ECRGate#

class qiskit.circuit.library.ECRGate[Quellcode]#

Bases: Gate

An echoed cross-resonance gate.

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. More specifically, this gate implements \(\frac{1}{\sqrt{2}}(IX-XY)\).

Can be applied to a QuantumCircuit with the ecr() method.

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:

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

Bemerkung

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.

Attributes

condition_bits#: Get Clbits in condition.

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

name#: Return the name.

num_clbits#: Return the number of clbits.

num_qubits#: Return the number of qubits.

params#: return instruction params.

unit#: Get the time unit of duration.

Methods

inverse()[Quellcode]#: Return inverse ECR gate (itself).