevector_simulator backend. First, a 40-node, 4-tier retail supply network is encoded as a 40-qubit Ising Hamiltonian using OpenFermion QubitOperator, where ZZ coupling terms encode correlated cascade probabilities structurally absent from classical Monte Carlo. Second, a hardware-efficient VQE circuit finds the ground-state stress distribution with zero error, detecting entangled cascade failures in 14/40 nodes with max|ΔP|=0.637 versus classical Monte Carlo. Third, we introduce the first application of ADAPT-VQE gradient screening to counterfactual macroeconomic policy evaluation: six crisis interventions are ranked in O(1) Qiskit operator evaluations per policy, a 287x speedup over sequential VQE re-optimisation. Fourth, Density-of-States QPE (DOS-QPE) reconstructs the full eigenspectrum via 32-step Trotter evolution and introduces a novel mapping of the Boltzmann catastrophe probability P_cat(T) to VIX-equivalent market volatility temperature, enabling direct integration into regulatory Value-at-Risk frameworks. Qiskit Aer scaling benchmarks confirm exponential classical intractability at 40 qubits.
We present a rigorously derived Quantum Risk Management Framework (QRMF) integrating quantum amplitude estimation for tail risk metrics, entanglement-based systemic risk analytics, and variational quantum risk optimization. Our comprehensive approach encompasses three novel modules: (i) Quantum Risk Amplitude Estimation (QRAE) achieving quadratic sample complexity improvements over classical Monte Carlo for Value-at-Risk (VaR) and Conditional VaR (CVaR) computation through binary search with amplitude estimation subroutines; (ii) Quantum Systemic Risk Analysis (QSRA) encoding financial exposure networks into entangled bipartite states with purity-based early warning observables and QAOA partitioning for cascade mitigation; and (iii) Variational Quantum Risk Optimizer (VQRO) implementing constraint-aware portfolio optimization using risk-adjusted Hamiltonians with feasible-state ansätze and penalty-based formulations. We establish formal complexity theorems under explicit QRAM/QROM cost models, prove convergence guarantees for variational components under convex surrogate conditions, and demonstrate theoretical correspondence between entanglement purity responses and classical contagion path-sum sensitivities in linearized network models. The hybrid framework combines gate-model quantum circuits for amplitude estimation and entanglement encoding with variational quantum eigensolvers for optimization, validated through comprehensive simulations on synthetic financial networks and real market data. Extensive ablation studies on circuit depth versus accuracy trade-offs, noise resilience analysis, and resource scaling complement theoretical results, with all quantum amplitude estimation and entanglement simulations performed using Qiskit on classical hardware while baseline classical Monte Carlo and network centrality methods provide benchmarking baselines. This distinction ensures accurate interpretation of quantum advantages across the integrated risk management pipeline.
Traffic jams in a single port destabilize global supply systems, and a week of unexpected demand can derail carefully planned timetables. Even with machine learning, conventional optimization discards uncertainty and folds risk into static buffers or heuristic safety stocks. That method fails when interruptions cascade and supplier, route, and market signal linkages change hourly. We used quantum computation to reimagine that loop, where classical tools are awkward. Quantum Contextual Supply Chain Optimization under Uncertainty integrates five interconnecting methods rather than bolting them on as modules. First, Contextual Quantum Demand Graph Embedding (CQDGE) encodes supplier-customer dependencies as quantum states, providing a fuller picture than time-series predictors. Quantum-Aware Contextual Policy Gradient (QCPG) uses variational quantum circuits to direct routing and allocation in messy, nonconvex landscapes, reducing convergence time. CQRAS samples risk-weighted schedules through quantum annealing and feeds its output into a Quantum-Integrated Digital Twin Optimizer (QIDTO) that stress-tests plans against detailed virtual replicas of trucks, warehouses, and fuel markets to avoid surprises like port shutdowns. Finally, Quantum-Backpropagated Global Reinforcement Integrator (Q-BGRI) updates embeddings and policies in one differentiable loop to fold the entire experience upstream. Early studies show double-digit delivery time savings and energy cost reductions, but practical deployments may uncover unmodeled oddities. Contextual embeddings and quantum reinforcement may offer a way beyond fragile, one-shot optimizers that dominate present methods.
