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