Simulate circuits containing PauliMeasurements using PauliFrames

[J-C-Q]

This PR adds a layer of abstraction that uses option 2 of #411 to make it easier to simulate circuits containing PauliMeasurements using PauliFrames.

• The PauliFrame contractor adds an extra qubit (at the end), which then gets used as an ancillary qubits for the PauliMeasurements.
• The apply! function has a method for PauliMeasurements that basically reuses ECC.naive_ancillary_paulimeasurement to convert a PauliMeasurement to a list of gates (which already have apply! methods) that perform the measurement using the ancillary qubit.
• Since PauliMeasurement is parametric, add a concrete_typeparams method for PauliMeasurements to make CompactifiedGate possible. (I'm not sure if the one possible type parameter I specify here is exhaustive... probably not.)

[Krastanov]

This is awesome, thank you!

I think we just need to add some tests (potentially including a test that uses @allocated to verify that memory is not churned).

[Krastanov]

I think this should be sMRZ

[J-C-Q]

Of course...

[Krastanov]

I agree with this change. I think now we need to update show and nqubits and maybe others. Thankfully, for show it can be as simple as using @view frame[:,1:end-1]

[Krastanov]

actually, we do not even have a show method implemented, so this probably only needs a correct nqubits

[J-C-Q]

I subtracted the ancillary qubit in the nqubits(f::PauliFrame) function. I think that should be fine.

[Krastanov]

Suggested change

	# this is inspired by ECC.naive_ancillary_paulimeasurement. Not sure if it's better to import and call that.
	# this is inspired by ECC.naive_syndrome_circuit

Better to keep it the way you did it here, as this is non-allocating while naive_syndrome_circuit would create a temporary array

[Krastanov]

The test failures happen due to this:

QuantumClifford.jl/test/test_ecc_syndromes.jl

Lines 33 to 36 in f69e49c

	pₙ = embed(naive_qubits, 1:dataqubits, p)
	pₛ = embed(shor_qubits, 1:dataqubits, p)
	mul_left!(naive_frames.frame, pₙ)
	mul_left!(shor_frames.frame, pₛ)

The cleanest way to fix this is probably to do mul_left!(tab(naive_frames), pₙ) instead of mul_left!(naive_frames.frame, pₙ)

with a newly defined

tab(p::PauliFrame) = @view p.frame[:,1:end-1] # to account of the buffer ancillary qubit

[J-C-Q]

Somehow this is more complicated because the view implementations for PauliFrame, Stabilizer and Tableau only allow one dimensional indexing as far as I can tell.

[Krastanov]

darn, you are right. Thankfully, here we are adding a qubit at the very end, so there is still an easy workaround

tab(pf::PauliFrame{Stabilizer{Tableau{V,F}}, M}) where {V,F,M} = Tableau{V,F}(pf.frame.tab.phases, pf.frame.tab.xzs, nqubits(pf))

If I am not getting this wrong, the internal indexing utilities of Tableau will take care of skipping over the extra qubit. This would need some testing though