# Setting the Initial State of Density Matrix Simulation in Cirq

I am trying to use the DensityMatrixSimulator in Cirq. I want to append gates to the circuit conditional on measurements. In order to reduce computational resources, I am trying to run these conditional gates by initializing another circuit with these conditional gates using the final state of the first measurement as the initial state. However, I am not sure how I can get the simulate method to accept the initial state matrix (see code below).

I get the ValueError of

ValueError: state_like was convertible to a numpy array, but its shape was neither the shape of a list of computational basis values (len(qid_shape)) nor the shape of a list or tensor of state vector amplitudes (qid_shape or (product(qid_shape),).

qid_shape=(2, 2)
np.array(state_like).shape=(2, 2, 2, 2)
np.array(state_like)=[[[[ 0.+0.j  0.-0.j]
[ 0.+0.j  0.-0.j]]

[[-0.+0.j  0.-0.j]
[-0.+0.j  0.-0.j]]]

[[[ 0.+0.j  0.-0.j]
[ 1.+0.j  0.-0.j]]

[[-0.+0.j  0.-0.j]
[-0.+0.j  0.-0.j]]]]


This is the code I am trying to run to figure out how to initialize the initial state of the second circuit.


qubits = cirq.LineQubit.range(2)

circuit = cirq.Circuit()

circuit.append(cirq.X(qubits[0]))
circuit.append(cirq.Z(qubits[1]))

s = cirq.DensityMatrixSimulator()

results = s.simulate(circuit)

r = cirq.DensityMatrixSimulator()

circuit2 = cirq.Circuit()

circuit2.append(cirq.X(qubits[0]))

circuit2.append(cirq.Z(qubits[1]))

results2 =r.simulate(circuit2, initial_state = results._final_simulator_state.density_matrix)


Instead of accessing results._final_simulator_state.density_matrix, which has a leading underscore implying you shouldn't be using it or relying on it to stay stable, use results.final_density_matrix. Making that substitution seems to result in the code working.
Separately, I think the fact that what you did doesn't work is a bug. It seems that the method doesn't recognize the shape (2,) * 2 * num_qubits as a valid shape for the density matrix as a tensor. I opened https://github.com/quantumlib/Cirq/issues/3958 to get it fixed.