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.



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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 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.

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.


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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.


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


The number of qubits this gate acts on.


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The number of parameters (weights) in the generator.


Returns an application of this gate to the given qubits.

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

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


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

*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.

Operations applying this gate to the target qubits.

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.


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An in-place version of permuted.


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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.

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


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.

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

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


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The symbol to use in circuit diagrams.


Creates a probabilistic channel with this gate.

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

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


Returns a LinearCombinationOfGates with this gate.

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

cirq.LinearCombinationOfGates containing self with a coefficient of coefficient.



Call self as a function.