qiskit.circuit.library.ECRGate

class ECRGate

An echoed RZX(pi/2) gate implemented using RZX(pi/4) and RZX(-pi/4).

This gate is maximally entangling and is equivalent to a CNOT up to single-qubit pre-rotations. The echoing procedure mitigates some unwanted terms (terms other than ZX) to cancel in an experiment.

Circuit Symbol:

     ┌─────────┐            ┌────────────┐┌────────┐┌─────────────┐
q_0: ┤0        ├       q_0: ┤0           ├┤ RX(pi) ├┤0            ├
     │   ECR   │   =        │  RZX(pi/4) │└────────┘│  RZX(-pi/4) │
q_1: ┤1        ├       q_1: ┤1           ├──────────┤1            ├
     └─────────┘            └────────────┘          └─────────────┘

Matrix Representation:

\[\begin{split}ECR\ q_0, q_1 = \frac{1}{\sqrt{2}} \begin{pmatrix} 0 & 1 & 0 & i \\ 1 & 0 & -i & 0 \\ 0 & i & 0 & 1 \\ -i & 0 & 1 & 0 \end{pmatrix}\end{split}\]

Note

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        ├
     │   ECR   │
q_1: ┤0        ├
     └─────────┘

\[\begin{split}ECR\ q_0, q_1 = \frac{1}{\sqrt{2}} \begin{pmatrix} 0 & 0 & 1 & i \\ 0 & 0 & i & 1 \\ 1 & -i & 0 & 0 \\ -i & 1 & 0 & 0 \end{pmatrix}\end{split}\]

Create new ECR gate.

__init__()

Create new ECR gate.

Methods

__init__()	Create new ECR 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()	Invert this instruction.
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.
soft_compare(other)	Soft comparison between gates.
to_matrix()	Return a numpy.array for the ECR 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

Return type

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], ...]
  

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.

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.

Parameters

• 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.

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

qiskit.circuit.ControlledGate

Raises

QiskitError – unrecognized mode or invalid ctrl_state

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

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()

Invert this instruction.

If the instruction is composite (i.e. has a definition), then its definition will be recursively inverted.

Special instructions inheriting from Instruction can implement their own inverse (e.g. T and Tdg, Barrier, etc.)

Returns

a fresh instruction for the inverse

Return type

qiskit.circuit.Instruction

Raises

CircuitError – if the instruction is not composite and an inverse has not been implemented for it.

is_parameterized()

Return True .IFF. instruction is parameterized else False

property label

Return gate label

Return type

str

mirror()

DEPRECATED: use instruction.reverse_ops().

Returns

a new instruction with sub-instructions

reversed.

Return type

qiskit.circuit.Instruction

property params

return instruction params.

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

qiskit.extensions.UnitaryGate

Raises

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.

Parameters

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

Returns

Containing the definition.

Return type

qiskit.circuit.Instruction

Raises

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.

Returns

a new instruction with

sub-instructions reversed.

Return type

qiskit.circuit.Instruction

soft_compare(other)

Soft comparison between gates. Their names, number of qubits, and classical bit numbers must match. The number of parameters must match. Each parameter is compared. If one is a ParameterExpression then it is not taken into account.

Parameters

other (instruction) – other instruction.

Returns

are self and other equal up to parameter expressions.

Return type

bool

to_matrix()

Return a numpy.array for the ECR gate.

property unit

Get the time unit of duration.

validate_parameter(parameter)

Gate parameters should be int, float, or ParameterExpression