qiskit.circuit.library.CRZGate¶
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class
CRZGate(theta, label=None, ctrl_state=None)[source]¶ Controlled-RZ gate.
This is a diagonal but non-symmetric gate that induces a phase on the state of the target qubit, depending on the control state.
Circuit symbol:
q_0: ────■──── ┌───┴───┐ q_1: ┤ Rz(λ) ├ └───────┘Matrix representation:
\[\begin{split}CRZ(\lambda)\ q_0, q_1 = I \otimes |0\rangle\langle 0| + RZ(\lambda) \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & e^{-i\frac{\lambda}{2}} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i\frac{\lambda}{2}} \end{pmatrix}\end{split}\]Note
In Qiskit’s convention, higher qubit indices are more significant (little endian convention). In many textbooks, controlled gates are presented with the assumption of more significant qubits as control, which in our case would be q_1. Thus a textbook matrix for this gate will be:
┌───────┐ q_0: ┤ Rz(λ) ├ └───┬───┘ q_1: ────■────\[\begin{split}CRZ(\lambda)\ q_1, q_0 = |0\rangle\langle 0| \otimes I + |1\rangle\langle 1| \otimes RZ(\lambda) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & e^{-i\frac{\lambda}{2}} & 0 \\ 0 & 0 & 0 & e^{i\frac{\lambda}{2}} \end{pmatrix}\end{split}\]See also
CU1Gate: Due to the global phase difference in the matrix definitions of U1 and RZ, CU1 and CRZ are different gates with a relative phase difference.Create new CRZ gate.
Methods
__init__(theta[, label, ctrl_state])Create new CRZ 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 CRZ gate (i.e.
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.
For a composite instruction, reverse the order of sub-instructions.
Return a numpy.array for the CRZ gate.
validate_parameter(parameter)Gate parameters should be int, float, or ParameterExpression
Attributes
Return the control state of the gate as a decimal integer.
Get the decompositions of the instruction from the SessionEquivalenceLibrary.
Return definition in terms of other basic gates.
Get the duration.
Return gate label
Get number of control qubits.
Get parameters from base_gate.
Get the time unit of duration.
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add_decomposition(decomposition)¶ Add a decomposition of the instruction to the SessionEquivalenceLibrary.
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assemble()¶ Assemble a QasmQobjInstruction
- Return type
Instruction
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broadcast_arguments(qargs, cargs)¶ Validation and handling of the arguments and its relationship.
For example,
cx([q[0],q[1]], q[2])meanscx(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], ...]
- Parameters
qargs (
List) – List of quantum bit arguments.cargs (
List) – List of classical bit arguments.
- Return type
Tuple[List,List]- Returns
A tuple with single arguments.
- Raises
CircuitError – If the input is not valid. For example, the number of arguments does not match the gate expectation.
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c_if(classical, val)¶ Add classical condition on register classical and value val.
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control(num_ctrl_qubits=1, label=None, ctrl_state=None)¶ Return controlled version of gate. See
ControlledGatefor usage.- Parameters
num_ctrl_qubits (
Optional[int]) – number of controls to add to gate (default=1)label (
Optional[str]) – optional gate labelctrl_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.
- Returns
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.
- Return type
- Raises
QiskitError – unrecognized mode or invalid ctrl_state
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copy(name=None)¶ Copy of the instruction.
- Parameters
name (str) – name to be given to the copied circuit, if None then the name stays the same.
- Returns
- a copy of the current instruction, with the name
updated if it was provided
- Return type
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property
ctrl_state¶ Return the control state of the gate as a decimal integer.
- Return type
int
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property
decompositions¶ Get the decompositions of the instruction from the SessionEquivalenceLibrary.
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property
definition¶ Return definition in terms of other basic gates. If the gate has open controls, as determined from self.ctrl_state, the returned definition is conjugated with X without changing the internal _definition.
- Return type
List
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property
duration¶ Get the duration.
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is_parameterized()¶ Return True .IFF. instruction is parameterized else False
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property
label¶ Return gate label
- Return type
str
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mirror()¶ DEPRECATED: use instruction.reverse_ops().
- Returns
- a new instruction with sub-instructions
reversed.
- Return type
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property
num_ctrl_qubits¶ Get number of control qubits.
- Returns
The number of control qubits for the gate.
- Return type
int
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property
params¶ Get parameters from base_gate.
- Returns
List of gate parameters.
- Return type
list
- Raises
CircuitError – Controlled gate does not define a base gate
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power(exponent)¶ Creates a unitary gate as gate^exponent.
- Parameters
exponent (float) – Gate^exponent
- Returns
To which to_matrix is self.to_matrix^exponent.
- Return type
- Raises
CircuitError – If Gate is not unitary
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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];).
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repeat(n)¶ Creates an instruction with gate repeated n amount of times.
- Parameters
n (int) – Number of times to repeat the instruction
- Returns
Containing the definition.
- Return type
- Raises
CircuitError – If n < 1.
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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.
- Returns
- a new instruction with
sub-instructions reversed.
- Return type
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property
unit¶ Get the time unit of duration.
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validate_parameter(parameter)¶ Gate parameters should be int, float, or ParameterExpression
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