Density matrix class and simulation

[Praveen91299]

Thought it would be useful for density simulation to allow for noise. Right now only Qiskit backend, would require to modify other backend simulator files. I'm not sure if I did the pull request right, see commit with ID f378f16

[kottmanj]

Looks good!
Will need some time to go over it, but I think we won't need many changes.
Could you provide a minimal example how to use (can be as a comment here)
as well as a unit-test (ideally at tests/test_backend.py)

[Praveen91299]

Hi Jakob, sorry got a bit caught up, I'm working on some test cases for the test_backend.py, will get it done soon. Here's a little snippet for it's use.

import tequila

circ = tequila.QCircuit()
circ += tequila.gates.X(target=[0])
circ +=  tequila.gates.H(target=[0])
circ += tequila.gates.CNOT(target=[1], control=[0])

#simulating density
density = tequila.simulate(circ, noise=tequila.circuit.noise.DepolarizingError(p=0.1, level=2))
print(density)

#simple density manipulations
print(density.n_qubits)
print(density.trace())

from openfermion import QubitOperator

HQ = QubitOperator('Z0 Z1', 1)
H = tequila.QubitHamiltonian.from_openfermion(HQ)
print(density.QubitHamiltonian_expectation(H))
print(density.QubitHamiltonian_variance(H))

Expected Output:

Tequila DensityMatrix over 2 qubits stored as sparse matrix
array([[ 0.475+0.j,  0.   +0.j,  0.   +0.j, -0.45 +0.j],
       [ 0.   +0.j,  0.025+0.j,  0.   +0.j,  0.   +0.j],
       [ 0.   +0.j,  0.   +0.j,  0.025+0.j,  0.   +0.j],
       [-0.45 +0.j,  0.   +0.j,  0.   +0.j,  0.475+0.j]])
2
(1.0000000000000002+0j)
(0.9000000000000002+0j)
(0.18999999999999984+0j)

I do have to note that we'd still need to modify for the other backends to allow for density simulation or flag otherwise.

[kottmanj]

Will lead to too many clashes with other applications.
return type of tq.simulate(circuit) is not clear from context anymore (wavefunction or density matrix)

Propose the following: Add simulate_density_matrix method. Within the method, check backend and only allow qiskit (because the simulation is not supported for others currently, as far as I understand).

[kottmanj]

Hi, Praveen, I am just following up on this (no time pressure, though).
PR looks good. I just need the comments addressed/implemented before I can merge it in, as we may face some issues otherwise.

[Praveen91299]

Hey Jakob, thanks for following up! Been a bit lazy on this, I'll get this done asap.

[kottmanj]

Hey Jakob, thanks for following up! Been a bit lazy on this, I'll get this done asap.

No worries, there is no time pressure. I just wanted to check if there are problems or if some of the comments are unclear.

[Praveen91299]

Hi Jakob, apologies for the delay again. My branch is a bit out-dated with main, will deal with the merge later. I've been looking into adding in density simulation and had a couple of questions, I've added a simulate_density() and do_simulate_density() in simulators_base.py and simulators_qiskit.py.

1. I am not sure in what precedence the simulate function calls these or where else I need to change code. I'm guessing simulator_api.py needs a simulate_density() function, please confirm.
2. What exactly is a compiled objective object (instantiated in simulators_api/simulate())?

[kottmanj]

Hi Jakob, apologies for the delay again. My branch is a bit out-dated with main, will deal with the merge later. I've been looking into adding in density simulation and had a couple of questions, I've added a simulate_density() and do_simulate_density() in simulators_base.py and simulators_qiskit.py.

1. I am not sure in what precedence the simulate function calls these or where else I need to change code. I'm guessing `simulator_api.py` needs a `simulate_density()` function, please confirm.

2. What exactly is a compiled objective object (instantiated in `simulators_api/simulate()`)?

Hi Praveen,
tight schedule. I will try to get back to you within this week. Please remind me if you don't hear back

[kottmanj]

[Praveen91299]

Thanks for the flow chart! Will let you know if any questions and hopefully wrap his up soon.