ECRGate

class ECRGate

Bases: qiskit.circuit.gate.Gate

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.

Methods Defined Here

to_matrix

Return a numpy.array for the ECR gate.

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 instruction label

Return type

str

params

return instruction params.

unit

Get the time unit of duration.