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# qiskit.circuit.library.RZZGate¶

class RZZGate(theta)[Quellcode]

A parameteric 2-qubit $$Z \otimes Z$$ interaction (rotation about ZZ).

This gate is symmetric, and is maximally entangling at $$\theta = \pi/2$$.

Circuit Symbol:

q_0: ───■────
│zz(θ)
q_1: ───■────


Matrix Representation:

\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{ZZ}(\theta) = exp(-i \th Z{\otimes}Z) = \begin{pmatrix} e^{-i \th} & 0 & 0 & 0 \\ 0 & e^{i \th} & 0 & 0 \\ 0 & 0 & e^{i \th} & 0 \\ 0 & 0 & 0 & e^{-i \th} \end{pmatrix}\end{split}\end{aligned}\end{align}

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

$\begin{split}R_{ZZ}(\theta) = \begin{pmatrix} RZ(\theta) & 0 \\ 0 & RZ(-\theta) \end{pmatrix}\end{split}$

Examples:

$R_{ZZ}(\theta = 0) = I$
$R_{ZZ}(\theta = 2\pi) = -I$
$R_{ZZ}(\theta = \pi) = - Z \otimes Z$
$\begin{split}R_{ZZ}(\theta = \frac{\pi}{2}) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1-i & 0 & 0 & 0 \\ 0 & 1+i & 0 & 0 \\ 0 & 0 & 1+i & 0 \\ 0 & 0 & 0 & 1-i \end{pmatrix}\end{split}$

Create new RZZ gate.

__init__(theta)[Quellcode]

Create new RZZ gate.

Methods

 __init__(theta) Create new RZZ gate. add_decomposition(decomposition) Add a decomposition of the instruction to the SessionEquivalenceLibrary. 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. Return inverse RZZ gate (i.e. Return True .IFF. DEPRECATED: use instruction.reverse_ops(). power(exponent) Creates a unitary gate as gate^exponent. Return a default OpenQASM string for the instruction. Creates an instruction with gate repeated n amount of times. For a composite instruction, reverse the order of sub-instructions. Return a numpy.array for the RZZ 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,q], q) means cx(q, q); cx(q, q). This method yields the arguments in the right grouping. In the given example:

in: [[q,q], q],[]
outs: [q, q], []
[q, q], []


• If len(qargs) == 1:

[q, q] -> [q],[q]

• If len(qargs) == 2:

[[q, q], [r, r]] -> [q, r], [q, r]
[[q], [r, r]]       -> [q, r], [q, r]
[[q, q], [r]]       -> [q, r], [q, r]

• If len(qargs) >= 3:

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

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 RZZ 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 -> c;).

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 RZZ gate.

property unit

Get the time unit of duration.

validate_parameter(parameter)

Gate parameters should be int, float, or ParameterExpression