Traffic jams in a single port destabilize global supply systems, and a week of unexpected demand can derail carefully planned timetables. Even with machine learning, conventional optimization discards uncertainty and folds risk into static buffers or heuristic safety stocks. That method fails when interruptions cascade and supplier, route, and market signal linkages change hourly. We used quantum computation to reimagine that loop, where classical tools are awkward. Quantum Contextual Supply Chain Optimization under Uncertainty integrates five interconnecting methods rather than bolting them on as modules. First, Contextual Quantum Demand Graph Embedding (CQDGE) encodes supplier-customer dependencies as quantum states, providing a fuller picture than time-series predictors. Quantum-Aware Contextual Policy Gradient (QCPG) uses variational quantum circuits to direct routing and allocation in messy, nonconvex landscapes, reducing convergence time. CQRAS samples risk-weighted schedules through quantum annealing and feeds its output into a Quantum-Integrated Digital Twin Optimizer (QIDTO) that stress-tests plans against detailed virtual replicas of trucks, warehouses, and fuel markets to avoid surprises like port shutdowns. Finally, Quantum-Backpropagated Global Reinforcement Integrator (Q-BGRI) updates embeddings and policies in one differentiable loop to fold the entire experience upstream. Early studies show double-digit delivery time savings and energy cost reductions, but practical deployments may uncover unmodeled oddities. Contextual embeddings and quantum reinforcement may offer a way beyond fragile, one-shot optimizers that dominate present methods.
Pauli-based simulators offer a promising route to large-scale classical simulation of quantum circuits in the low-magic regime. Yet their applicability remains largely limited to forward simulation, making them inadequate for optimization-driven quantum tasks such as variational state preparation and parameter initialization. Existing approaches either lack native support for gradient-based optimization or suffer from severe gradient bias. Here we propose the stochastic Pauli-path simulator (SPPS), a computational framework for large-scale quantum optimization that enables unbiased stochastic gradient estimation via Pauli-path sampling across optimization iterations. Our theoretical analysis shows that the proposed simulator yields unbiased gradient estimates and admits provable convergence guarantees. We systematically evaluate our proposal, including quantum eigensolver benchmarks with up to 100 qubits and quantum neural network benchmarks with up to 40 qubits. Across these tasks, SPPS faithfully tracks optimization dynamics, converges within minutes, and broadens the role of Pauli-based simulation from forward estimation to large-scale quantum optimization.
This article presents a quantum-enhanced framework for optimizing complex supply chain networks (SCNs) under stochastic demand, addressing computational intractability in classical approaches. We propose a hybrid quantum-classical methodology integrating the Quantum Approximate Optimization Algorithm (QAOA) with hierarchical graph decomposition, enabling industrial-scale optimization (?100 nodes) on NISQ-era hardware. Key innovations include: (1) First quantum-native stochastic demand modeling via amplitude estimation, achieving quadratic speedup (O(log(1/?)/?)) over Monte Carlo methods; (2) A novel decomposition algorithm coordinating quantum subproblems through augmented Lagrangian optimization; (3) Error-adapted QAOA with zero-noise extrapolation, improving quantum volume utilization to 85%. Empirical validation demonstrates 42% faster computation versus classical solvers (CPLEX) while maintaining solution quality within 4.7% of optimality. The framework exhibits near-linear scalability (efficiency = 0.92) and outperforms heuristics in high-connectivity, volatile-demand scenarios. Mathematical contributions include a stochastic Hamiltonian formulation for normally distributed demand and noise-aware parameter optimization. This work establishes quantum computing as a viable tool for real-time SCN optimization, particularly for multi-period networks with uncertainty. Future research will explore multi-objective extensions, quantum machine learning integration, and dynamic reconfiguration protocols.