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QuantumBlockEncoding/Robin/SymmetryFourSlotBlockEncoding.lean

50 explicit public declarations in source order.

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def · line 24

QuantumBlockEncoding.Robin.warmRobinPairSystemToOriginal

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin pair system to original”. Map a reversal-pair coordinate back to the original 'Fin 8' basis.

def warmRobinPairSystemToOriginal
    (index : WarmRobinSymmetrySystem) : Fin 8 :=
  if index.1.val = 0 then
    warmRobinPairLow index.2
  else
    warmRobinPairHigh index.2

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theorem · line 31

QuantumBlockEncoding.Robin.warmRobinPairSystemToOriginal_zero

Compiled Compiled

Lean checks the proposition indexed as “warm robin pair system to original zero”; the hypotheses and conclusion in the code panel fix its exact scope.

@[simp] theorem warmRobinPairSystemToOriginal_zero (pair : Fin 4) :
    warmRobinPairSystemToOriginal (0, pair) = warmRobinPairLow pair := by

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theorem · line 35

QuantumBlockEncoding.Robin.warmRobinPairSystemToOriginal_one

Compiled Compiled

Lean checks the proposition indexed as “warm robin pair system to original one”; the hypotheses and conclusion in the code panel fix its exact scope.

@[simp] theorem warmRobinPairSystemToOriginal_one (pair : Fin 4) :
    warmRobinPairSystemToOriginal (1, pair) = warmRobinPairHigh pair := by

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theorem · line 40

QuantumBlockEncoding.Robin.warmRobinPairSystemToOriginal_bijective

Compiled Compiled

Lean checks the proposition indexed as “warm robin pair system to original bijective”; the hypotheses and conclusion in the code panel fix its exact scope. Pair coordinates enumerate the original eight basis states exactly once.

theorem warmRobinPairSystemToOriginal_bijective :
    Function.Bijective warmRobinPairSystemToOriginal := by

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def · line 45

QuantumBlockEncoding.Robin.warmRobinPairSystemEquiv

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin pair system equiv”. Equivalence between pair coordinates and the original Robin basis.

noncomputable def warmRobinPairSystemEquiv :
    WarmRobinSymmetrySystem ≃ Fin 8 :=
  Equiv.ofBijective warmRobinPairSystemToOriginal
    warmRobinPairSystemToOriginal_bijective

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theorem · line 50

QuantumBlockEncoding.Robin.warmRobinPairSystemEquiv_apply

Compiled Compiled

Lean checks the proposition indexed as “warm robin pair system equiv apply”; the hypotheses and conclusion in the code panel fix its exact scope.

@[simp] theorem warmRobinPairSystemEquiv_apply
    (index : WarmRobinSymmetrySystem) :
    warmRobinPairSystemEquiv index = warmRobinPairSystemToOriginal index := by

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theorem · line 55

QuantumBlockEncoding.Robin.warmRobinPairSystemToOriginal_symm

Compiled Compiled

Lean checks the proposition indexed as “warm robin pair system to original symm”; the hypotheses and conclusion in the code panel fix its exact scope.

@[simp] theorem warmRobinPairSystemToOriginal_symm (system : Fin 8) :
    warmRobinPairSystemToOriginal (warmRobinPairSystemEquiv.symm system) = system := by

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def · line 61

QuantumBlockEncoding.Robin.warmRobinSymmetryBasisChange

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin symmetry basis change”. The symmetry-sector-to-pair basis change: one exact Hadamard-like rotation.

noncomputable def warmRobinSymmetryBasisChange :
    _root_.Matrix WarmRobinSymmetrySystem WarmRobinSymmetrySystem ℂ :=
  warmRobinUniformBitPrepare ⊗ₖ
    (1 : _root_.Matrix (Fin 4) (Fin 4) ℂ)

/-- The symmetry basis change is unitary. -/

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theorem · line 67

QuantumBlockEncoding.Robin.warmRobinSymmetryBasisChange_unitary

Compiled Compiled

Lean checks the proposition indexed as “warm robin symmetry basis change unitary”; the hypotheses and conclusion in the code panel fix its exact scope. The symmetry basis change is unitary.

theorem warmRobinSymmetryBasisChange_unitary :
    warmRobinSymmetryBasisChange ∈
      _root_.Matrix.unitaryGroup WarmRobinSymmetrySystem ℂ := by

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theorem · line 75

QuantumBlockEncoding.Robin.star_warmRobinUniformBitPrepare_apply

Compiled Compiled

Lean checks the proposition indexed as “star warm robin uniform bit prepare apply”; the hypotheses and conclusion in the code panel fix its exact scope. Every entry of the real two-dimensional basis change is self-conjugate.

