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# TwoLocal

class qiskit.circuit.library.TwoLocal(num_qubits=None, rotation_blocks=None, entanglement_blocks=None, entanglement='full', reps=3, skip_unentangled_qubits=False, skip_final_rotation_layer=False, parameter_prefix='θ', insert_barriers=False, initial_state=None, name='TwoLocal', flatten=None)

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Bases: NLocal

The two-local circuit.

The two-local circuit is a parameterized circuit consisting of alternating rotation layers and entanglement layers. The rotation layers are single qubit gates applied on all qubits. The entanglement layer uses two-qubit gates to entangle the qubits according to a strategy set using entanglement. Both the rotation and entanglement gates can be specified as string (e.g. 'ry' or 'cx'), as gate-type (e.g. RYGate or CXGate) or as QuantumCircuit (e.g. a 1-qubit circuit or 2-qubit circuit).

A set of default entanglement strategies is provided:

• 'full' entanglement is each qubit is entangled with all the others.
• 'linear' entanglement is qubit $i$ entangled with qubit $i + 1$, for all $i \in \{0, 1, ... , n - 2\}$, where $n$ is the total number of qubits.
• 'reverse_linear' entanglement is qubit $i$ entangled with qubit $i + 1$, for all $i \in \{n-2, n-3, ... , 1, 0\}$, where $n$ is the total number of qubits. Note that if entanglement_blocks = 'cx' then this option provides the same unitary as 'full' with fewer entangling gates.
• 'pairwise' entanglement is one layer where qubit $i$ is entangled with qubit $i + 1$, for all even values of $i$, and then a second layer where qubit $i$ is entangled with qubit $i + 1$, for all odd values of $i$.
• 'circular' entanglement is linear entanglement but with an additional entanglement of the first and last qubit before the linear part.
• 'sca' (shifted-circular-alternating) entanglement is a generalized and modified version of the proposed circuit 14 in Sim et al.(opens in a new tab). It consists of circular entanglement where the ‘long’ entanglement connecting the first with the last qubit is shifted by one each block. Furthermore the role of control and target qubits are swapped every block (therefore alternating).

The entanglement can further be specified using an entangler map, which is a list of index pairs, such as

>>> entangler_map = [(0, 1), (1, 2), (2, 0)]

If different entanglements per block should be used, provide a list of entangler maps. See the examples below on how this can be used.

>>> entanglement = [entangler_map_layer_1, entangler_map_layer_2, ... ]

Barriers can be inserted in between the different layers for better visualization using the insert_barriers attribute.

For each parameterized gate a new parameter is generated using a ParameterVector. The name of these parameters can be chosen using the parameter_prefix.

Examples

>>> two = TwoLocal(3, 'ry', 'cx', 'linear', reps=2, insert_barriers=True)
>>> print(two)  # decompose the layers into standard gates
┌──────────┐ ░            ░ ┌──────────┐ ░            ░ ┌──────────┐
q_0: ┤ Ry(θ[0]) ├─░───■────────░─┤ Ry(θ[3]) ├─░───■────────░─┤ Ry(θ[6]) ├
├──────────┤ ░ ┌─┴─┐      ░ ├──────────┤ ░ ┌─┴─┐      ░ ├──────────┤
q_1: ┤ Ry(θ[1]) ├─░─┤ X ├──■───░─┤ Ry(θ[4]) ├─░─┤ X ├──■───░─┤ Ry(θ[7]) ├
├──────────┤ ░ └───┘┌─┴─┐ ░ ├──────────┤ ░ └───┘┌─┴─┐ ░ ├──────────┤
q_2: ┤ Ry(θ[2]) ├─░──────┤ X ├─░─┤ Ry(θ[5]) ├─░──────┤ X ├─░─┤ Ry(θ[8]) ├
└──────────┘ ░      └───┘ ░ └──────────┘ ░      └───┘ ░ └──────────┘
>>> two = TwoLocal(3, ['ry','rz'], 'cz', 'full', reps=1, insert_barriers=True)
>>> qc = QuantumCircuit(3)
>>> qc += two
>>> print(qc.decompose().draw())
┌──────────┐┌──────────┐ ░           ░ ┌──────────┐ ┌──────────┐
q_0: ┤ Ry(θ[0]) ├┤ Rz(θ[3]) ├─░──■──■─────░─┤ Ry(θ[6]) ├─┤ Rz(θ[9]) ├
├──────────┤├──────────┤ ░  │  │     ░ ├──────────┤┌┴──────────┤
q_1: ┤ Ry(θ[1]) ├┤ Rz(θ[4]) ├─░──■──┼──■──░─┤ Ry(θ[7]) ├┤ Rz(θ[10]) ├
├──────────┤├──────────┤ ░     │  │  ░ ├──────────┤├───────────┤
q_2: ┤ Ry(θ[2]) ├┤ Rz(θ[5]) ├─░─────■──■──░─┤ Ry(θ[8]) ├┤ Rz(θ[11]) ├
└──────────┘└──────────┘ ░           ░ └──────────┘└───────────┘
>>> entangler_map = [[0, 1], [1, 2], [2, 0]]  # circular entanglement for 3 qubits
>>> two = TwoLocal(3, 'x', 'crx', entangler_map, reps=1)
>>> print(two)  # note: no barriers inserted this time!
┌───┐                             ┌──────────┐┌───┐
q_0: |0>┤ X ├─────■───────────────────────┤ Rx(θ[2]) ├┤ X ├
├───┤┌────┴─────┐            ┌───┐└─────┬────┘└───┘
q_1: |0>┤ X ├┤ Rx(θ[0]) ├─────■──────┤ X ├──────┼──────────
├───┤└──────────┘┌────┴─────┐└───┘      │     ┌───┐
q_2: |0>┤ X ├────────────┤ Rx(θ[1]) ├───────────■─────┤ X ├
└───┘            └──────────┘                 └───┘
>>> entangler_map = [[0, 3], [0, 2]]  # entangle the first and last two-way
>>> two = TwoLocal(4, [], 'cry', entangler_map, reps=1)
>>> circuit = two + two
>>> print(circuit.decompose().draw())  # note, that the parameters are the same!
q_0: ─────■───────────■───────────■───────────■──────
│           │           │           │
q_1: ─────┼───────────┼───────────┼───────────┼──────
│      ┌────┴─────┐     │      ┌────┴─────┐
q_2: ─────┼──────┤ Ry(θ[1]) ├─────┼──────┤ Ry(θ[1]) ├
┌────┴─────┐└──────────┘┌────┴─────┐└──────────┘
q_3: ┤ Ry(θ[0]) ├────────────┤ Ry(θ[0]) ├────────────
└──────────┘            └──────────┘
>>> layer_1 = [(0, 1), (0, 2)]
>>> layer_2 = [(1, 2)]
>>> two = TwoLocal(3, 'x', 'cx', [layer_1, layer_2], reps=2, insert_barriers=True)
>>> print(two)
┌───┐ ░            ░ ┌───┐ ░       ░ ┌───┐
q_0: ┤ X ├─░───■────■───░─┤ X ├─░───────░─┤ X ├
├───┤ ░ ┌─┴─┐  │   ░ ├───┤ ░       ░ ├───┤
q_1: ┤ X ├─░─┤ X ├──┼───░─┤ X ├─░───■───░─┤ X ├
├───┤ ░ └───┘┌─┴─┐ ░ ├───┤ ░ ┌─┴─┐ ░ ├───┤
q_2: ┤ X ├─░──────┤ X ├─░─┤ X ├─░─┤ X ├─░─┤ X ├
└───┘ ░      └───┘ ░ └───┘ ░ └───┘ ░ └───┘

