qiskit.circuit.library.RZXGate

class RZXGate(theta)

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:

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

Nota

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)

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

Tipo de retorno

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], ...]
  

Parâmetros

• qargs (List) – List of quantum bit arguments.

• cargs (List) – List of classical bit arguments.

Tipo de retorno

Tuple[List, List]

Retorna

A tuple with single arguments.

Levanta

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.

Parâmetros

• 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.

Retorna

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.

Tipo de retorno

qiskit.circuit.ControlledGate

Levanta

QiskitError – unrecognized mode or invalid ctrl_state

copy(name=None)

Copy of the instruction.

Parâmetros

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

Retorna

a copy of the current instruction, with the name

updated if it was provided

Tipo de retorno

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()

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

Tipo de retorno

str

mirror()

DEPRECATED: use instruction.reverse_ops().

Retorna

a new instruction with sub-instructions

reversed.

Tipo de retorno

qiskit.circuit.Instruction

property params

return instruction params.

power(exponent)

Creates a unitary gate as gate^exponent.

Parâmetros

exponent (float) – Gate^exponent

Retorna

To which to_matrix is self.to_matrix^exponent.

Tipo de retorno

qiskit.extensions.UnitaryGate

Levanta

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.

Parâmetros

n (int) – Number of times to repeat the instruction

Retorna

Containing the definition.

Tipo de retorno

qiskit.circuit.Instruction

Levanta

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.

Retorna

a new instruction with

sub-instructions reversed.

Tipo de retorno

qiskit.circuit.Instruction

to_matrix()

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