BaconShor33.txt

// Bacon-Shor 3x3 CCZ gate

// Definitions
// P0(q) -- preparing qubit q in |0>
// Pp(q) -- preparing qubit q in |+>
// Id(q) -- identity gate on qubit q
// H(q)  -- Hadamard on qubit q
// S(q)  -- Phase gate on qubit q
// K(q)  -- S.H gate (H followed by S) on qubit q
// Sinv(q) -- inverse S gate on qubit q
// Kinv(q) -- inverse K gate on qubit q
// CX(p,q) -- CNOT from qubit p to q
// CZ(p,q) -- controlled-Z between qubits p and q
// CCZ(p,q,r) -- controlled-controlled-Z between qubits p, q, and r
// MeasZ(q) -- measures qubit q in the Z-basis
// MeasX(q) -- measures qubit q in the X-basis

// Circuits are broken into timesteps by newlines - a qubit should only be
//  involved in at most 1 gate per timestep
// Circuits are organized into subcircuits by "def". Subcircuits take sets of
//  input and output qubits as arguments. Input qubits are never prepared
//  within the subcircuit, and output qubits are never measured.


// Fault-tolerantly prepares a logical |+> state in the 3x3 Bacon-Shor code
def LogicalPlus(in=(), out=(1,2,3,4,5,6,7,8,9)):

  P0(1)
  Pp(2)
  P0(4)
  Pp(5)
  P0(7)
  Pp(8)

  P0(3)
  P0(6)
  P0(9)
  CX(2,1)
  CX(5,4)
  CX(8,7)

  Id(1)
  CX(2,3)
  Id(4)
  CX(5,6)
  Id(7)
  CX(8,9)


// Fault-tolerantly prepares a logical |0> state in the 3x3 Bacon-Shor code
def LogicalZero(in=(), out=(1,2,3,4,5,6,7,8,9)):

  Pp(1)
  Pp(2)
  Pp(3)
  P0(4)
  P0(5)
  P0(6)

  Pp(7)
  Pp(8)
  Pp(9)
  CX(1,4)
  CX(2,5)
  CX(3,6)

  Id(1)
  CX(7,4)
  Id(2)
  CX(8,5)
  Id(3)
  CX(9,6)


// Implements Steane error-correction on the 3x3 Bacon-Shor code, ending in Z-gauge
def ErrorCorrectionXtoZ(in=out=(1,2,3,4,5,6,7,8,9)):

  LogicalZero(in=(), out=(10,11,12,13,14,15,16,17,18))
  LogicalPlus(in=(), out=(19,20,21,22,23,24,25,26,27))

  CX(10,1)
  CX(11,2)
  CX(12,3)
  CX(13,4)
  CX(14,5)
  CX(15,6)
  CX(16,7)
  CX(17,8)
  CX(18,9)

  CX(1,19)
  CX(2,20)
  CX(3,21)
  CX(4,22)
  CX(5,23)
  CX(6,24)
  CX(7,25)
  CX(8,26)
  CX(9,27)
  MeasX(10)
  MeasX(11)
  MeasX(12)
  MeasX(13)
  MeasX(14)
  MeasX(15)
  MeasX(16)
  MeasX(17)
  MeasX(18)

  Id(1)
  Id(2)
  Id(3)
  Id(4)
  Id(5)
  Id(6)
  Id(7)
  Id(8)
  Id(9)
  MeasZ(19)
  MeasZ(20)
  MeasZ(21)
  MeasZ(22)
  MeasZ(23)
  MeasZ(24)
  MeasZ(25)
  MeasZ(26)
  MeasZ(27)


// Implements Steane error-correction on the 3x3 Bacon-Shor code, ending in X-gauge
def ErrorCorrectionZtoX(in=out=(1,2,3,4,5,6,7,8,9)):

  LogicalZero(in=(), out=(10,11,12,13,14,15,16,17,18))
  LogicalPlus(in=(), out=(19,20,21,22,23,24,25,26,27))

  CX(1,19)
  CX(2,20)
  CX(3,21)
  CX(4,22)
  CX(5,23)
  CX(6,24)
  CX(7,25)
  CX(8,26)
  CX(9,27)

  CX(10,1)
  CX(11,2)
  CX(12,3)
  CX(13,4)
  CX(14,5)
  CX(15,6)
  CX(16,7)
  CX(17,8)
  CX(18,9)
  MeasZ(19)
  MeasZ(20)
  MeasZ(21)
  MeasZ(22)
  MeasZ(23)
  MeasZ(24)
  MeasZ(25)
  MeasZ(26)
  MeasZ(27)

  MeasX(10)
  MeasX(11)
  MeasX(12)
  MeasX(13)
  MeasX(14)
  MeasX(15)
  MeasX(16)
  MeasX(17)
  MeasX(18)


// The circuit for logical CCZ
def FaultTolerantCCZ(in=out=(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)):

  ErrorCorrectionXtoZ(in=out=(1,2,3,4,5,6,7,8,9))
  ErrorCorrectionXtoZ(in=out=(10,11,12,13,14,15,16,17,18))
  ErrorCorrectionXtoZ(in=out=(19,20,21,22,23,24,25,26,27))

  CCZ(1,10,19)
  CCZ(2,14,26)
  CCZ(3,18,24)
  CCZ(4,13,22)
  CCZ(5,17,20)
  CCZ(6,12,27)
  CCZ(7,16,25)
  CCZ(8,11,23)
  CCZ(9,15,21)

  CCZ(1,10,22)
  CCZ(2,14,20)
  CCZ(3,18,27)
  CCZ(4,13,25)
  CCZ(5,17,23)
  CCZ(6,12,21)
  CCZ(7,16,19)
  CCZ(8,11,26)
  CCZ(9,15,24)

  CCZ(1,16,19)
  CCZ(2,11,26)
  CCZ(3,15,24)
  CCZ(4,10,22)
  CCZ(5,14,20)
  CCZ(6,18,27)
  CCZ(7,13,25)
  CCZ(8,17,23)
  CCZ(9,12,21)

  ErrorCorrectionZtoX(in=out=(1,2,3,4,5,6,7,8,9))
  ErrorCorrectionZtoX(in=out=(10,11,12,13,14,15,16,17,18))
  ErrorCorrectionZtoX(in=out=(19,20,21,22,23,24,25,26,27))