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class qiskit.circuit.library.Isometry(isometry, num_ancillas_zero, num_ancillas_dirty, epsilon=1e-10)

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Bases: Instruction

Decomposition of arbitrary isometries from mm to nn qubits.

In particular, this allows to decompose unitaries (m=n) and to do state preparation (m=0m=0).

The decomposition is based on [1].


[1] Iten et al., Quantum circuits for isometries (2016).

Phys. Rev. A 93, 032318(opens in a new tab).


  • isometry (np.ndarray) – An isometry from mm to :math`n` qubits, i.e., a complex np.ndarray of dimension 2n×2m2^n \times 2^m with orthonormal columns (given in the computational basis specified by the order of the ancillas and the input qubits, where the ancillas are considered to be more significant than the input qubits).
  • num_ancillas_zero (int(opens in a new tab)) – Number of additional ancillas that start in the state 0|0\rangle (the nmn-m ancillas required for providing the output of the isometry are not accounted for here).
  • num_ancillas_dirty (int(opens in a new tab)) – Number of additional ancillas that start in an arbitrary state.
  • epsilon (float(opens in a new tab)) – Error tolerance of calculations.



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.


The parameters of this Instruction. Ideally these will be gate angles.


Get the time unit of duration.




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Return the adjoint of the unitary.



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Invert this instruction.

If annotated is False, the inverse instruction is implemented as a fresh instruction with the recursively inverted definition.

If annotated is True, the inverse instruction is implemented as AnnotatedOperation, and corresponds to the given instruction annotated with the “inverse modifier”.

Special instructions inheriting from Instruction can implement their own inverse (e.g. T and Tdg, Barrier, etc.) In particular, they can choose how to handle the argument annotated which may include ignoring it and always returning a concrete gate class if the inverse is defined as a standard gate.


annotated (bool(opens in a new tab)) – if set to True the output inverse gate will be returned as AnnotatedOperation.


The inverse operation.


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



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Isometry parameter has to be an ndarray.

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