|---| | [ View source on GitHub](https://github.com/tensorflow/quantum/blob/v0.7.6/tensorflow_quantum/python/util.py#L728-L832) | Return a Cirq circuit with exponential operator forms. tfq.util.exponential( operators, coefficients=None ) ### Used in the notebooks | Used in the tutorials | |---| | - [Quantum data](https://www.tensorflow.org/quantum/tutorials/quantum_data) | Construct an exponential form of given `operators` and `coefficients`. Operators to be exponentiated are specified in `operators` as [`cirq.PauliSum`](https://quantumai.google/reference/python/cirq/PauliSum) or [`cirq.PauliString`](https://quantumai.google/reference/python/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.


| ## Args || |---|---| | `operators` | Python `list` or `tuple` of [`cirq.PauliSum`](https://quantumai.google/reference/python/cirq/PauliSum) or [`cirq.PauliString`](https://quantumai.google/reference/python/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. |



| ## Returns || |---|---| | A [`cirq.Circuit`](https://quantumai.google/reference/python/cirq/Circuit) containing exponential form of given `operators` and `coefficients`. ||



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