# openfermion.circuits.ParityPreservingFermionicGate

The Jordan-Wigner transform of $$\exp(-i H)$$ for a fermionic

Hamiltonian $$H$$.

Each subclass corresponds to a set of generators $$\{G_i\}$$ corresponding to the family of Hamiltonians $\sum_i w_i G_i + \text{h.c.}$$, where the weights$$w_i \in \mathbb C$ are specified by the instance.

The Jordan-Wigner mapping maps the fermionic modes $(0, \ldots, n - 1)$$to qubits$$(0, \ldots, n - 1)$, respectively.

Each generator $$G_i$$ must be a linear combination of fermionic monomials consisting of an even number of creation/annihilation operators. This is so that the Jordan-Wigner transform acts only on the gate's qubits, even when the fermionic modes are offset as part of a larger Jordan-Wigner string.

weights The weights of the terms in the Hamiltonian.
absorb_exponent Whether to absorb the given exponent into the weights. If true, the exponent of the return gate is 1. Defaults to False.

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

num_controls: Total number of control qubits. control_values: For which control qubit values to apply the sub gate. A sequence of length num_controls where each entry is an integer (or set of integers) corresponding to the qubit value (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.

### 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.

### fswap

View source

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

### 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.

### 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).

### 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.

#### Throws:

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

### wire_symbol

View source

The symbol to use in circuit diagrams.

### __call__

Call self as a function.

### __truediv__

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