Parameters

## Attributes

### ancillas

Returns a list of ancilla bits in the order that the registers were added.

### calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form {'gate_name': {(qubits, params): schedule}}

### clbits

Returns a list of classical bits in the order that the registers were added.

### entanglement

Get the entanglement strategy.

Returns

The entanglement strategy, see get_entangler_map() for more detail on how the format is interpreted.

### entanglement_blocks

The blocks in the entanglement layers.

Returns

The blocks in the entanglement layers.

### extension_lib

Default value: 'include "qelib1.inc";'

### flatten

Returns whether the circuit is wrapped in nested gates/instructions or flattened.

### global_phase

Return the global phase of the current circuit scope in radians.

Default value: 'OPENQASM 2.0;'

### initial_state

Return the initial state that is added in front of the n-local circuit.

Returns

The initial state.

### insert_barriers

If barriers are inserted in between the layers or not.

Returns

True, if barriers are inserted in between the layers, False if not.

### instances

Default value: 159

### layout

Return any associated layout information about the circuit

This attribute contains an optional TranspileLayout object. This is typically set on the output from transpile() or PassManager.run() to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the transpile() function, an initial layout which permutes the qubits based on the selected physical qubits on the Target, and a final layout which is an output permutation caused by SwapGates inserted during routing.

The user provided metadata associated with the circuit.

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

### num_ancillas

Return the number of ancilla qubits.

### num_clbits

Return number of classical bits.

### num_layers

Return the number of layers in the n-local circuit.

Returns

The number of layers in the circuit.

### num_parameters_settable

The number of total parameters that can be set to distinct values.

This does not change when the parameters are bound or exchanged for same parameters, and therefore is different from num_parameters which counts the number of unique Parameter objects currently in the circuit.

Returns

The number of parameters originally available in the circuit.

Note

This quantity does not require the circuit to be built yet.

### num_qubits

Returns the number of qubits in this circuit.

Returns

The number of qubits.

### op_start_times

Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

Returns

List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.

Raises

AttributeError(opens in a new tab) – When circuit is not scheduled.

### ordered_parameters

The parameters used in the underlying circuit.

This includes float values and duplicates.

Examples

>>> # prepare circuit ...
>>> print(nlocal)
┌───────┐┌──────────┐┌──────────┐┌──────────┐
q_0: ┤ Ry(1) ├┤ Ry(θ[1]) ├┤ Ry(θ[1]) ├┤ Ry(θ[3]) ├
└───────┘└──────────┘└──────────┘└──────────┘
>>> nlocal.parameters
{Parameter(θ[1]), Parameter(θ[3])}
>>> nlocal.ordered_parameters
[1, Parameter(θ[1]), Parameter(θ[1]), Parameter(θ[3])]

Returns

The parameters objects used in the circuit.

### parameter_bounds

The parameter bounds for the unbound parameters in the circuit.

Returns

A list of pairs indicating the bounds, as (lower, upper). None indicates an unbounded parameter in the corresponding direction. If None is returned, problem is fully unbounded.

### preferred_init_points

The initial points for the parameters. Can be stored as initial guess in optimization.

Returns

The initial values for the parameters, or None, if none have been set.

### prefix

Default value: 'circuit'

### qregs

Type: list[QuantumRegister]

A list of the quantum registers associated with the circuit.

### qubits

Returns a list of quantum bits in the order that the registers were added.

### reps

The number of times rotation and entanglement block are repeated.

Returns

The number of repetitions.

### rotation_blocks

The blocks in the rotation layers.

Returns

The blocks in the rotation layers.

## Methods

### get_entangler_map

get_entangler_map(rep_num, block_num, num_block_qubits)

Overloading to handle the special case of 1 qubit where the entanglement are ignored.

Return type