Fermionic simulation gate family.

Inherits From: InterchangeableQubitsGate, Gate

Used in the notebooks

Used in the tutorials

Contains all two qubit interactions that preserve excitations, up to single-qubit rotations and global phase.

The unitary matrix of this gate is:

[[1, 0, 0, 0],
 [0, a, b, 0],
 [0, b, a, 0],
 [0, 0, 0, c]]


a = cos(theta)
b = -i·sin(theta)
c = exp(-i·phi)

Note the difference in sign conventions between FSimGate and the ISWAP and CZPowGate:

FSimGate(θ, φ) = ISWAP**(-2θ/π) CZPowGate(exponent=-φ/π)

theta Swap angle on the |01⟩ |10⟩ subspace, in radians. Determined by the strength and duration of the XX+YY interaction. Note: uses opposite sign convention to the iSWAP gate. Maximum strength (full iswap) is at pi/2.
phi Controlled phase angle, in radians. Determines how much the |11⟩ state is phased. Note: uses opposite sign convention to the CZPowGate. Maximum strength (full cz) is at pi.





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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: 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.


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The number of qubits this gate acts on.


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Returns an application of this gate to the given qubits.

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


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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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Returns a key that differs between non-interchangeable qubits.


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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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Call self as a function.


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