enhancements

ext/QuantumCliffordJuMPExt/min_distance_mixed_integer_programming.jl

@@ -10,7 +10,7 @@ even overlap with each X-check of the stabilizer binary representation `stab`.
 an odd overlap with logical-X operator `logicOp` on the i-th logical qubit.
 
 Specifically, it calculates the minimum Hamming weight \$d_{Z}\$ for the Z-type
-logical operator, and the minimum distance for X-type logical operators is the same.
+logical operator. The minimum distance for X-type logical operators is the same.
 
 ### Background on Minimum Distance
 
@@ -59,9 +59,9 @@ julia> distance(Steane7())
 3
 ```
 
-The minimum distance problem for quantum codes is *NP-hard*, and this hardness extends
-to multiplicative and additive approximations, even when restricted to stabilizer or
-CSS codes, with the result established through a reduction from classical problems in
+!!! note The minimum distance problem for quantum codes is *NP-hard*, and this hardness
+extends to multiplicative and additive approximations, even when restricted to stabilizer
+or CSS codes, with the result established through a reduction from classical problems in
 the CWS framework using a 4-cycle free graph [kapshikar2023hardness](@cite). Despite
 this, methods that improve on brute-force approaches are actively explored.
 
@@ -136,6 +136,22 @@ julia> code_n(c1), code_k(c1), distance(c1)
 (48, 6, 8)
 ```
 
+!!!Since the [[48, 6, 8]] GB code does not have specific lower and upper bounds
+(e.g., consider [[48, 6, 5 ≤ d ≤ 8]]), the minimum distance for all `Z`-type and
+`X`-type logical qubits remains the same. In this context, the *exact* minimum
+distance is provided.
+
+```jldoctest examples
+julia> distance(c1, all_logical_qubits=true)
+Dict{Int64, Int64} with 6 entries:
+  5 => 8
+  4 => 8
+  6 => 8
+  2 => 8
+  3 => 8
+  1 => 8
+```
+
 ### Applications
 
 - The first usecase of the MIP approach was the code capacity Most Likely
@@ -147,25 +163,23 @@ to a mixed integer linear program and using the GNU Linear Programming Kit.
 the code distance was calculated using the mixed integer programming approach.
 
 """
-function distance(c::Stabilizer; num_logical_qubits=code_k(c), upper_bound=false)
-    lx, _ = get_lx_lz(c)
-    H = stab_to_gf2(parity_checks(c))
-    H = SparseMatrixCSC{Int, Int}(H)
-    hx = get_stab_hx(H)
-    1 <= num_logical_qubits < code_k(c) && return _minimum_distance(hx, lx[num_logical_qubits, :]) # for large instances
-    1 <= num_logical_qubits <= code_k(c) || throw(ArgumentError("The number of logical qubits must be between 1 and $(code_k(c)) inclusive"))
-    if num_logical_qubits == code_k(c)
-        weights = []
-        for i in 1:num_logical_qubits
-            w = _minimum_distance(hx, lx[num_logical_qubits, :])
-            push!(weights, w)
-        end
-        if upper_bound
-            return minimum(weights), maximum(weights) # return upper bound of minimum distance if required.
-        else
-            return minimum(weights)
-        end
+function distance(c::Stabilizer; upper_bound=false, logical_qubit=code_k(c), all_logical_qubits=false, logical_operator_type=:X)
+    1 <= logical_qubit <= code_k(c) || throw(ArgumentError("The number of logical qubit must be between 1 and $(code_k(c)) inclusive"))
+    logical_operator_type == :X || logical_operator_type == :Z || throw(ArgumentError("Invalid type of logical operator: Use :X or :Z"))
+    l = get_lx_lz(c)[1]
+    H = SparseMatrixCSC{Int, Int}(stab_to_gf2(parity_checks(c)))
+    h = get_stab(H, :X)
+    if logical_operator_type == :Z
+        l = get_lx_lz(c)[2]
+        H = SparseMatrixCSC{Int, Int}(stab_to_gf2(parity_checks(c)))
+        h = get_stab(H, :Z)
+    end
+    weights = Dict{Int, Int}()
+    for i in 1:logical_qubit
+        w = _minimum_distance(h, l[i, :])
+        weights[i] = w
     end
+    return upper_bound ? maximum(values(weights)) : (all_logical_qubits ? weights : minimum(values(weights)))
 end
 
 # Computing minimum distance for quantum LDPC codes is a NP-Hard problem,

ext/QuantumCliffordJuMPExt/util.jl

@@ -1,10 +1,14 @@
-function get_stab_hx(matrix::SparseMatrixCSC{Int, Int})
+function get_stab(matrix::SparseMatrixCSC{Int, Int}, logical_operator_type::Symbol)
     rows, cols = size(matrix)
-    rhs_start = div(cols, 2) + 1
-    rhs_cols = matrix[:, rhs_start:cols]
-    non_zero_rows_rhs = unique(rhs_cols.rowval)
-    zero_rows_rhs = setdiff(1:rows, non_zero_rows_rhs)
-    return matrix[zero_rows_rhs, :]
+    if logical_operator_type == :Z
+        col_range = 1:div(cols, 2)
+    else logical_operator_type == :X
+        col_range = div(cols, 2) + 1:cols
+    end
+    submatrix = matrix[:, col_range]
+    non_zero_rows = unique(submatrix.rowval)
+    zero_rows = setdiff(1:rows, non_zero_rows)
+    return matrix[zero_rows, :]
 end
 
