qiskit.circuit.library.RZXGate¶

class RZXGate(theta)[Quellcode]¶

A parameteric 2-qubit \(Z \otimes X\) interaction (rotation about ZX).

This gate is maximally entangling at \(\theta = \pi/2\).

The cross-resonance gate (CR) for superconducting qubits implements a ZX interaction (however other terms are also present in an experiment).

Circuit Symbol:

     ┌─────────┐
q_0: ┤0        ├
     │  Rzx(θ) │
q_1: ┤1        ├
     └─────────┘

Matrix Representation:

\[ \begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{ZX}(\theta)\ q_0, q_1 = exp(-i \frac{\theta}{2} X{\otimes}Z) = \begin{pmatrix} \cos(\th) & 0 & -i\sin(\th) & 0 \\ 0 & \cos(\th) & 0 & i\sin(\th) \\ -i\sin(\th) & 0 & \cos(\th) & 0 \\ 0 & i\sin(\th) & 0 & \cos(\th) \end{pmatrix}\end{split}\end{aligned}\end{align} \]

Bemerkung

In Qiskit’s convention, higher qubit indices are more significant (little endian convention). In the above example we apply the gate on (q_0, q_1) which results in the \(X \otimes Z\) tensor order. Instead, if we apply it on (q_1, q_0), the matrix will be \(Z \otimes X\):

     ┌─────────┐
q_0: ┤1        ├
     │  Rzx(θ) │
q_1: ┤0        ├
     └─────────┘

\[ \begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{ZX}(\theta)\ q_1, q_0 = exp(-i \frac{\theta}{2} Z{\otimes}X) = \begin{pmatrix} \cos(\th) & -i\sin(\th) & 0 & 0 \\ -i\sin(\th) & \cos(\th) & 0 & 0 \\ 0 & 0 & \cos(\th) & i\sin(\th) \\ 0 & 0 & i\sin(\th) & \cos(\th) \end{pmatrix}\end{split}\end{aligned}\end{align} \]

This is a direct sum of RX rotations, so this gate is equivalent to a uniformly controlled (multiplexed) RX gate:

\[\begin{split}R_{ZX}(\theta)\ q_1, q_0 = \begin{pmatrix} RX(\theta) & 0 \\ 0 & RX(-\theta) \end{pmatrix}\end{split}\]

Examples:

\[R_{ZX}(\theta = 0) = I\]

\[R_{ZX}(\theta = 2\pi) = -I\]

\[R_{ZX}(\theta = \pi) = -i Z \otimes X\]

\[\begin{split}RZX(\theta = \frac{\pi}{2}) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 0 & -i & 0 \\ 0 & 1 & 0 & i \\ -i & 0 & 1 & 0 \\ 0 & i & 0 & 1 \end{pmatrix}\end{split}\]

Create new RZX gate.

__init__(theta)[Quellcode]¶: Create new RZX gate.

Methods

`__init__`(theta)	Create new RZX gate.
`add_decomposition`(decomposition)	Add a decomposition of the instruction to the SessionEquivalenceLibrary.
`assemble`()	Assemble a QasmQobjInstruction
`broadcast_arguments`(qargs, cargs)	Validation and handling of the arguments and its relationship.
`c_if`(classical, val)	Add classical condition on register classical and value val.
`control`([num_ctrl_qubits, label, ctrl_state])	Return controlled version of gate.
`copy`([name])	Copy of the instruction.
`inverse`()	Return inverse RZX gate (i.e.
`is_parameterized`()	Return True .IFF.
`mirror`()	DEPRECATED: use instruction.reverse_ops().
`power`(exponent)	Creates a unitary gate as gate^exponent.
`qasm`()	Return a default OpenQASM string for the instruction.
`repeat`(n)	Creates an instruction with gate repeated n amount of times.
`reverse_ops`()	For a composite instruction, reverse the order of sub-instructions.
`to_matrix`()	Return a numpy.array for the RZX gate.
`validate_parameter`(parameter)	Gate parameters should be int, float, or ParameterExpression

Attributes

`decompositions`	Get the decompositions of the instruction from the SessionEquivalenceLibrary.
`definition`	Return definition in terms of other basic gates.
`duration`	Get the duration.
`label`	Return gate label
`params`	return instruction params.
`unit`	Get the time unit of duration.

add_decomposition(decomposition)¶: Add a decomposition of the instruction to the SessionEquivalenceLibrary.

assemble()¶

Assemble a QasmQobjInstruction

Rückgabetyp: Instruction

broadcast_arguments(qargs, cargs)¶

Validation and handling of the arguments and its relationship.

