Standard Gates¶
While some simulators may allow access to other gate sets, the standard gates recognized by PECOS are:
Initializations¶
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 \(|1\rangle\) |
Unitaries¶
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' |
\(X \rightarrow -Y\), \(Z \rightarrow Z\) |
Hamadard-like:
'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¶
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 |