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James Wootton
@decodoku
, 27 tweets, 13 min read Read on Twitter
There are a lot of basic operations to play with in quantum computers. Here is a tweet-length summary of as many as will fit in a twitter thread.

There are also links to the #IBMQ 'Introduction to Quantum Circuits' where you can find out more.
The H or Hadamard gate rotates the states |0〉and |1〉to |+〉and |-〉, respectively. It is useful for making superpositions. As a Clifford gate, it is useful for moving information between the x and z bases.
quantum-computing.ibm.com/support/guides…
The controlled-NOT gate acts on a pair of qubits, with one acting as ‘control’ and the other as ‘target. It performs an X on the target whenever the control is in state |1〉. If the control qubit is in a superposition, this gate creates entanglement.
quantum-computing.ibm.com/support/guides…
The identity gate is actually the absence of a gate. It ensures that nothing is applied to a qubit for one unit of gate time.
One of the three physical gates: the single qubit gates that everything else is compiled down into for #IBMQ hardware. It has three parameters that allow the construction of any single qubit gate, Has a duration of one unit of gate time.
quantum-computing.ibm.com/support/guides…
Another one of the three physical gates. The two parameters control two different rotations within the gate. Has a duration of one unit of gate time.
quantum-computing.ibm.com/support/guides…
One of the three physical gates. Equivalent to Rz. This can be implemented by the control software, requiring no actual manipulation of the qubits, and so effectively has a duration of zero.
quantum-computing.ibm.com/support/guides…
The Rx gate requires a single parameter: an angle expressed in radians. On the Bloch sphere, this gate corresponds to rotating the qubit state around the x axis by the given angle.
quantum-computing.ibm.com/support/guides…
The Ry gate requires a single parameter: an angle expressed in radians. On the Bloch sphere, this gate corresponds to rotating the qubit state around the y axis by the given angle.
quantum-computing.ibm.com/support/guides…
The Rz gate requires a single parameter: an angle expressed in radians. On the Bloch sphere, this gate corresponds to rotating the qubit state around the z axis by the given angle.
quantum-computing.ibm.com/support/guides…
The Pauli X gate has the property of flipping the |0〉state to |1〉, and vice versa. It is equivalent to Rx for the angle pi.quantum-computing.ibm.com/support/guides…
The Pauli Y gate is equivalent to Ry for the angle pi. It is also equivalent to the combined effect of X and Z.
quantum-computing.ibm.com/support/guides…
The Pauli Z gate has the property of flipping the |+〉to |-〉, and vice versa. It is equivalent to Rz for the angle pi.
quantum-computing.ibm.com/support/guides…
The S gate is equivalent to Rz for the angle pi/2. As a Clifford gate, it is useful for moving information between the x and y bases.
quantum-computing.ibm.com/support/guides…
The inverse of the S gate. Equivalent to Rz for the angle pi/2. As a Clifford gate, it is useful for moving information between the x and y bases.
quantum-computing.ibm.com/support/guides…
The T gate is equivalent to Rz for the angle pi/4. Fault-tolerant quantum computers will compile all quantum programs down to just the T gate and its inverse, as well as the Clifford gates.
quantum-computing.ibm.com/support/guides…
The inverse of the T gate, which is equivalent to Rz for the angle -pi/4. Fault-tolerant quantum computers will compile all quantum programs down to just the T gate and its inverse, as well as the Clifford gates.
The controlled-Hadamard gate, like the controlled-NOT, acts on a control and target qubit. It performs an H on the target whenever the control is in state |1〉. It is the official quantum gate of Switzerland.
quantum-computing.ibm.com/support/guides…
The controlled-Y gate, like the controlled-NOT, acts on a control and target qubit. It performs a Y on the target whenever the control is in state |1〉.
quantum-computing.ibm.com/support/guides…
The controlled-Z gate, like the controlled-NOT, acts on a control and target qubit. It performs a Z on the target whenever the control is in state |1〉.
quantum-computing.ibm.com/support/guides…
The controlled-Rz gate, like the controlled-NOT, acts on a control and target qubit. It performs a Rz rotation on the target whenever the control is in state |1〉.
The controlled-U3 gate, like the controlled-NOT, acts on a control and target qubit. It performs a Rz rotation on the target whenever the control is in state |1〉.
The ccX gate, commonly known as the Toffoli, has two control qubits and one target. At applies an X to the target only when both controls are in state |1〉.
quantum-computing.ibm.com/support/guides…
The SWAP gate simply swaps the states of two qubits.
quantum-computing.ibm.com/support/guides…
Measurement in the standard basis, also known as the z basis or computational basis. Can be used to implement any kind of measurement when combined with other gates. It is not a reversible operation.
quantum-computing.ibm.com/support/guides…
For this gate, and many that follow it, it is good to find out what the weird | and 〉are all about. This is explained here
quantum-computing.ibm.com/support/guides…
I think that should be two units, actually.
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