For example, cx([q[0],q[1]], q[2]) means cx(q[0], q[2]); cx(q[1], q[2]). This method yields the arguments in the right grouping. In the given example:

in: [[q[0],q[1]], q[2]],[]
outs: [q[0], q[2]], []
      [q[1], q[2]], []

The general broadcasting rules are:

If len(qargs) == 1:
```
[q[0], q[1]] -> [q[0]],[q[1]]
```

If len(qargs) == 2:

[[q[0], q[1]], [r[0], r[1]]] -> [q[0], r[0]], [q[1], r[1]]
[[q[0]], [r[0], r[1]]]       -> [q[0], r[0]], [q[0], r[1]]
[[q[0], q[1]], [r[0]]]       -> [q[0], r[0]], [q[1], r[0]]

If len(qargs) >= 3:

[q[0], q[1]], [r[0], r[1]],  ...] -> [q[0], r[0], ...], [q[1], r[1], ...]

Parameter

qargs (List) – List of quantum bit arguments.
cargs (List) – List of classical bit arguments.

Rückgabetyp

Tuple[List, List]

Rückgabe

A tuple with single arguments.

Verursacht

CircuitError – If the input is not valid. For example, the number of arguments does not match the gate expectation.

c_if(classical, val)¶: Add classical condition on register classical and value val.

control(num_ctrl_qubits=1, label=None, ctrl_state=None)¶

Return controlled version of gate. See ControlledGate for usage.

Parameter

num_ctrl_qubits (Optional[int]) – number of controls to add to gate (default=1)
label (Optional[str]) – optional gate label
ctrl_state (Union[int, str, None]) – The control state in decimal or as a bitstring (e.g. ‚111‘). If None, use 2**num_ctrl_qubits-1.

Rückgabe

Controlled version of gate. This default algorithm uses num_ctrl_qubits-1 ancillae qubits so returns a gate of size num_qubits + 2*num_ctrl_qubits - 1.

Rückgabetyp

qiskit.circuit.ControlledGate

Verursacht

QiskitError – unrecognized mode or invalid ctrl_state

copy(name=None)¶

Copy of the instruction.

Parameter

name (str) – name to be given to the copied circuit, if None then the name stays the same.

Rückgabe

a copy of the current instruction, with the name: updated if it was provided

Rückgabetyp

qiskit.circuit.Instruction

property decompositions¶: Get the decompositions of the instruction from the SessionEquivalenceLibrary.

property definition¶: Return definition in terms of other basic gates.

property duration¶: Get the duration.

inverse()[Quellcode]¶: Return inverse RZX gate (i.e. with the negative rotation angle).

is_parameterized()¶: Return True .IFF. instruction is parameterized else False

property label¶

Return gate label

Rückgabetyp: str

mirror()¶

DEPRECATED: use instruction.reverse_ops().

Rückgabe

a new instruction with sub-instructions: reversed.

Rückgabetyp

qiskit.circuit.Instruction

property params¶: return instruction params.

power(exponent)¶

Creates a unitary gate as gate^exponent.

Parameter: exponent (float) – Gate^exponent
Rückgabe: To which to_matrix is self.to_matrix^exponent.
Rückgabetyp: qiskit.extensions.UnitaryGate
Verursacht: CircuitError – If Gate is not unitary

qasm()¶

Return a default OpenQASM string for the instruction.

Derived instructions may override this to print in a different format (e.g. measure q[0] -> c[0];).

repeat(n)¶

Creates an instruction with gate repeated n amount of times.

Parameter: n (int) – Number of times to repeat the instruction
Rückgabe: Containing the definition.
Rückgabetyp: qiskit.circuit.Instruction
Verursacht: CircuitError – If n < 1.

reverse_ops()¶

For a composite instruction, reverse the order of sub-instructions.

This is done by recursively reversing all sub-instructions. It does not invert any gate.

Rückgabe

a new instruction with: sub-instructions reversed.

Rückgabetyp

qiskit.circuit.Instruction

to_matrix()[Quellcode]¶: Return a numpy.array for the RZX gate.

property unit¶: Get the time unit of duration.

validate_parameter(parameter)¶: Gate parameters should be int, float, or ParameterExpression