(w0 |10⟩⟨01| + h.c.) + w1 |11⟩⟨11| interaction.

With weights $$(w_0, w_1)$$ and exponent $$t$$, this gate's matrix is defined as

$e^{-i t H},$

where

$H = \left(w_0 \left| 10 \right\rangle\left\langle 01 \right| + \text{h.c.}\right) - w_1 \left| 11 \right\rangle \left\langle 11 \right|.$

This corresponds to the Jordan-Wigner transform of

$H = (w_0 a^{\dagger}_i a_{i+1} + \text{h.c.}) + w_1 a_{i}^{\dagger} a_{i+1}^{\dagger} a_{i} a_{i+1},$

where $$a_i$$ and $$a_{i+1}$$ are the annihilation operators for the fermionic modes $$i$$ and $$(i+1)$$, respectively mapped to the first and second qubits on which this gate acts.

weights The weights of the terms in the Hamiltonian.

exponent

fermion_generator The FermionOperator G such that the gate's unitary is exp(-i t G) with exponent t using the Jordan-Wigner transformation.
global_shift

qubit_generator_matrix The matrix G such that the gate's unitary is exp(-i t G) with exponent t.

## Methods

View source

### controlled

Returns a controlled version of this gate. If no arguments are specified, defaults to a single qubit control.

Args
num_controls Total number of control qubits.
control_values Which control computational basis state to apply the sub gate. A sequence of length num_controls where each entry is an integer (or set of integers) corresponding to the computational basis state (or set of possible values) where that control is enabled. When all controls are enabled, the sub gate is applied. If unspecified, control values default to 1.
control_qid_shape The qid shape of the controls. A tuple of the expected dimension of each control qid. Defaults to (2,) * num_controls. Specify this argument when using qudits.

Returns
A cirq.Gate representing self controlled by the given control values and qubits. This is a cirq.ControlledGate in the base implementation, but subclasses may return a different gate type.

### fermion_generator_components

View source

The FermionOperators $$(G_i)_i$$ such that the gate's fermionic generator is $$\sum_i w_i G_i + \text{h.c.}$$ where $$(w_i)_i$$ are the gate's weights.

### from_interaction_operator

View source

Constructs the gate corresponding to the specified term in the Hamiltonian.

### fswap

View source

Update the weights of the gate to effect conjugation by an FSWAP on the i-th and (i+1)th qubits.

### interaction_operator_generator

View source

Constructs the Hamiltonian corresponding to the gate's generator.

### num_qubits

The number of qubits this gate acts on.

### num_weights

View source

The number of parameters (weights) in the generator.

### on

Returns an application of this gate to the given qubits.

Args
*qubits The collection of qubits to potentially apply the gate to.

Returns: a cirq.Operation which is this gate applied to the given qubits.

### on_each

Returns a list of operations applying the gate to all targets.

Args
*targets The qubits to apply this gate to. For single-qubit gates this can be provided as varargs or a combination of nested iterables. For multi-qubit gates this must be provided as an Iterable[Sequence[Qid]], where each sequence has num_qubits qubits.

Returns
Operations applying this gate to the target qubits.

Raises
ValueError If targets are not instances of Qid or Iterable[Qid]. If the gate qubit number is incompatible.
TypeError If a single target is supplied and it is not iterable.

### permute

View source

An in-place version of permuted.

### permuted

View source

Returns a gate with the Jordan-Wigner ordering changed.

If the Jordan-Wigner ordering of the original gate is given by init_pos, then the returned gate has Jordan-Wigner ordering (0, ..., n - 1), where n is the number of qubits on which the gate acts.

Args
init_pos A permutation of (0, ..., n - 1).

### qubit_index_to_equivalence_group_key

Returns a key that differs between non-interchangeable qubits.

### validate_args

Checks if this gate can be applied to the given qubits.

By default checks that:

• inputs are of type Qid
• len(qubits) == num_qubits()
• qubit_i.dimension == qid_shape[i] for all qubits

Child classes can override. The child implementation should call super().validate_args(qubits) then do custom checks.

Args
qubits The sequence of qubits to potentially apply the gate to.

Raises
ValueError The gate can't be applied to the qubits.

### wire_symbol

View source

The symbol to use in circuit diagrams.

### with_probability

Creates a probabalistic channel with this gate.

Args
probability floating point value between 0 and 1, giving the probability this gate is applied.

Returns
cirq.RandomGateChannel that applies self with probability probability and the identity with probability 1-p.

### wrap_in_linear_combination

Returns a LinearCombinationOfGates with this gate.

Args
coefficient number coefficient to use in the resulting cirq.LinearCombinationOfGates object.

Returns
cirq.LinearCombinationOfGates containing self with a coefficient of coefficient.

### __call__

Call self as a function.

### __truediv__

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[{ "type": "thumb-up", "id": "easyToUnderstand", "label":"Easy to understand" },{ "type": "thumb-up", "id": "solvedMyProblem", "label":"Solved my problem" },{ "type": "thumb-up", "id": "otherUp", "label":"Other" }]