@[simp] theorem star_warmRobinUniformBitPrepare_apply
    (row column : Fin 2) :
    star (warmRobinUniformBitPrepare row column) =
      warmRobinUniformBitPrepare row column := by

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theorem · line 88

QuantumBlockEncoding.Robin.warmRobinUniformScalar_square_complex

Compiled Compiled

Lean checks the proposition indexed as “warm robin uniform scalar square complex”; the hypotheses and conclusion in the code panel fix its exact scope. The common real selector amplitude has squared magnitude '1/2'.

@[simp] theorem warmRobinUniformScalar_square_complex :
    (((Real.sqrt 2 / 2 : Real) : ℂ) *
      ((Real.sqrt 2 / 2 : Real) : ℂ)) = (1 / 2 : ℂ) := by

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theorem · line 101

QuantumBlockEncoding.Robin.warmRobinSymmetryBasisChange_apply

Compiled Compiled

Lean checks the proposition indexed as “warm robin symmetry basis change apply”; the hypotheses and conclusion in the code panel fix its exact scope. Entry formula for the exact symmetry basis change.

@[simp] theorem warmRobinSymmetryBasisChange_apply
    (row column : WarmRobinSymmetrySystem) :
    warmRobinSymmetryBasisChange row column =
      if row.2 = column.2 then
        warmRobinUniformBitPrepare row.1 column.1
      else 0 := by

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theorem · line 111

QuantumBlockEncoding.Robin.star_warmRobinSymmetryBasisChange_apply

Compiled Compiled

Lean checks the proposition indexed as “star warm robin symmetry basis change apply”; the hypotheses and conclusion in the code panel fix its exact scope. Entry formula for the adjoint symmetry basis change.

@[simp] theorem star_warmRobinSymmetryBasisChange_apply
    (row column : WarmRobinSymmetrySystem) :
    star warmRobinSymmetryBasisChange row column =
      if row.2 = column.2 then
        star (warmRobinUniformBitPrepare column.1 row.1)
      else 0 := by

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theorem · line 123

QuantumBlockEncoding.Robin.warmRobinSymmetryBasisChange_mul_pairRow

Compiled Compiled

Lean checks the proposition indexed as “warm robin symmetry basis change mul pair row”; the hypotheses and conclusion in the code panel fix its exact scope. Left multiplication preserves the pair index and sums only over sectors.

theorem warmRobinSymmetryBasisChange_mul_pairRow
    {columnType : Type*} [Fintype columnType]
    (operator : _root_.Matrix WarmRobinSymmetrySystem columnType ℂ)
    (rowSide : Fin 2) (rowPair : Fin 4) (column : columnType) :
    (warmRobinSymmetryBasisChange * operator)
        (rowSide, rowPair) column =
      ∑ side : Fin 2,
        warmRobinUniformBitPrepare rowSide side *
          operator (side, rowPair) column := by

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theorem · line 145

QuantumBlockEncoding.Robin.mul_star_warmRobinSymmetryBasisChange_pairColumn

Compiled Compiled

Lean checks the proposition indexed as “mul star warm robin symmetry basis change pair column”; the hypotheses and conclusion in the code panel fix its exact scope. Right multiplication by the adjoint also preserves the pair index.

theorem mul_star_warmRobinSymmetryBasisChange_pairColumn
    {rowType : Type*} [Fintype rowType]
    (operator : _root_.Matrix rowType WarmRobinSymmetrySystem ℂ)
    (row : rowType) (columnSide : Fin 2) (columnPair : Fin 4) :
    (operator * star warmRobinSymmetryBasisChange)
        row (columnSide, columnPair) =
      ∑ side : Fin 2,
        operator row (side, columnPair) *
          star (warmRobinUniformBitPrepare columnSide side) := by

