QuantumExpanders.jl

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QuantumExpanders is a   Julia Language   package for constructing quantum Tanner codes. To install QuantumExpanders, please open Julia's interactive session (known as REPL) and press the ] key in the REPL to use the package mode, and then type:

pkg> add https://github.com/QuantumSavory/QuantumExpanders.jl.git

To update, just type up in the package mode.

The library provides the following methods to construct explicit instances of Quantum Tanner codes.

graph TD
    QuantumTannerCodes["Quantum Tanner Codes"] --> RandomMethods["Random Methods"]
    QuantumTannerCodes --> DeterministicMethods["Deterministic Methods"]

    subgraph "Random construction"
        RandomMethods --> RandomQuantumTannerCode["`random_quantum_Tanner_code`"]
    end

    subgraph "Deterministic construction"
        DeterministicMethods --> QuantumTannerCode["`QuantumTannerCode`"]
        DeterministicMethods --> GeneralizedQuantumTannerCode["`GeneralizedQuantumTannerCode`"]
    end

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Here is the novel [[360, 61, (3, 10)]] quantum Tanner code constructed from Morgenstern Ramanujan graphs for even prime power q.

julia> l = 1; i = 2;

julia> q = 2^l
2

julia> Δ = q+1
3

julia> SL₂, B = morgenstern_generators(l, i)
[ Info: |SL₂(𝔽(4))| = 60
(SL(2,4), Oscar.MatrixGroupElem{Nemo.FqFieldElem, Nemo.FqMatrix}[[o+1 o+1; 1 o+1], [o+1 1; o+1 o+1], [o+1 o; o o+1]])

julia> A = alternative_morgenstern_generators(B, FirstOnly())
4-element Vector{Oscar.MatrixGroupElem{Nemo.FqFieldElem, Nemo.FqMatrix}}:
 [0 1; 1 o+1]
 [o+1 1; 1 0]
 [o+1 o+1; o 0]
 [0 o+1; o o+1]

julia> rng = MersenneTwister(892529278);

julia> hx, hz = random_quantum_Tanner_code(0.75, SL₂, A, B, rng=rng);
(length(group), length(A), length(B)) = (60, 4, 3)
length(group) * length(A) * length(B) = 720
[ Info: |V₀| = |V₁| = |G| = 60
[ Info: |E_A| = Δ|G| = 240, |E_B| = Δ|G| = 180
[ Info: |Q| = Δ²|G|/2 = 360
Hᴬ = [1 1 1 0]
Hᴮ = [0 1 1; 1 1 0]
Cᴬ = [1 1 0 0; 1 0 1 0; 0 0 0 1]
Cᴮ = [1 1 1]
size(Cˣ) = (3, 12)
size(Cᶻ) = (2, 12)
r1 = rank(𝒞ˣ) = 179
r2 = rank(𝒞ᶻ) = 120

julia> c = CSS(hx, hz);

julia> import JuMP; import HiGHS;

julia> code_n(c), code_k(c)
(360, 61)

julia> distance(c, DistanceMIPAlgorithm(solver = name ,logical_operator_type = :Z,time_limit = 900)), distance(c, DistanceMIPAlgorithm(solver = name ,logical_operator_type = :X,time_limit = 900))
(3, 10)

Support

QuantumExpanders.jl is developed by many volunteers, managed at Prof. Krastanov's lab at University of Massachusetts Amherst.

The development effort is supported by The NSF Engineering and Research Center for Quantum Networks, and by NSF Grant 2346089 "Research Infrastructure: CIRC: New: Full-stack Codesign Tools for Quantum Hardware".

Bounties

We run many bug bounties and encourage submissions from novices (we are happy to help onboard you in the field).