Applied Quantum Computing Case Study — Public Policy & Machine Learning

Public Policy & ML- Hybrid VQE Accelerates NP‑Hard Redistricting Optimisation

1 | Civic Tech Brief
A non‑profit must propose congressional redistricting maps that satisfy contiguity, equal‑population, and partisan‑fairness constraints—an NP‑hard combinatorial search. Classical simulated annealing (GPU) takes hours per state at 1 K map iterations.

2 | Solution Outline
Use Variational Quantum Eigensolver (VQE) on QPU to find lower‑energy (fairer) district boundary sets; GPU handles constraint scoring, QPU solves Hamiltonian minimisation.

3 | Workflow

Civic Tech Quantum Workflow (VQE + GPU Timeline)

🧠 Key Components:

• GPU handles:

  • Building adjacency matrix (county graph)

  • Encoding fairness/contiguity constraints into Hamiltonian

  • Scoring (energy), gradient (∇E) via SPSA optimizer

• QPU (e.g. Rigetti Aspen-M) runs VQE circuits to evaluate energy for given θ (parameter vector)

• Sidecar (gRPC service) handles communication between classical and quantum layers

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⚖️ Optimization Objective:

Minimize a Hamiltonian:

H = α·(population variance) + β·(partisan bias) + γ·(boundary cuts)

Subject to: contiguity, equal-pop, compactness.

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4 | Quil Sample

Code repository for doing hands on exercise Indicative Project Source code

HAMILTONIAN = """
# qubit indexed counties
#   H = Σ w_ij Zi Zj + Σ b_i Zi
"""
from pyquil import Program, get_qc
from openfermion.utils import qubit_operator_sparse

prog = Program()              # Add parameterised RX,RZ gates ...
qc = get_qc("Aspen-M-2")
result = qc.compile_and_run(prog, shots=1000)

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5 | Kubernetes Considerations
1. Add PriorityClass for qpu-gateway (score 100000) so it preempts non‑critical pods if node pressure.
2. Gateway taint toleration for CPU‑only nodes.

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6 | Outcomes
1. Average objective energy 7 % lower than best classical anneal after 15 min compute budget.
2. Generated 25 candidate maps per state (Ohio, Georgia) vs. 8 previously, giving policy analysts richer option space.

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7 | Ethical Notice
1. All data open‑sourced; algorithmic choices published for transparency.
2. Quantum layer did not bias fairness metric; rather improved search coverage.

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