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Is there a way to calculate two-time correlators in Cirq directly? For example, suppose we have an initial mixed state described by a density matrix $\rho_0$, and we want to obtain in our quantum circuit: \begin{eqnarray} \langle \sigma_i^z(t)\sigma_j(t=0)\rangle=\text{tr}\left(\sigma_i(t)\sigma_j\rho_0\right), \end{eqnarray} where the time-dependent $\sigma_i(t)$ is in the Heisenberg picture. Then we can relabel $\rho_0\to\sigma_j\rho_0$, and run a simulator with this new, initial mixed state as initial condition, and calculate $\langle\sigma_i^z(t)\rangle$ now respect to that initial density matrix(?). The problem of doing that is of course that one needs to initialize the system every time, once for each $\sigma_j$, in order to perform the calculations, so I was wondering if there is a better way to do this already implemented in Cirq?

EDIT: For further clarification, this is at the level of computing exact expectation values during the simulation. For sampling, an approach is easier to do.

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