DensityMatrix backend fixes

[mgarnier59]

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Context (if applicable): Density matrix backend.

Description of the change:

• Modified the normalization of density matrices from Frobenius (2-norm) to trace norm
• Added checks in the initialization of DensityMatrix to check for unit trace and hermiticity of the input data
• Modified the tests accordingly (normalization, hermiticity). For evolution tests, used unitary operators from scipy.stats.unitary_group. Can be modified in the future.

Related issue: None.

also see that checks (github actions) pass. If lint check keeps failing, try installing black==22.8.0 as behavior seems to vary across versions.

[mgarnier59]

New commit solving the issues we mentionned as well as a few updates:

• refactored 2-qubit gates application with evolve method (actually works for arbitrary number of qubits, tested for 1-, 2- and 3- qubits)
• rewrote the tensor contraction in a clearer way to avoid confusion (as I experienced) but kept the previous implementation as comment if need be.
• removed scipy from density_matrix.py
• added data validation with Exceptions instead of asserts
• added scipy and random to setup.py
• added tests according to new features

For the feature, maybe generic data validation like checking operators are square matrices of size $2^N \times 2^N$ can be mutualised with the density matrix that just adds further conditions on top of that (hermiticity, unit trace). Maybe put those methods in a specific file?

[shinich1]

Nice! Will take a look through later.

Maybe put those methods in a specific file?

good idea, sounds like a portable feature outside this simulator. maybe a new file in in graphix/sim/?

[mgarnier59]

good idea, sounds like a portable feature outside this simulator. maybe a new file in in graphix/sim/?

Actually I was thinking of it while working on the kraus.pyfile that requires the same types of checks. So either we move kraus (we might rename it) in graphix/sim/ or we include the checks in graphix/ but that doesn't really matter much.

[shinich1]

@mgarnier59 maybe graphix/sim/quantum_channel.py, but as you say it does not matter much at this stage. let's continue with whatever that works for you, we then deal with file arrangement after all the implementation part is ready :)

[shinich1]

@mgarnier59 I just assigned you to the PR (sorry I haven't done this yet). Do you see the button for squash and merge now?

[mgarnier59]

@mgarnier59 I just assigned you to the PR (sorry I haven't done this yet). Do you see the button for squash and merge now?

@shinich1 Hey. Nope I don't see it. Maybe I don't have the correct rights?