# Isometry

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

Bases: `Instruction`

Decomposition of arbitrary isometries from $m$ to $n$ qubits.

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

The decomposition is based on [1].

**References:**

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

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

**Parameters**

**isometry**(*np.ndarray*) – An isometry from $m$ to :math`n` qubits, i.e., a complex`np.ndarray`

of dimension $2^n \times 2^m$ 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 $|0\rangle$ (the $n-m$ 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.

## Attributes

### base_class

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)
True
>>> type(XGate()) is XGate
False
>>> XGate().base_class is XGate
True
```

In general, you should not rely on the precise class of an instruction; within a given circuit, it is expected that `Instruction.name`

should be a more suitable discriminator in most situations.

### condition

The classical condition on the instruction.

### 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

### mutable

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.

### name

Return the name.

### num_clbits

Return the number of clbits.

### num_qubits

Return the number of qubits.

### params

The parameters of this `Instruction`

. Ideally these will be gate angles.

### unit

Get the time unit of duration.

## Methods

### inv_gate

### inverse

`inverse(annotated=False)`

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.

**Parameters**

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

.

**Returns**

The inverse operation.

**Raises**

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