IndisputableMonolith.Physics.QuantumMolecularDesignDepthC4

   1import Mathlib
   2import IndisputableMonolith.Physics.MolecularPhysicsFromRS
   3import IndisputableMonolith.Physics.QuantumComputingDepthFromRS
   4
   5/-!
   6# C4: Quantum Molecular Design Depth
   7
   8Five molecular energy levels times five quantum gate types gives 25 prepared
   9state classes. Since 25 <= 2^5, a 5-bit addressing depth is enough to index
  10the whole RS-preparable class.
  11
  12This is the Lean-safe part of C4. The stronger physical claim, that a specific
  13molecular target can be reached in five two-qubit layers under a chosen gate
  14model, remains an empirical/algorithmic claim.
  15
  16Lean status: 0 sorry, 0 axiom.
  17-/
  18
  19namespace IndisputableMonolith
  20namespace Physics
  21namespace QuantumMolecularDesignDepthC4
  22
  23open MolecularPhysicsFromRS
  24open QuantumComputingDepthFromRS
  25
  26def molecularQuantumStateClasses : ℕ :=
  27  Fintype.card MolecularEnergyLevel * Fintype.card QuantumGateType
  28
  29theorem molecularQuantumStateClasses_25 :
  30    molecularQuantumStateClasses = 25 := by
  31  unfold molecularQuantumStateClasses
  32  rw [molecularEnergyCount, quantumGateTypeCount]
  33
  34theorem molecularQuantumStateClasses_le_2pow5 :
  35    molecularQuantumStateClasses ≤ 2 ^ 5 := by
  36  rw [molecularQuantumStateClasses_25]
  37  norm_num
  38
  39theorem twoPowerFour_lt_stateClasses :
  40    2 ^ 4 < molecularQuantumStateClasses := by
  41  rw [molecularQuantumStateClasses_25]
  42  norm_num
  43
  44structure QuantumMolecularDepthCert where
  45  state_classes_25 : molecularQuantumStateClasses = 25
  46  addressable_by_five_bits : molecularQuantumStateClasses ≤ 2 ^ 5
  47  not_addressable_by_four_bits : 2 ^ 4 < molecularQuantumStateClasses
  48
  49def quantumMolecularDepthCert : QuantumMolecularDepthCert where
  50  state_classes_25 := molecularQuantumStateClasses_25
  51  addressable_by_five_bits := molecularQuantumStateClasses_le_2pow5
  52  not_addressable_by_four_bits := twoPowerFour_lt_stateClasses
  53
  54end QuantumMolecularDesignDepthC4
  55end Physics
  56end IndisputableMonolith
  57