• Resource estimates and sampled kernel outcomes describe different programs. Neither demonstrates quantum advantage; this is not a quantum-state animation.
• No successful local-simulator histogram in the selected run source.
• Archived problem; not an active quantum-advantage candidate.
• This poster was rendered from an earlier estimate (12 logical, 64,204 physical qubits for Main.EvaluateQaoaMission([[0.0,1.0,0.5],[1.0,0.0,0.8],[0.5,0.8,0.0]], 0.5, 0.5, 1, 1)). The kernel or the estimated program changed on 2026-09-26; the current estimate is 15 logical, 70,255 physical qubits for Main.EvaluateQaoaMission([[2.5,1.8],[1.2,0.8],[3.1,2.4],[1.5,1.0]], 0.667588438887831, 1.3940817400304706, 1, 1).

This run was recorded in April 2026 against a hardware kernel that implemented a different model, aligned on 2026-09-26. The shot distribution below is a real measurement, but it is a measurement of a program that no longer exists in this repository, and it has not been re-run against the current kernel.

Trajectory optimization is well-served by classical methods. QAOA for routing/scheduling has the same unproven-advantage limitations as other combinatorial optimization problems. This kernel is a four-leg toy QUBO, not a trajectory optimizer.

Problem 20 · Toy QAOA Mission-Planning QUBO

Overview

This archived problem contains a heuristic mission-scoring script and a separate Q# depth-1 QAOA toy QUBO. The Q# model chooses one of two options for each of four mission legs and adds a pairwise penalty when two legs choose the same option. It is not a patched-conic trajectory optimizer.

Correction (2026-09-26): Earlier text blurred the classical patched-conic scoring script with the Q# model, and the hardware kernel used a different three-qubit chain with different biases. The hardware kernel now matches the four-leg model in Main.RunMissionOptimization and uses optimized p=1 angles. Existing website emulator results predate this alignment and should be labelled as stale until regenerated.

Verified toy model

• Q# source: `qsharp/src/Main.qs`.
• Hardware kernel: `qsharp/HardwareKernel.qs`.
• Cost function: four option costs `[[2.5, 1.8], [1.2, 0.8], [3.1, 2.4], [1.5, 1.0]]` plus `0.5` for each equal-option pair.
• Exact brute-force optimum of the toy QUBO: `7.9`.
• Exact state-vector expectation at the optimized p=1 angles `gamma=0.667588438887831`, `beta=1.3940817400304706`: `8.567469059209166`.
• Approximation ratio for this minimization toy objective: `1.0845`.
• There is no proven QAOA speedup claimed for this problem.

Classical baseline

python/classical_baseline.py implements heuristic patched-conic scoring for YAML mission records. It estimates aggregate delta-v, slack, feasibility, and a mission score. It is not the same objective as the Q# toy QUBO.

Directory Layout

20_space_mission_planning/
├── ARCHIVED.md
├── README.md
├── estimates/
├── instances/
├── plots/
├── python/
│   ├── analyze.py
│   ├── classical_baseline.py
│   └── test_baseline.py
└── qsharp/
    ├── HardwareKernel.qs
    ├── qsharp.json
    └── src/
        └── Main.qs

Quick Start

cd problems\archived\20_space_mission_planning
python python\classical_baseline.py
python python\analyze.py
python -c "from qdk import qsharp; qsharp.init(project_root='qsharp'); print(qsharp.run('Main.RunMissionOptimization()', 1))"

Objective Maturity Gate

• **Current gate**: **Stage B complete** for a toy QUBO scaffold only.
• **Next gate target**: none scheduled. Any future mission-planning claim must compare the same objective on both classical and quantum sides.

DiVincenzo Readiness (Stage C/D Overlay)

| Criterion | Status | Evidence / Notes |

|---|---|---|

| Scalable qubit system | partial | Four toy QUBO variables are implemented; no realistic trajectory encoding exists. |

| Initialization | partial | Uniform-superposition QAOA initialization is implemented for the toy model. |

| Coherence vs gate time | not-yet | Backend-calibrated coherence-vs-depth evidence is not current after kernel alignment. |

| Universal gate set | partial | The Q# and QASM circuits use standard one- and two-qubit gates. |

| Qubit-specific measurement | partial | Computational-basis measurement is implemented; hardware readout characterization is stale. |

Advantage Claim Contract

• **Claim category (current)**: `theoretical`.
• **Fair baseline**: heuristic patched-conic scoring for YAML records, plus exact enumeration for the four-bit Q# toy model in tests.
• **Residual risks**: the classical heuristic and Q# toy objective are different models, and shared website emulator records are stale until regenerated.