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construct and test quantum Tanner code using LPS Ramanujan graphs #30

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construct and test quantum Tanner code using LPS Ramanujan graphs #30

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44 changes: 44 additions & 0 deletions test/test_lubotzky_phillips_sarnak_ramanujan.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -116,4 +116,48 @@
@test length(SL_center) == expected_sl_size
end
end

@testset "Quantum Tanner codes based on LPS Ramanujan Graphs" begin
test_pairs = [( 5, 29),
(13, 17)]
for (p, q) in test_pairs
@info "Testing with p = $p, q = $q"
@test is_prime(p) && p % 4 == 1
@test is_prime(q) && q % 4 == 1 && p != q
# Build the finite field
F = GF(q)
# Compute the Legendre symbol (p/q)
symbol = legendre_symbol(p, q)
if symbol == -1
n = q*(q^2-1)
F = GF(q)
GL2 = GL(2, F)
Z = scalar_matrices_GL(GL2)
PG, morphism = quo(GL2, Z)
solutions = solve_four_squares(p)
solutions_processed = process_solutions(solutions, p)
generators = lps_generators(solutions_processed, F, p)
gl_gens = [GL2(mat) for mat in generators]
PG_gens = [morphism(gen) for gen in gl_gens]
PG_group = projective_special_linear_group(2, q)
hx, hz = gen_code(0.4, PG_group, PG_gens, PG_gens, bipartite=false)
elseif symbol == 1
F = GF(q)
SL2 = SL(2, F)
Z = scalar_matrices_SL(SL2)
PG, morphism = quo(SL2, Z)
solutions = solve_four_squares(p)
solutions_processed = process_solutions(solutions, p)
generators = lps_generators(solutions_processed, F, p)
# det((1/√p)*[a+ib c+id; -c+id a-ib]) = (1/p)*p = 1
s = sqrt(F(p))
s_inv = inv(s)
generators_scaled = [s_inv * mat for mat in generators]
sl_gens = [SL2(mat) for mat in generators_scaled]
PG_gens = [morphism(gen) for gen in sl_gens]
PG_group = projective_special_linear_group(2, q)
hx, hz = gen_code(0.4, PG_group, PG_gens, PG_gens, bipartite=false)
end
end
end
end
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