The Spacetime Metric

Level 6 · Research preparation · advanced assessment

Complete-cycle quantum energy audit

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

Complete all three challenges. Show assumptions, units, uncertainty, and the boundary between calculation, model-dependent inference, observation, and unresolved claim.

Challenge 1 · derivation

Derive the complete-cycle balance

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.

Required deliverables

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

Scoring criteria · 20 points

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

Challenge 2 · analysis

Optimize against honest null benchmarks

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.

Required 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 · 20 points

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

Challenge 3 · design

Preregister a closed-cycle device test

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.

Required deliverables

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

Scoring criteria · 20 points

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

Instructor solution outlines

Look for reasoning that survives inspection

1. Derive the complete-cycle balance

  • Assign energy flows to preparation, measurement, feedback, extraction, and reset.
  • Include the controller and memory among the resources that must be restored.
  • A positive extraction stage does not imply positive complete-cycle work.

2. Optimize against honest null benchmarks

  • Compute net work only where every declared stage and state-return flag is present.
  • Tune on one subset and confirm the selected condition on held-out cycles.
  • Attribute an advantage only relative to the strongest preregistered comparable benchmark.

3. Preregister a closed-cycle device test

  • Measure every energy channel on a common clock and calibration basis.
  • Use randomized shams and known-energy injections.
  • Require both energy closure and reproducible state return before interpreting net output.