Merge pull request #40 from nzy1997/clifford_tab

Clifford tableaux method

src/TensorQEC.jl

@@ -20,6 +20,7 @@ using LuxorGraphPlot
 export pauli_basis, pauli_decomposition, pauli_mapping
 import Yao.YaoArrayRegister.StaticArrays: SizedVector
 import Yao.YaoArrayRegister.LuxurySparse
+export arrayreg2sumofpaulis
 
 # Mod
 export Mod2
@@ -46,7 +47,7 @@ export measure_circuit_fault_tol,  measure_circuit_steane,measure_circuit, measu
 export make_table, save_table, load_table,correct_circuit,show_table,TruthTable,table_inference
 
 # clifford group
-export pauli_group, clifford_group, clifford_simulate,to_perm_matrix,perm_of_paulistring,paulistring_annotate,annotate_history,annotate_circuit_pics
+export pauli_group, clifford_group, clifford_simulate,to_perm_matrix,perm_of_paulistring,paulistring_annotate,annotate_history,annotate_circuit_pics,perm_of_pauligroup
 
 # simulation
 export ComplexConj, SymbolRecorder,IdentityRecorder, ein_circ, QCInfo, qc2enisum
@@ -56,6 +57,9 @@ export coherent_error_unitary, error_quantum_circuit,toput, error_pairs,fidelity
 export SimpleTannerGraph,sydrome_extraction,product_graph,CSSTannerGraph,plot_graph,dual_graph,get_graph,belief_propagation,random_ldpc,random_error_qubits,check_decode, check_linear_indepent,ldpc2tensor
 export tensor_infer,osd,mod2matrix_inverse,bp_osd,tensor_osd
 
+# tableaux
+export Tableau, new_tableau,tableau_simulate
+
 @const_gate CCZ::ComplexF64 = diagm([1, 1,1,1,1,1,1,-1])
 
 include("mod2.jl")
@@ -67,7 +71,8 @@ include("codes.jl")
 include("encoder.jl")
 include("inferences.jl")
 include("measurement.jl")
-include("tablemake.jl")       
+include("tablemake.jl")
 include("simulation.jl")
 include("ldpc.jl")
+include("tableaux.jl")
 end

src/cliffordgroup.jl

@@ -79,7 +79,7 @@ struct CliffordTable{N, Ti}
 end
 
 """
-    perm_of_paulistring(pm::PermMatrix, ps::PauliString, pos::Vector{Int})
+    perm_of_paulistring(ps::PauliString, operation::Pair{Vector{Int}, <:PermMatrix})
 
 Map the Pauli string `ps` by a permutation matrix `pm`. Return the mapped Pauli string and the phase factor.
 
@@ -99,6 +99,12 @@ function perm_of_paulistring(ps::PauliString, operation::Pair{Vector{Int}, <:Per
     v[pos]=[mod(div(pm.perm[ps_perm_num]-1, 4^(j-1)), 4)+1 for j in 1:length(pos)]
     return PauliString(v...), pm.vals[ps_perm_num]
 end
+_complex2int(x) = x==1+0im ? 0 : x==0+1im ? 1 : x==-1+0im ? 2 : 3
+function perm_of_pauligroup(pg::PauliGroup, operation::Pair{Vector{Int}, <:PermMatrix})
+    ps, val = perm_of_paulistring(pg.ps, operation)
+
+    return PauliGroup(_mul_coeff(pg.coeff,_complex2int(val)), ps)
+end
 
 """
     CliffordSimulateResult{N}

src/codes.jl

@@ -176,6 +176,11 @@ function stabilizers(::Code832)
 	return pauli_string
 end
 
+"""
+	Code422
+
+Construct a [[4,2,2]] CSS code instance.
+"""
 struct Code422 end
 
 function stabilizers(::Code422)

src/paulistring.jl

@@ -177,7 +177,7 @@ function tensor2sumofpaulis(t::AbstractArray)
 	return SumOfPaulis([t[ci]=>PauliString(ci.I) for ci in CartesianIndices(t)] |> vec)
 end
 densitymatrix2sumofpaulis(dm::DensityMatrix) = tensor2sumofpaulis(real.(pauli_decomposition(dm.state)))
-
+arrayreg2sumofpaulis(reg::ArrayReg) = densitymatrix2sumofpaulis(density_matrix(reg))
 # inputs:
 # - n is the size of the toric code
 # - k is the Pauli operator, 1 for I, 2 for X, 3 for Y, 4 for Z

