Standard Gates

While some simulators may allow access to other gate sets, the standard gates recognized by PECOS are:


State initializations in Pauli bases:

'init |+>' (Re)initiate the state \(|+\rangle\)
'init |->' (Re)initiate the state \(|-\rangle\)
'init |+i>' (Re)initiate the state \(|+i\rangle\)
'init |-i>' (Re)initiate the state \(|-i\rangle\)
'init |0>' (Re)initiate the state \(|0\rangle\)
'init |1>' (Re)initiate the state \(|1\rangle\)


Pauli operations:

'I' \(X\rightarrow X\), \(Z\rightarrow Z\)
'X' \(X\rightarrow X\), \(Z\rightarrow -Z\)
'Y' \(X\rightarrow -X\), \(Z\rightarrow -Z\)
'Z' \(X\rightarrow -X\), \(Z\rightarrow Z\)

Square-root of Pauli operations:

'Q' \(X \rightarrow X\), \(Z \rightarrow -Y\)
'R' \(X \rightarrow -Z\), \(Z \rightarrow X\)
'S' \(X \rightarrow Y\), \(Z \rightarrow Z\)
'Qd' \(X \rightarrow X\), \(Z \rightarrow Y\)
'Rd' \(X \rightarrow Z\), \(Z \rightarrow -X\)
'Sd' \(X \rightarrow -Y\), \(Z \rightarrow Z\)


'H'}, ``'H+z+x'}, or ``'H1' Hadamard: \(X\leftrightarrow Z\)
'H-z-x' or 'H2' \(X\leftrightarrow -Z\)
'H+y-z' or 'H3' \(X\rightarrow Y\), \(Z\rightarrow -Z\)
'H-y-z' or 'H4' \(X\rightarrow -Y\), \(Z\rightarrow -Z\)
'H-x+y' or 'H5' \(X\rightarrow -X\), \(\rightarrow Y\)
'H-x-y' or 'H6' \(X\rightarrow -X\), \(Z\rightarrow -Y\)

Rotations about the face of an octahedron:

'F1' \(X \rightarrow Y\rightarrow Z \rightarrow X\)
'F2' \(X \rightarrow -Z\), \(Z \rightarrow Y\)
'F3' \(X \rightarrow Y\), \(Z \rightarrow -X\)
'F4' \(X \rightarrow Z\), \(Z \rightarrow -Y\)
'F1d' \(X\rightarrow Z\rightarrow Y \rightarrow X\)
'F2d' \(X \rightarrow -Y\), \(Z \rightarrow -X\)
'F3d' \(X \rightarrow -Z\), \(Z \rightarrow -Y\)
'F4d' \(X \rightarrow -Y\), \(Z \rightarrow X\)

Two-qubit gates:

'CNOT' The controlled-X gate
'CZ' The controlled-Z gate
'SWAP' Swap two qubits
'G' Equivalent to: \(CZ_{1,2}\;H_1 \otimes H_2\; CZ_{1,2}\)


Measurements in Pauli bases:

'measure X' Measure in the \(X\)-basis
'measure Y' Measure in the \(Y\)-basis
'measure Z' Measure in the \(Z\)-basis