Skip to main contentIBM Quantum Documentation
You are viewing the API reference for an old version of Qiskit SDK. Switch to latest version


class qiskit.circuit.library.ECRGate(*args, _force_mutable=False, **kwargs)

GitHub(opens in a new tab)

Bases: SingletonGate

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 12(IXXY)\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:

ECR q0,q1=12(010i10i00i01i010)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}

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 XZX \otimes Z tensor order. Instead, if we apply it on (q_1, q_0), the matrix will be ZXZ \otimes X:

     │   ECR   │
ECR q0,q1=12(001i00i11i00i100)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}

Create new ECR gate.



Get the base class of this instruction. This is guaranteed to be in the inheritance tree of self.

The “base class” of an instruction is the lowest class in its inheritance tree that the object should be considered entirely compatible with for _all_ circuit applications. This typically means that the subclass is defined purely to offer some sort of programmer convenience over the base class, and the base class is the “true” class for a behavioural perspective. In particular, you should not override base_class if you are defining a custom version of an instruction that will be implemented differently by hardware, such as an alternative measurement strategy, or a version of a parametrised gate with a particular set of parameters for the purposes of distinguishing it in a Target from the full parametrised gate.

This is often exactly equivalent to type(obj), except in the case of singleton instances of standard-library instructions. These singleton instances are special subclasses of their base class, and this property will return that base. For example:

>>> isinstance(XGate(), XGate)
>>> type(XGate()) is XGate
>>> XGate().base_class is XGate

In general, you should not rely on the precise class of an instruction; within a given circuit, it is expected that should be a more suitable discriminator in most situations.


The classical condition on the instruction.


Get Clbits in condition.


Get the decompositions of the instruction from the SessionEquivalenceLibrary.


Return definition in terms of other basic gates.


Get the duration.


Return instruction label


Is this instance is a mutable unique instance or not.

If this attribute is False the gate instance is a shared singleton and is not mutable.


Return the name.


Return the number of clbits.


Return the number of qubits.


return instruction params.


Get the time unit of duration.




Return inverse ECR gate (itself).

Was this page helpful?
Report a bug or request content on GitHub.