# 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' $$X \rightarrow -Y$$, $$Z \rightarrow Z$$

 '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