Horizontal concatenation for Tableaux

[Fe-r-oz]

For hcat, it seems we would need a something like this if we suppose that we have a s1 as 4x4 and s2 as 4x4 stabilizers

julia> hcat(s1, s2),
1-element Vector{Stabilizer{QuantumClifford.Tableau{Vector{UInt8}, Matrix{UInt64}}}}:
 Stabilizer 4×8

julia> vcat(s1, s2)
2-element Vector{Stabilizer{QuantumClifford.Tableau{Vector{UInt8}, Matrix{UInt64}}}}:
 Stabilizer 4×4
 Stabilizer 4×4

This will give method error was we are dealing with AbstractVectors

julia> hcat(s1, s2)
1×2 Matrix{Stabilizer{QuantumClifford.Tableau{Vector{UInt8}, Matrix{UInt64}}}}:
 Stabilizer 4×4  Stabilizer 4×4

I have added the if check that Tableus rows must be the same for horizontal concatenation.

julia> using QuantumClifford.ECC
julia> s1 = random_stabilizer(4)
+ X_XZ
+ X_ZX
- ZX_Y
+ _YXZ

julia> s2 = random_stabilizer(4)
+ _XYY
+ ZYXY
+ _YYX
- ZXYY

julia> vcat(s1,s2)
+ X_XZ
+ X_ZX
- ZX_Y
+ _YXZ
+ _XYY
+ ZYXY
+ _YYX
- ZXYY

I am trying to figure out what happends to the phase vector, In the vcat it is concatenated vertically which makes sense but in hcat, we don't want. We want the size of phase vector to remain the same but phases modified maybe

julia> hcat(s1,s2)
+ + becomes + ? X_XZ_XYY
+ + becomes + ? X_ZXZYXY
+ - becomes - ? ZX_Y_YYX
- + becomes - ? _YXZZXYY

At the moment, hcat is not performing as expected

julia> using QuantumClifford.ECC
julia> s1 = random_stabilizer(4)
- X_XZ
- _YYX
- Y__X
- ZYXY

julia> s2 = random_stabilizer(4)
+ ZXYZ
- XX_X
- ZYZ_
+ _XXX

julia> s2 = random_stabilizer(2)
+ XX
- YZ

julia> hcat(s1, s2)
ERROR: ArgumentError: All Tableaus must have the same number of qubits for horizontal concatenation.
Stacktrace:
 [1] hcat
   @ ~/GitHub/QuantumClifford/QuantumClifford.jl/src/QuantumClifford.jl:929 [inlined]
 [2] hcat(::Stabilizer{QuantumClifford.Tableau{Vector{UInt8}, Matrix{UInt64}}}, ::Stabilizer{QuantumClifford.Tableau{Vector{UInt8}, Matrix{UInt64}}})
   @ QuantumClifford ~/GitHub/QuantumClifford/QuantumClifford.jl/src/QuantumClifford.jl:937
 [3] top-level scope
   @ REPL[6]:1

julia> s2 = random_stabilizer(4)
+ X_ZY
- XYZ_
- X__Y
+ ZZZX

julia> hcat(s1, s2) gives me the s1
- X_XZ
- _YYX
- Y__X
- ZYXY

I have trouble understanding what's hcat xzs is doing inside the vcat function, If xzs are horizontal arrays then horizontally concatenating them form a matrix which makes sense. Since xzs is an AbstractMatrix and hcating them (not sure whats hcat is doing, maybe we are creating a vector of matrices by hcatting then we can perform vcat by wrapper of stabilizers for vcat?

function Base.vcat(tabs::Tableau...)
    Tableau(
        vcat((s.phases for s in tabs)...),
        tabs[1].nqubits,
        hcat((s.xzs for s in tabs)...)) ❓ 
end

Thanks for your help!

[Fe-r-oz]

A very minor addition towards right track maybe, We need sum(s.nqubits for s in tabs), previouly I was doing tabs[1].nqubits,

julia> s1 = random_stabilizer(4)
+ XX_X
- ZXZY
+ ZYX_
+ YYZ_

julia> s2 = random_stabilizer(4)
- _XYX
+ ZZZX
+ YYYZ
- YZX_

julia> hcat(s1, s2) # maybe right track
+ XX_X____
- ZXZY____
+ ZYX_____
+ YYZ_____

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 6 lines in your changes missing coverage. Please review.

Project coverage is 82.77%. Comparing base (dddaedb) to head (f7e0a71).

Files	Patch %	Lines
src/QuantumClifford.jl	0.00%	6 Missing ⚠️

Additional details and impacted files

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[Krastanov]

Thanks for starting this draft. I left a few quick comments that hopefully would be of help.

You know, but just a reminder, this also will need to have tests.

[Krastanov]

It is a French word, so the plural is a bit weird: tableaux, not tableaus.

[Krastanov]

same spelling issue

[Krastanov]

I do not think this would actually work, as the xzs array is padded with zeros. Probably it would be necessary to first allocate the empty larger tableau and to insert the smaller tableaux at the appropriate indices. I think the setindex functions are already relatively efficient and can be used directly here.

[Krastanov]

you also see this in the example you have already posted as a comment above