Is your feature request related to a use case or problem? Please describe.
The operation $e^{i \theta P}$ where $P$ is a pauli string, appears a lot in discussions around rotations and magic states. Cirq has a a general way for representing exponentials of pauli strings $e^{i \theta \sum_k P_k}$ called PauliSumExponential however the pauli strings are stored as sparse strings (i.e. dropping identitiy operations) which results in the wrong unitary.
Example P=XI $\theta = \frac{\pi}{4}$ correct unitary should be
$$
\frac{1}{\sqrt{2}} (I_4 + i X \otimes I_2)
$$
but cirq gives
>>> cirq.unitary(cirq.PauliSumExponential(cirq.DensePauliString('XI')(*cirq.LineQubit.range(2)), exponent=np.pi/4))
array([[0.70710678+0.j , 0. +0.70710678j],
[0. +0.70710678j, 0.70710678+0.j ]])Describe the solution you'd like
ideally a fix to the PauliSumExponential operation or a new gate for representing the exponential of one pauli string
What is the urgency from your perspective for this issue? Is it blocking important work?
P2 - we should do it in the next couple of quarters
Is your feature request related to a use case or problem? Please describe.$e^{i \theta P}$ where $P$ is a pauli string, appears a lot in discussions around rotations and magic states. Cirq has a a general way for representing exponentials of pauli strings $e^{i \theta \sum_k P_k}$ called PauliSumExponential however the pauli strings are stored as sparse strings (i.e. dropping identitiy operations) which results in the wrong unitary.
The operation
Example$\theta = \frac{\pi}{4}$ correct unitary should be
P=XIbut cirq gives
Describe the solution you'd like
ideally a fix to the PauliSumExponential operation or a new gate for representing the exponential of one pauli string
What is the urgency from your perspective for this issue? Is it blocking important work?
P2 - we should do it in the next couple of quarters