 function get_lx_lz(c::Stabilizer)

test/test_ecc_coprime_bivaraite_bicycle.jl

@@ -2,8 +2,10 @@
     using Nemo
     using Nemo: gcd
     using Hecke
+    using JuMP
+    using GLPK
     using Hecke: group_algebra, GF, abelian_group, gens
-    using QuantumClifford.ECC: two_block_group_algebra_codes, code_k, code_n
+    using QuantumClifford.ECC: two_block_group_algebra_codes, code_k, code_n, distance
 
     @testset "Reproduce Table 2 wang2024coprime" begin
         # [[30,4,6]]
@@ -14,6 +16,7 @@
         B = 𝜋 + 𝜋^3 + 𝜋^8
         c = two_block_group_algebra_codes(A, B)
         @test gcd([l,m]) == 1
+        @test distance(c) == 6
         @test code_n(c) == 30 && code_k(c) == 4
 
         # [[42,6,6]]
@@ -24,6 +27,7 @@
         B = 𝜋 + 𝜋^3 + 𝜋^11
         c = two_block_group_algebra_codes(A, B)
         @test gcd([l,m]) == 1
+        @test distance(c) == 6
         @test code_n(c) == 42 && code_k(c) == 6
 
         # [[70,6,8]]
@@ -34,6 +38,7 @@
         B = 1 + 𝜋 + 𝜋^12;
         c = two_block_group_algebra_codes(A, B)
         @test gcd([l,m]) == 1
+        @test distance(c) == 8
         @test code_n(c) == 70 && code_k(c) == 6
 
         # [[108,12,6]]

test/test_ecc_generalized_bicycle_codes.jl

@@ -1,18 +1,32 @@
 @testitem "ECC GB" begin
     using Hecke
-    using QuantumClifford.ECC: generalized_bicycle_codes, code_k, code_n
+    using JuMP
+    using GLPK
+    using QuantumClifford.ECC: generalized_bicycle_codes, code_k, code_n, distance
 
     # codes taken from Table 1 of [lin2024quantum](@cite)
     # Abelian 2BGA codes can be viewed as GB codes.
-    @test code_n(generalized_bicycle_codes([0 , 15, 16, 18], [0 ,  1, 24, 27], 35)) == 70
-    @test code_k(generalized_bicycle_codes([0 , 15, 16, 18], [0 ,  1, 24, 27], 35)) == 8
-    @test code_n(generalized_bicycle_codes([0 ,  1,  3,  7], [0 ,  1, 12, 19], 27)) == 54
-    @test code_k(generalized_bicycle_codes([0 ,  1,  3,  7], [0 ,  1, 12, 19], 27)) == 6
-    @test code_n(generalized_bicycle_codes([0 , 10,  6, 13], [0 , 25, 16, 12], 30)) == 60
-    @test code_k(generalized_bicycle_codes([0 , 10,  6, 13], [0 , 25, 16, 12], 30)) == 6
-    @test code_n(generalized_bicycle_codes([0 ,  9, 28, 31], [0 ,  1, 21, 34], 36)) == 72
-    @test code_k(generalized_bicycle_codes([0 ,  9, 28, 31], [0 ,  1, 21, 34], 36)) == 8
-    @test code_n(generalized_bicycle_codes([0 ,  9, 28, 13], [0 ,  1, 21, 34], 36)) == 72
-    @test code_k(generalized_bicycle_codes([0 ,  9, 28, 13], [0 ,  1,  3, 22], 36)) == 10
+
+    codes = [generalized_bicycle_codes([0 ,  1,  3,  7], [0 ,  1, 12, 19], 27), # [[54, 6,  9]]
+             generalized_bicycle_codes([0 , 10,  6, 13], [0 , 25, 16, 12], 30), # [[60, 6, 10]]
+             generalized_bicycle_codes([0 , 15, 16, 18], [0 ,  1, 24, 27], 35), # [[70, 8, 10]]
+             generalized_bicycle_codes([0 ,  9, 28, 31], [0 ,  1, 21, 34], 36), # [[72, 8, 10]]
+             generalized_bicycle_codes([0 ,  9, 28, 13], [0 ,  1,  3, 22], 36)] # [[72, 8,  9]]
+
+    n_values = [54, 60, 70, 72, 72]
+    k_values = [6 , 6 , 8 , 8 , 10]
+    d_values = [9 , 10, 10, 10,  9]
+
+    for i in 1:length(n_values)
+        @test code_n(codes[i]) == n_values[i]
+    end
+
+    for i in 1:length(n_values)
+        @test code_k(codes[i]) == k_values[i]
+    end
+
+    for i in 1:length(d_values)
+        j = rand(1:code_k(codes[i]))
+        @test distance(codes[i], logical_qubit=j) == d_values[i]
     end
 end