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theorem · line 167

QuantumBlockEncoding.Robin.warmRobinIntegerTarget_pair_high_low

Compiled Compiled

Lean checks the proposition indexed as “warm robin integer target pair high low”; the hypotheses and conclusion in the code panel fix its exact scope. Lower-left pair block equals the upper-right pair block by centrosymmetry.

theorem warmRobinIntegerTarget_pair_high_low
    (row column : Fin 4) :
    warmRobinIntegerTarget (warmRobinPairHigh row) (warmRobinPairLow column) =
      warmRobinIntegerTarget (warmRobinPairLow row) (warmRobinPairHigh column) := by

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theorem · line 176

QuantumBlockEncoding.Robin.warmRobinIntegerTarget_pair_high_high

Compiled Compiled

Lean checks the proposition indexed as “warm robin integer target pair high high”; the hypotheses and conclusion in the code panel fix its exact scope. The high-high pair block equals the low-low block.

theorem warmRobinIntegerTarget_pair_high_high
    (row column : Fin 4) :
    warmRobinIntegerTarget (warmRobinPairHigh row) (warmRobinPairHigh column) =
      warmRobinIntegerTarget (warmRobinPairLow row) (warmRobinPairLow column) := by

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def · line 185

QuantumBlockEncoding.Robin.warmRobinPairNormalizedTargetRat

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin pair normalized target rat”. The fixed integer target, reordered by reversal pairs and divided by '224'.

def warmRobinPairNormalizedTargetRat :
    _root_.Matrix WarmRobinSymmetrySystem WarmRobinSymmetrySystem Rat :=
  fun row column =>
    warmRobinIntegerTargetRat
      (warmRobinPairSystemToOriginal row)
      (warmRobinPairSystemToOriginal column) / 224

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theorem · line 192

QuantumBlockEncoding.Robin.warmRobinPairNormalizedTargetRat_zero_zero

Compiled Compiled

Lean checks the proposition indexed as “warm robin pair normalized target rat zero zero”; the hypotheses and conclusion in the code panel fix its exact scope.

@[simp] theorem warmRobinPairNormalizedTargetRat_zero_zero
    (row column : Fin 4) :
    warmRobinPairNormalizedTargetRat (0, row) (0, column) =
      (warmRobinIntegerTarget
        (warmRobinPairLow row) (warmRobinPairLow column) : Rat) / 224 := by

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theorem · line 199

QuantumBlockEncoding.Robin.warmRobinPairNormalizedTargetRat_zero_one

Compiled Compiled

Lean checks the proposition indexed as “warm robin pair normalized target rat zero one”; the hypotheses and conclusion in the code panel fix its exact scope.

@[simp] theorem warmRobinPairNormalizedTargetRat_zero_one
    (row column : Fin 4) :
    warmRobinPairNormalizedTargetRat (0, row) (1, column) =
      (warmRobinIntegerTarget
        (warmRobinPairLow row) (warmRobinPairHigh column) : Rat) / 224 := by

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theorem · line 206

QuantumBlockEncoding.Robin.warmRobinPairNormalizedTargetRat_one_zero

Compiled Compiled

Lean checks the proposition indexed as “warm robin pair normalized target rat one zero”; the hypotheses and conclusion in the code panel fix its exact scope.

@[simp] theorem warmRobinPairNormalizedTargetRat_one_zero
    (row column : Fin 4) :
    warmRobinPairNormalizedTargetRat (1, row) (0, column) =
      (warmRobinIntegerTarget
        (warmRobinPairLow row) (warmRobinPairHigh column) : Rat) / 224 := by

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theorem · line 216

QuantumBlockEncoding.Robin.warmRobinPairNormalizedTargetRat_one_one

Compiled Compiled

Lean checks the proposition indexed as “warm robin pair normalized target rat one one”; the hypotheses and conclusion in the code panel fix its exact scope.

