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# tfq.util.exponential

Return a Cirq circuit with exponential operator forms.

### Used in the notebooks

Used in the tutorials

Construct an exponential form of given `operators` and `coefficients`. Operators to be exponentiated are specified in `operators` as `cirq.PauliSum` or `cirq.PauliString`. Parameters are given by `coefficients`.

Note that only operators whose standard representations consist of terms which all commute can be exponentiated. This allows use of the identity exp(A+B+...) = exp(A)exp(B)... else there would need to be automatic handling of Trotterization and convergence, which is not supported yet.

`operators` Python `list` or `tuple` of `cirq.PauliSum` or `cirq.PauliString` objects to be exponentiated. Here are simple examples. Let q = cirq.GridQubit(0, 0) E.g. operator = 0.5 * X(q) -> exp(-i * 0.5 * X(q)) operator = 0.5 * cirq.PauliString({q: cirq.I}) -> exp(-i * 0.5)*np.eye(2) Be careful of the negation and the PauliString of the identity gate.
`coefficients` (Optional) Python `list` of Python `str`, `float` or `sympy.Symbol` object of parameters. Defaults to None, then all coefficients of `operators` are set to 1.0.

A `cirq.Circuit` containing exponential form of given `operators` and `coefficients`.

`TypeError` If `operators` (or its terms) is/are of an invalid type.

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