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QR-SPPS: Quantum-Native Retail Supply Chain Risk Simulation via VQE, ADAPT-VQE Counterfactual Policy Ranking, and DOS-QPE Boltzmann Tail Risk Quantification

Sumit Tapas Chongder

Abstract

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.

QR-SPPS: Quantum-Native Retail Supply Chain Risk Simulation via VQE, ADAPT-VQE Counterfactual Policy Ranking, and DOS-QPE Boltzmann Tail Risk Quantification

Abstract

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.

Paper Structure

This paper contains 38 sections, 12 equations, 6 figures, 8 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Quantum Computing Approach
  3. Contributions
  4. Related Work
  5. Qiskit Implementation Framework
  6. Software Stack
  7. VQE Circuit Design
  8. Pipeline Workflow
  9. Supply Chain Ising Formulation
  10. 40-Node Network Definition
  11. Ising Hamiltonian Encoding
  12. Sub-Network Verification
  13. Shock Scenarios
  14. VQE: Ground State with Zero Error
  15. Qiskit VQE Implementation
  16. ...and 23 more sections

Figures (6)

  • Figure 1: QR-SPPS 40-node supply chain network. Node colour encodes tier; node size $\propto$ VQE stress probability $P(|1\rangle)$; edge width $\propto J_{ij}$. Simulated via Qiskit Aer statevector_simulator.
  • Figure 2: Hamiltonian validation. Left: 12-qubit eigenspectrum (NumPy exact diag.), $E_0^{[12]}=-14.772$ a.u., $\Delta=2.740$ a.u. Centre: Linear energy density; slope $-2.062$ a.u./qubit, $R^2=0.985$. Right: Energy density bars at 4--12q and extrapolated 30q and 40q values.
  • Figure 3: VQE results (Qiskit Aer). Left: 5 COBYLA restarts converging to $E_0^{[30\mathrm{q}]}=-54.296$ a.u. Centre: Depth study; all depths achieve $<10^{-7}$ error. Right: Quantum advantage map $\Delta P_i$; red bars exceed $|\Delta P|=0.15$; 14/40 nodes.
  • Figure 4: ADAPT-VQE policy analysis (Qiskit Aer). Left: Energy change $\Delta E^{[40\mathrm{q}]}$; negative = stabilisation. Centre: Gradient $g_\mathcal{P}$; Supplier subsidy leads at 3.764. Right: Node-level stress heatmap (6 policies $\times$ 40 nodes).
  • Figure 5: DOS-QPE results (Qiskit Aer). Top: Survival amplitude $A(t)$; density of states $D(E)$; Fourier spectrum (Nyquist = 1.550, no aliasing). Bottom: Boltzmann tail risk $P_{\mathrm{cat}}(T)$ (6 policies); cascade heatmap (40 nodes, 8 snapshots); tier-level cascade trajectories.
  • ...and 1 more figures