@[simp] theorem warmRobinPairNormalizedTargetRat_one_one
    (row column : Fin 4) :
    warmRobinPairNormalizedTargetRat (1, row) (1, column) =
      (warmRobinIntegerTarget
        (warmRobinPairLow row) (warmRobinPairLow column) : Rat) / 224 := by

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def · line 226

QuantumBlockEncoding.Robin.warmRobinPairNormalizedTargetComplex

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin pair normalized target complex”. Complex view of the pair-ordered normalized Robin target.

def warmRobinPairNormalizedTargetComplex :
    _root_.Matrix WarmRobinSymmetrySystem WarmRobinSymmetrySystem ℂ :=
  fun row column => (warmRobinPairNormalizedTargetRat row column : ℂ)

/-- Complex view of the direct-sum sector target. -/

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def · line 231

QuantumBlockEncoding.Robin.warmRobinFourSlotSectorTargetComplex

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot sector target complex”. Complex view of the direct-sum sector target.

def warmRobinFourSlotSectorTargetComplex :
    _root_.Matrix WarmRobinSymmetrySystem WarmRobinSymmetrySystem ℂ :=
  fun row column => (warmRobinFourSlotSectorTarget row column : ℂ)

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theorem · line 276

QuantumBlockEncoding.Robin.warmRobinSymmetryBasisChange_conjugates_target

Compiled Compiled

Lean checks the proposition indexed as “warm robin symmetry basis change conjugates target”; the hypotheses and conclusion in the code panel fix its exact scope. The exact symmetry transform reconstructs the pair-ordered Robin matrix.

theorem warmRobinSymmetryBasisChange_conjugates_target :
    warmRobinSymmetryBasisChange *
        (warmRobinFourSlotSectorTargetComplex *
          star warmRobinSymmetryBasisChange) =
      warmRobinPairNormalizedTargetComplex := by

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def · line 322

QuantumBlockEncoding.Robin.warmRobinFourSlotPairLogicalUnitary

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot pair logical unitary”. Conjugate the sector logical unitary back to reversal-pair coordinates.

noncomputable def warmRobinFourSlotPairLogicalUnitary :
    _root_.Matrix
      (LCUIndex (Fin 2) (Fin 4) WarmRobinSymmetrySystem)
      (LCUIndex (Fin 2) (Fin 4) WarmRobinSymmetrySystem) ℂ :=
  conjugateSystem warmRobinSymmetryBasisChange
    warmRobinFourSlotMiddleLogicalUnitary

/-- The pair-basis logical unitary remains exactly unitary. -/

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theorem · line 330

QuantumBlockEncoding.Robin.warmRobinFourSlotPairLogicalUnitary_unitary

Compiled Compiled

Lean checks the proposition indexed as “warm robin four slot pair logical unitary unitary”; the hypotheses and conclusion in the code panel fix its exact scope. The pair-basis logical unitary remains exactly unitary.

theorem warmRobinFourSlotPairLogicalUnitary_unitary :
    warmRobinFourSlotPairLogicalUnitary ∈
      _root_.Matrix.unitaryGroup
        (LCUIndex (Fin 2) (Fin 4) WarmRobinSymmetrySystem) ℂ := by

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theorem · line 339

QuantumBlockEncoding.Robin.warmRobinFourSlotPairLogicalUnitary_cleanSystemBlock

Compiled Compiled

Lean checks the proposition indexed as “warm robin four slot pair logical unitary clean system block”; the hypotheses and conclusion in the code panel fix its exact scope. Its clean system block is the pair-ordered normalized Robin target.

theorem warmRobinFourSlotPairLogicalUnitary_cleanSystemBlock :
    cleanSystemBlock warmRobinFourSlotPairLogicalUnitary 0 0 =
      warmRobinPairNormalizedTargetComplex := by

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theorem · line 348

QuantumBlockEncoding.Robin.warmRobinFourSlotPairLogicalUnitary_cleanEntry

Compiled Compiled

Lean checks the proposition indexed as “warm robin four slot pair logical unitary clean entry”; the hypotheses and conclusion in the code panel fix its exact scope. Entry form of the pair-basis clean-block certificate.

theorem warmRobinFourSlotPairLogicalUnitary_cleanEntry
    (row column : WarmRobinSymmetrySystem) :
    warmRobinFourSlotPairLogicalUnitary
        (0, (0, row)) (0, (0, column)) =
      warmRobinPairNormalizedTargetComplex row column := by

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def · line 358

QuantumBlockEncoding.Robin.warmRobinFourSlotProductSystemEquiv

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot product system equiv”. Reindex only the system component from pair order to original 'Fin 8'.