src/tableaux.jl

@@ -0,0 +1,60 @@
+struct Tableau{N}
+    tabx::Vector{PauliGroup{N}}
+    tabz::Vector{PauliGroup{N}}
+end
+
+function new_tableau(n::Int)
+    return Tableau([PauliGroup(0,paulistring(n,2,i)) for i in 1:n], [PauliGroup(0,paulistring(n,4,i)) for i in 1:n])
+end
+
+Base.show(io::IO, ::MIME"text/plain", tab::Tableau) = show(io, tab)
+function Base.show(io::IO, tab::Tableau{N}) where {N}
+    for i in 1:N
+        print(io, "X$(i): ", tab.tabx[i], "\n")
+    end
+    for i in 1:N
+        print(io, "Z$(i): ", tab.tabz[i], "\n")
+    end
+end
+
+
+function tableau_simulate(tab::Tableau{N}, operation::Pair{Vector{Int}, <:PermMatrix}) where N
+    return Tableau([perm_of_pauligroup(tab.tabx[i], operation) for i in 1:N], [perm_of_pauligroup(tab.tabz[i], operation) for i in 1:N])
+end
+
+function tableau_simulate(tab::Tableau{N}, qc::ChainBlock) where N
+    qc = simplify(qc; rules=[to_basictypes, Optimise.eliminate_nested])
+    gatedict=Dict{UInt64, PermMatrix}()
+    for _gate in qc
+        gate = toput(_gate)
+        key = hash(gate.content)
+        if haskey(gatedict, key) 
+            tab = tableau_simulate(tab, collect(gate.locs)=>gatedict[key])
+        else 
+            pm = to_perm_matrix(Int8, UInt8, pauli_repr(mat(gate.content)))
+            push!(gatedict, key => pm)
+            tab = tableau_simulate(tab, collect(gate.locs)=>pm)
+        end
+    end
+    return tab
+end
+function tableau_simulate(qc::ChainBlock)
+    tab = new_tableau(nqubits(qc))
+    return tableau_simulate(tab, qc)
+end
+function tableau_simulate(ps::PauliString{N}, qc::ChainBlock) where N
+    tab = tableau_simulate(qc)
+    res = PauliGroup{N}(0, paulistring(N, 1,1))
+    count = 0
+    for i in 1:N
+        if ps.ids[i] == 2
+            res *= tab.tabx[i]
+        elseif ps.ids[i] == 4
+            res *= tab.tabz[i]
+        elseif ps.ids[i] == 3
+            res *= tab.tabx[i] * tab.tabz[i]
+            count += 1
+        end
+    end
+    return PauliGroup{N}(_mul_coeff(res.coeff,count), res.ps)
+end

test/cliffordgroup.jl

@@ -46,6 +46,16 @@ end
 	@test ps2.ids == (2, 3, 2, 2)
 end
 
+@testset "perm_of_pauligroup" begin
+	ps = PauliString(2,3,4,3,2,1)
+	pg = PauliGroup(1, ps)
+	pm = TensorQEC.to_perm_matrix(Int8, Int, pauli_repr(ConstGate.CNOT))
+
+	pg2 = perm_of_pauligroup(pg, [2, 3]=>pm)
+	ps2, val = perm_of_paulistring(ps, [2, 3]=>pm)
+	@test pg2 == PauliGroup(1, ps2)
+end
+
 @testset "clifford_simulate" begin
 	qc = chain(put(5, 1 => H), control(5, 1, 2 => Z), control(5, 3, 4 => X), control(5, 5, 3 => X), put(5, 1 => X))
 	ps = PauliString((4, 3, 1, 3, 2))
@@ -68,3 +78,4 @@ end
 
 	annotate_circuit_pics(res)
 end
+

test/paulibasis.jl

@@ -16,6 +16,18 @@ end
 	@test mat(sp) ≈ dm.state
 end
 
+@testset "arrayreg2sumofpaulis" begin 
+	reg = rand_state(3)
+	dm = density_matrix(reg)
+	sp1 = arrayreg2sumofpaulis(reg)
+	@test mat(sp1) ≈ dm.state
+
+	reg = ghz_state(3)
+	dm = density_matrix(reg)
+	sp2 = arrayreg2sumofpaulis(reg)
+	@test mat(sp2) ≈ dm.state
+end
+
 @testset "pauli_string_map" begin
 	ps = PauliString(2,3,4,3,2,1)
 	@test TensorQEC.pauli_string_map(ps, pauli_mapping(mat(ComplexF64,cnot(2,1,2))), [5,6]).ids ==(2,3,4,3,2,2)

test/runtests.jl

@@ -46,4 +46,8 @@ end
 
 @testset "ldpc" begin
     include("ldpc.jl")
+end
+
+@testset "tableau" begin
+    include("tableaux.jl")
 end

test/tableaux.jl

@@ -0,0 +1,31 @@
+using Test, TensorQEC, TensorQEC.Yao, TensorQEC.LinearAlgebra
+
+@testset "new_tableau" begin
+	tab2 = new_tableau(2)
+	@test getfield.(tab2.tabx,:ps) == [paulistring(2,2,1), paulistring(2,2,2)]
+	@test getfield.(tab2.tabz,:ps) == [paulistring(2,4,1), paulistring(2,4,2)]
+
+	tab3 = new_tableau(3)
+	@test getfield.(tab3.tabx,:ps) == [paulistring(3,2,1), paulistring(3,2,2), paulistring(3,2,3)]
+	@test getfield.(tab3.tabz,:ps) == [paulistring(3,4,1), paulistring(3,4,2), paulistring(3,4,3)]
+	@show tab3
+end
+
+@testset "tableau_simulate" begin
+	tab = new_tableau(2)
+	tab2 = tableau_simulate(tab, [1]=>to_perm_matrix(Int8, Int, TensorQEC.pauli_repr(H)))
+	@test getfield.(tab2.tabx,:ps) == [paulistring(2,4,1), paulistring(2,2,2)]
+	@test getfield.(tab2.tabz,:ps) == [paulistring(2,2,1), paulistring(2,4,2)]
+
+	tab = new_tableau(3)
+	tab2 = tableau_simulate(tab, [1,3]=>to_perm_matrix(Int8, Int, TensorQEC.pauli_repr(ConstGate.CNOT)))
+	@test getfield.(tab2.tabx,:ps) == [paulistring(3,2,(1,3)), paulistring(3,2,2), paulistring(3,2,3)]
+	@test getfield.(tab2.tabz,:ps) == [paulistring(3,4,(1)), paulistring(3,4,2), paulistring(3,4,(1,3))]
+
+	qc = chain(put(5, 1 => H), control(5, 1, 2 => Z), control(5, 3, 4 => X), control(5, 5, 3 => X), put(5, 1 => X))
+	ps = PauliString((4, 3, 1, 3, 2))
+	res = clifford_simulate(ps, qc)
+	res2 = tableau_simulate(ps, qc)
+	@test res.output == res2.ps
+	@test res.phase == im^res2.coeff
+end