BaconShor39.txt

// Bacon-Shor 3x9 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
// A(qi-qf) Ð single-qubit gate A applied transversally on qubits qi,qi+1,...,qf
// B(pi-pf,qi-qf) Ð two-qubit gate B applied transversally from qubit pi to qi, from pi+1 to qi+1,...,from pf to qi 
// C(pi-pf,qi-pf,ri-rf) Ð three-qubit gate C applied transversally between qubit pi, qi, and ri, between pi+1, qi+1, and ri+1,...,between pf, qf, and rf.

// 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 3x9 Bacon-Shor code
def LogicalPlus(in=(), out=(1,2,...,27)):
  
  P0(5)
  Pp(6)
  P0(14)
  Pp(15)
  P0(23)
  Pp(24)  

  P0(4)
  CX(6,5)
  P0(7)  
  P0(13)
  CX(15,14)
  P0(16)  
  P0(22)
  CX(24,23)
  P0(25) 

  P0(3)
  CX(5,4)
  CX(6,7)
  P0(8)
  P0(12)
  CX(14,13)
  CX(15,16)
  P0(17)
  P0(21)
  CX(23,22)
  CX(24,25)
  P0(26)
 
  P0(2)
  CX(4,3)
  Id(5)
  Id(6)
  CX(7,8)
  P0(9)
  P0(11)
  CX(13,12)
  Id(14)
  Id(15)
  CX(16,17)
  P0(18)
  P0(20)
  CX(22,21)
  Id(23)
  Id(24)
  CX(25,26)
  P0(27)

  P0(1)
  CX(3,2)
  Id(4)
  Id(5)
  Id(6)
  Id(7)
  CX(8,9)
  P0(10)
  CX(12,11)
  Id(13)
  Id(14)
  Id(15)
  Id(16)
  CX(17,18)
  P0(19)
  CX(21,20)
  Id(22)
  Id(23)
  Id(24)
  Id(25)
  CX(26,27)

  CX(2,1)
  Id(3)
  Id(4)
  Id(5)
  Id(6)
  Id(7)
  Id(8)
  CX(9,28)
  CX(11,10)
  Id(12)
  Id(13)
  Id(14)
  Id(15)
  Id(16)
  Id(17)
  CX(18,29)
  CX(20,19)
  Id(21)
  Id(22)
  Id(23)
  Id(24)
  Id(25)
  Id(26)
  CX(27,30)

  CX(1,28)
  Id(2)
  Id(3)
  Id(4)
  Id(5)
  Id(6)
  Id(7)
  Id(8)
  Id(9)
  CX(10,29)
  Id(11)
  Id(12)
  Id(13)
  Id(14)
  Id(15)
  Id(16)
  Id(17)
  Id(18)
  CX(19,30)
  Id(20)
  Id(21)
  Id(22)
  Id(23)
  Id(24)
  Id(25)
  Id(26)
  Id(27)

  Id(1-27)
  MeasZ(28-30)


// Fault-tolerantly prepares a logical |0> state in the 3x9 Bacon-Shor code
def LogicalZero(in=(), out=(1,2,...,27)):
  
  Pp(1-9)
  P0(10-18)
  
  Pp(19-27)
  CX(1-9,10-18)

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


// Implements Steane error-correction on the 3x9 Bacon-Shor code
def ErrorCorrection (in=out=(1,2,...,27)):
  LogicalZero(in=(), out=(28,29,...,54))
  LogicalPlus(in=(), out=(55,56,...,81))

  CX(1-27,55-81)
 
  CX(28-54,1-27)
  MeasZ(55-81)

  Id(1-27)
  MeasX(28-54)


// The circuit for logical CCZ
def FaultTolerantCCZ(in=out=(1,2,...,81)):

  ErrorCorrection(in=out=(1,2,...,27))
  ErrorCorrection(in=out=(28,29,...,54))
  ErrorCorrection(in=out=(55,56,...,81))

  CCZ(1-27,28-54,55-81)
  
  ErrorCorrection(in=out=(1,2,...,27))
  ErrorCorrection(in=out=(28,29,...,54))
  ErrorCorrection(in=out=(55,56,...,81))