noncomputable def warmRobinFourSlotProductSystemEquiv :
    LCUIndex (Fin 2) (Fin 4) WarmRobinSymmetrySystem ≃
      LCUIndex (Fin 2) (Fin 4) (Fin 8) :=
  Equiv.prodCongr (Equiv.refl (Fin 2))
    (Equiv.prodCongr (Equiv.refl (Fin 4)) warmRobinPairSystemEquiv)

/-- Flatten coefficient × selector × original system into six qubits. -/

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def · line 365

QuantumBlockEncoding.Robin.warmRobinFourSlotOriginalIndexEquiv

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot original index equiv”. Flatten coefficient × selector × original system into six qubits.

def warmRobinFourSlotOriginalIndexEquiv :
    LCUIndex (Fin 2) (Fin 4) (Fin 8) ≃ Fin (gridSize 6) :=
  (Equiv.prodCongr (Equiv.refl (Fin 2)) finProdFinEquiv).trans
    finProdFinEquiv

/-- The six primitive wires interpreted as coefficient, selector, and system
registers through the already-certified T2 flattening.  Consequently q0--q2
are system, q3--q4 are selector, and q5 is coefficient. -/

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def · line 373

QuantumBlockEncoding.Robin.warmRobinFourSlotProductBitsEquiv

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot product bits equiv”. The six primitive wires interpreted as coefficient, selector, and system registers through the already-certified T2 flattening.

def warmRobinFourSlotProductBitsEquiv :
    PrimitiveBasis 6 ≃ LCUIndex (Fin 2) (Fin 4) (Fin 8) :=
  (primitiveBasisLEEquiv 6).trans warmRobinFourSlotOriginalIndexEquiv.symm

/-- Primitive little-endian indexing is exactly the original T2 index map. -/

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theorem · line 378

QuantumBlockEncoding.Robin.warmRobinFourSlotProductBitsEquiv_index

Compiled Compiled

Lean checks the proposition indexed as “warm robin four slot product bits equiv index”; the hypotheses and conclusion in the code panel fix its exact scope. Primitive little-endian indexing is exactly the original T2 index map.

theorem warmRobinFourSlotProductBitsEquiv_index (bits : PrimitiveBasis 6) :
    warmRobinFourSlotOriginalIndexEquiv
        (warmRobinFourSlotProductBitsEquiv bits) =
      primitiveBasisLEEquiv 6 bits := by

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theorem · line 386

QuantumBlockEncoding.Robin.warmRobinFourSlotProductBitsEquiv_all_basis

Compiled Compiled

Lean checks the proposition indexed as “warm robin four slot product bits equiv all basis”; the hypotheses and conclusion in the code panel fix its exact scope. Regression over all 64 basis states, stated as the concrete register formula consumed by executable backends.

theorem warmRobinFourSlotProductBitsEquiv_all_basis :
    ∀ bits : PrimitiveBasis 6,
      (warmRobinFourSlotOriginalIndexEquiv
          (warmRobinFourSlotProductBitsEquiv bits)).val =
        (bits 0).val + 2 * (bits 1).val + 4 * (bits 2).val +
        8 * (bits 3).val + 16 * (bits 4).val + 32 * (bits 5).val := by

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def · line 397

QuantumBlockEncoding.Robin.warmRobinFourSlotIndexEquiv

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot index equiv”. Combined system reindexing and six-qubit flattening.

noncomputable def warmRobinFourSlotIndexEquiv :
    LCUIndex (Fin 2) (Fin 4) WarmRobinSymmetrySystem ≃
      Fin (gridSize 6) :=
  warmRobinFourSlotProductSystemEquiv.trans
    warmRobinFourSlotOriginalIndexEquiv

/-- Flat clean index for an original Robin system basis state. -/

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def · line 404

QuantumBlockEncoding.Robin.warmRobinFourSlotCleanIndex

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot clean index”. Flat clean index for an original Robin system basis state.

noncomputable def warmRobinFourSlotCleanIndex (system : Fin 8) : Fin (gridSize 6) :=
  warmRobinFourSlotIndexEquiv
    (0, (0, warmRobinPairSystemEquiv.symm system))

