# Complete-cycle quantum energy audit

Close every preparation, control, feedback, extraction, and reset channel before evaluating a net-work claim.

## Learner edition

## 1. Derive the complete-cycle balance

**Task type:** derivation

For a measured-and-feedback quantum cycle, derive the first-law balance including working-medium energy, extracted work, heat, measurement/control work, memory reset, and state return. Show the condition under which a partial-cycle gain disappears.

### Deliverables

- Stage-resolved symbolic ledger
- Complete-cycle net-work expression
- State-return and ideal-limit checks

### Scoring criteria

- Energy terms and signs: 8 points
- Information/control costs included: 7 points
- Cycle-closure checks: 5 points

## 2. Optimize against honest null benchmarks

**Task type:** analysis

Using a synthetic cycle dataset, estimate net work and uncertainty across feedback strength and temperature. Compare with no-feedback, randomized-feedback, and best classical-controller benchmarks.

### Deliverables

- Complete-cycle records for at least 24 conditions
- Net-work confidence intervals and benchmark plot
- Optimization-bias correction or held-out confirmation

### Scoring criteria

- Ledger closes for each condition: 7 points
- Benchmarks and uncertainty are appropriate: 7 points
- Optimization bias is controlled: 6 points

## 3. Preregister a closed-cycle device test

**Task type:** design

Design a device-level test of a restricted quantum-energy claim with independent metering of drive, control, refrigeration, reset, and useful output. Specify drift controls and an outcome that closes the claim.

### Deliverables

- System boundary and metering diagram
- Null, sham, and calibration schedule
- Unblinding, closure, and replication rules

### Scoring criteria

- Boundary includes all required resources: 7 points
- Metrology can resolve the claimed effect: 7 points
- Decision rules prevent partial-ledger claims: 6 points

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Evidence rule: distinguish calculation, model-dependent inference, experimental observation, and unresolved claim in every response.