noncliff: Inner Product between two GeneralizedStabilizers #423
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The PR is ready for review. There is an unrelated doctest errors that were fixed in #416 that is why one extra CI-error. Thank you! |
| The inner product of two [`GeneralizedStabilizer`](@ref) states, `sm₁` and `sm₂`. | ||
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| ```jldoctest | ||
| julia> using QuantumOpticsBase; using LinearAlgebra; # hide |
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do not hide these, otherwise the reader might not know how to run these examples
| ``` | ||
| """ | ||
| function LinearAlgebra.dot(sm₁::GeneralizedStabilizer, sm₂::GeneralizedStabilizer) | ||
| return real(tr(Operator(sm₁)' * Operator(sm₂))) |
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This just converts the two generalized stabilizers to density matrices. This is an exponentially expensive operation that does not seem to be implementing what is shown in the paper. This can be a useful correctness test in the test suite, but it is not an appropriate implementation for this library.
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Indeed. Thank you!
I think the right hand side (shown in the proof section) is the faster version that uses in-place operations.
| @@ -82,6 +82,7 @@ end | |||
| apply!(sm, embed(n, i, pcT)) | |||
| smcopy = copy(sm) | |||
| @test smcopy == sm | |||
| @test dot(sm, smcopy) ≈ 1 | |||
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having tests that do not always use the same state on both sides would make this much more trustworthy
Yup. The stabilizer union between two generalized stabilizers is a prerequisite for the original in-place implementation described in the paper. The algorithm relies on the subroutine detailed in Theorem 16, called 'stabilizer union.' I think we can leverage the |
This PR implements the Inner Product between two Generalized Stabilizers. Inspired from V.Section B of the base paper.