/-- Six-qubit matrix in the original system order. -/

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def · line 409

QuantumBlockEncoding.Robin.warmRobinFourSlotFlatUnitary

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot flat unitary”. Six-qubit matrix in the original system order.

noncomputable def warmRobinFourSlotFlatUnitary :
    _root_.Matrix (Fin (gridSize 6)) (Fin (gridSize 6)) ℂ :=
  _root_.Matrix.reindexAlgEquiv ℂ ℂ warmRobinFourSlotIndexEquiv
    warmRobinFourSlotPairLogicalUnitary

/-- Reindexing preserves exact unitarity. -/

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theorem · line 415

QuantumBlockEncoding.Robin.warmRobinFourSlotFlatUnitary_unitary

Compiled Compiled

Lean checks the proposition indexed as “warm robin four slot flat unitary unitary”; the hypotheses and conclusion in the code panel fix its exact scope. Reindexing preserves exact unitarity.

theorem warmRobinFourSlotFlatUnitary_unitary :
    warmRobinFourSlotFlatUnitary ∈
      _root_.Matrix.unitaryGroup (Fin (gridSize 6)) ℂ := by

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theorem · line 422

QuantumBlockEncoding.Robin.warmRobinFourSlotFlatUnitary_reindex

Compiled Compiled

Lean checks the proposition indexed as “warm robin four slot flat unitary reindex”; the hypotheses and conclusion in the code panel fix its exact scope. Applying the flat matrix at flattened indices recovers the product entry.

@[simp] theorem warmRobinFourSlotFlatUnitary_reindex
    (row column :
      LCUIndex (Fin 2) (Fin 4) WarmRobinSymmetrySystem) :
    warmRobinFourSlotFlatUnitary
        (warmRobinFourSlotIndexEquiv row)
        (warmRobinFourSlotIndexEquiv column) =
      warmRobinFourSlotPairLogicalUnitary row column := by

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theorem · line 432

QuantumBlockEncoding.Robin.warmRobinPairNormalizedTargetComplex_symm

Compiled Compiled

Lean checks the proposition indexed as “warm robin pair normalized target complex symm”; the hypotheses and conclusion in the code panel fix its exact scope. Pair-ordered target at inverse-reindexed indices is the original target.

theorem warmRobinPairNormalizedTargetComplex_symm
    (row column : Fin 8) :
    warmRobinPairNormalizedTargetComplex
        (warmRobinPairSystemEquiv.symm row)
        (warmRobinPairSystemEquiv.symm column) =
      ((warmRobinIntegerTargetRat row column / 224 : Rat) : ℂ) := by

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theorem · line 442

QuantumBlockEncoding.Robin.warmRobinFourSlotFlatUnitary_cleanBlock

Compiled Compiled

Lean checks the proposition indexed as “warm robin four slot flat unitary clean block”; the hypotheses and conclusion in the code panel fix its exact scope. The flat clean block is exactly the original fixed Robin target.

theorem warmRobinFourSlotFlatUnitary_cleanBlock
    (row column : Fin 8) :
    warmRobinFourSlotFlatUnitary
        (warmRobinFourSlotCleanIndex row)
        (warmRobinFourSlotCleanIndex column) =
      ((RobinEvolution.warmRobinTarget row column /
        RobinEvolution.warmRobinNormalizer : Rat) : ℂ) := by

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def · line 458

QuantumBlockEncoding.Robin.warmRobinFourSlotT2Schedule

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot t 2 schedule”. Fair T2 logical-stage schedule for the four-slot construction.

def warmRobinFourSlotT2Schedule : LayeredCircuit :=
  [ [ Gate.oneQubit "T2 selector-H-0" 0
    , Gate.oneQubit "T2 selector-H-1" 1
    , Gate.oneQubit "T2 symmetry-basis-change" 3 ]
  , [ Gate.oracleCall "T2 controlled amplitude rotation" ]
  , [ Gate.oracleCall "T2 sector-preserving SELECT" ]
  , [ Gate.oneQubit "T2 selector-H-0 dagger" 0
    , Gate.oneQubit "T2 selector-H-1 dagger" 1
    , Gate.oneQubit "T2 symmetry-basis-change dagger" 3 ]
  ]

