OpenQASM qelib1.inc

OpenQASM provides built-in support for only two Quantum Gates, the CX or CNOT gate and the U Gate. Though the combination of these Gates can be used to create any Quantum Gate, it is not always convenient to perform operations using these two Quantum Gates. Therefore, it makes sense to create standard Quantum Gates by using these Gates. The qelib1.inc file is a commonly used file when writing Quantum Algorithms in OpenQASM because it contains definitions of various standard Quantum Gates. In this chapter of the OpenQASM Tutorial, you will go through the Quantum Gates described in the qelib1.inc file.

Note– Not all of the Quantum Gates might be useful to you. In fact, many won’t be useful to you. The below section is just for reference and feel free to skip parts of it.

Quantum Gates in qelib1.inc File

The following table covers the Quantum Gates which are included in the qelib1.inc file.

Gate Name	Gate in OpenQASM 2	Brief Description
U3 Gate	u3	3-parameter 2-pulse single qubit gate.
U2 Gate	u2	2-parameter 1-pulse single qubit gate
U1 Gate	u1	1-parameter 0-pulse single qubit gate
CX Gate	cx	controlled-NOT. Equivalent to CX Gate in OpenQASM.
Id or I Gate	id	Identity Gate
U0 Gate	u0	Identity Gate
U Gate	u	Generic single qubit gate
P Gate	p	Phase Gate
X Gate	x	Bit Flip Gate or NOT Gate
Y Gate	y	Bit and Phase Flip Gate
Z Gate	z	Phase Flip Gate
H Gate	h	Hadamard Gate
S Gate	s	The S Gate. Also known as Square-root of Z Gate.
S – Dagger Gate	sdg	The Sdg Gate, inverse of S Gate.
T Gate	t	The T Gate. Also known as fourth-root of Z Gate.
T – Dagger Gate	tdg	The Tdg Gate, inverse of T Gate.
RX Gate	rx	The RX Gate, performs rotation about X axis on Bloch Sphere.
RY Gate	ry	The RY Gate, performs rotation about Y axis on Bloch Sphere.
RZ Gate	rz	The RZ Gate, performs rotation about Z axis on Bloch Sphere.
SX Gate	sx	The SX Gate. Also known as the Square-root of X Gate.
SX – Dagger Gate	sxdg	The SXdg Gate, inverse of SX Gate.
CZ Gate	cz	The CZ Gate or controlled-Phase change Gate.
CY Gate	cy	The CY Gate or controlled-Y Gate.
Swap Gate	swap	Swaps the state of two Qubits.
CH Gate	ch	The CH or controlled-H Gate.
C3 or Toffoli Gate	ccx	The CC-NOT Gate or Toffoli Gate.
CSwap or Fredkin Gate	cswap	The CSwap or controlled Swap Gate.
CRX Gate	crx	The Controlled RX Gate.
CRY Gate	cry	The Controlled RY Gate.
CRZ Gate	crz	The Controlled RZ Gate.
CP Gate	cu1	The Controlled Phase Rotation
CP Gate	cp	The Controlled Phase Rotation
CU Gate	cu3	The Controlled U3 Gate
CSX Gate	csx	The Controlled SX Gate.
CU Gate	cu	The Controlled U3 Gate
RXX Gate	rxx	Two Qubit XX Rotation
RZZ Gate	rzz	Two Qubit ZZ Rotation
RCCX Gate	rccx	The relative phase CCX Gate.
RC3X Gate	rc3x	The relative-phase 3-controlled X gate.
C3X Gate	c3x	The 3-controlled X gate.
C3SX Gate	c3sqrtx	The 3-controlled SX gate
C4X Gate	c4x	4-controlled X gate

Including the qelib1.inc File

The qelib1.inc file can be parsed inside another OpenQASM file by using the following syntax-

include "qelib1.inc";