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def · line 470

QuantumBlockEncoding.Robin.warmRobinFourSlotT2Circuit

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot t 2 circuit”. The corresponding logical gate list.

def warmRobinFourSlotT2Circuit : Circuit :=
  warmRobinFourSlotT2Schedule.flatten

/-- Exact resource row under the declared T2 logical-stage convention. -/

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def · line 474

QuantumBlockEncoding.Robin.warmRobinFourSlotT2Resource

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot t 2 resource”. Exact resource row under the declared T2 logical-stage convention.

def warmRobinFourSlotT2Resource : Resource :=
  warmRobinFourSlotT2Schedule.resource

/-- The operator-first clean-block predicate for the four-slot route. -/

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def · line 478

QuantumBlockEncoding.Robin.warmRobinFourSlotBlockContainsTarget

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot block contains target”. The operator-first clean-block predicate for the four-slot route.

def warmRobinFourSlotBlockContainsTarget : Prop :=
  ∀ row column : Fin 8,
    warmRobinFourSlotFlatUnitary
        (warmRobinFourSlotCleanIndex row)
        (warmRobinFourSlotCleanIndex column) =
      warmRobinQueryTarget.operator row column /
        warmRobinQueryTarget.normalizer

/-- The clean-block predicate is discharged by the original-basis theorem. -/

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theorem · line 487

QuantumBlockEncoding.Robin.warmRobinFourSlotBlockContainsTarget_proof

Compiled Compiled

Lean checks the proposition indexed as “warm robin four slot block contains target proof”; the hypotheses and conclusion in the code panel fix its exact scope. The clean-block predicate is discharged by the original-basis theorem.

theorem warmRobinFourSlotBlockContainsTarget_proof :
    warmRobinFourSlotBlockContainsTarget := by

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def · line 494

QuantumBlockEncoding.Robin.warmRobinFourSlotOperatorCandidate

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot operator candidate”. Four-slot T2 candidate for the fixed 'N=8' Robin target.

noncomputable def warmRobinFourSlotOperatorCandidate :
    OperatorBlockEncodingCandidate ℂ 3 where
  auxiliaryQubits := 3
  target := warmRobinQueryTarget
  unitary := warmRobinFourSlotFlatUnitary
  layout := {
    systemQubits := 3
    signalQubits := 3
    pureAncillas := 0
  }
  circuit := warmRobinFourSlotT2Circuit

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def · line 514

QuantumBlockEncoding.Robin.warmRobinFourSlotVerifiedBlockEncoding

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot verified block encoding”. Fully verified T2 block encoding for the four-slot symmetry route.

noncomputable def warmRobinFourSlotVerifiedBlockEncoding :
    VerifiedOperatorBlockEncoding ℂ 3 where
  candidate := warmRobinFourSlotOperatorCandidate
  unitaryProof := warmRobinFourSlotFlatUnitary_unitary
  blockProof := warmRobinFourSlotBlockContainsTarget_proof

/-- Under one T2 logical-stage convention, four slots strictly improve the
Hadamard-8 route: gate count and depth tie, while the clean layout uses one
fewer auxiliary qubit. -/

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theorem · line 523

QuantumBlockEncoding.Robin.warmRobinFourSlotT2Cost_betterThan_hadamard8

Compiled Compiled

Lean checks the proposition indexed as “warm robin four slot t 2 cost better than hadamard 8”; the hypotheses and conclusion in the code panel fix its exact scope. Under one T2 logical-stage convention, four slots strictly improve the Hadamard-8 route: gate count and depth tie, while the clean layout uses one fewer auxiliary qubit.

theorem warmRobinFourSlotT2Cost_betterThan_hadamard8 :
    warmRobinFourSlotOperatorCandidate.cost.betterThan
      warmRobinHadamard8OperatorCandidate.cost := by

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def · line 535

QuantumBlockEncoding.Robin.warmRobinFourSlotT3BlockedLeaf

Compiled Compiled

This definition gives the library's named construction or computation for “warm robin four slot t 3 blocked leaf”. Honest boundary: primitive synthesis and refinement remain a T3 obligation.

def warmRobinFourSlotT3BlockedLeaf : String :=
  "prove that a concrete primitive circuit refines warmRobinFourSlotFlatUnitary and certify its primitive resource counts"

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