Known Quantum Codes

AugmentedBravyiBaconShorCode(
    A::Union{Nemo.FqMatrix, Nemo.fpMatrix, Hecke.SMat, SparseArrays.SparseMatrixCSC}
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return the local, augmented Bravyi–Bacon–Shor subsystem code associated with the binary matrix A.

BaconShorCode(
    m::Int64,
    n::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return the Bacon-Shor subsystem code on a m x n lattice.

BaconShorCode(
    d::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return the Bacon-Shor subsystem code on a d x d lattice.

BravyiBaconShorCode(
    A::Union{Nemo.FqMatrix, Nemo.fpMatrix, Hecke.SMat, SparseArrays.SparseMatrixCSC}
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return the generalied Bacon-Shor code defined by Bravyi in "Subsystem Codes With Spatially Local Generators", (2011).

CleveGottesmanCode(

) -> Union{StabilizerCode, StabilizerCodeCSS}

Return the [[8, 3, 3]] Cleve-Gottesman (Eight-qubit) code. This is a small non-degenerate stabilizer code.

ColorCode4612(
    d::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS}

Return the 4.6.12 Archimedean Color Code on a grid of size d. Stabilizers sit on the square (4), hexagonal (6), and dodecagonal (12) faces.

FiveQubitCode() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[5, 1, 3]]$ perfect qubit stabilizer code.

GaugedShorCode() -> Union{SubsystemCode, SubsystemCodeCSS}

Return the $[[9, 1, 4, 3]]$ gauged Shor subsystem code with four gauge qubits and dressed distance three. Its gauge group is generated by the stabilizers together with the four anticommuting gauge-operator pairs.

GeneralizedBaconShorCode(
    A::Union{Nemo.FqMatrix, Nemo.fpMatrix, Hecke.SMat, SparseArrays.SparseMatrixCSC}
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return the generalized Bacon–Shor subsystem code associated with the support of the binary matrix A. Its gauge group is generated by weight-two $X$ operators joining consecutive occupied sites in each column and weight-two $Z$ operators joining consecutive occupied sites in each row.

GrossCode(

) -> BBCode{Oscar.MPolyQuoRing{Nemo.fpMPolyRingElem}, Oscar.MPolyQuoRingElem{Nemo.fpMPolyRingElem}, Oscar.MPolyQuoRingElem{Nemo.fpMPolyRingElem}}

Return the [[144, 12, 12]] gross code.

HCode(k::Int64) -> StabilizerCodeCSS

Return the [[k + 4, k, 2]] H code from https://errorcorrectionzoo.org/c/quantum_h.

HaahsCubicCode(L::Int64) -> StabilizerCodeCSS

Return Haah's Cubic Code (Type 15) on a 3D periodic lattice of size L. This is a CSS fracton model with 2 qubits per vertex. The dimension k fluctuates based on the number-theoretic properties of L.

HeavyHexCode(
    d::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return a Heavy-Hex subsystem code on a periodic grid of size d. Data qubits sit on the vertices and edges of a hexagonal lattice.

HeavySquareCode(
    d::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return a Heavy-Square subsystem code on a periodic grid of size d. Data qubits sit on the vertices and edges of a square lattice.

LocalBravyiBaconShorCode(
    A::Union{Nemo.FqMatrix, Nemo.fpMatrix, Hecke.SMat, SparseArrays.SparseMatrixCSC}
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return the local Bravyi–Bacon–Shor subsystem code associated with the binary matrix A. Qubits fill the row and column intervals spanned by the support of A; the gauge group uses nearest-neighbor $XX$ and $ZZ$ generators and single-qubit generators at added zero entries.

NappPreskill3DCode(
    m::Int64,
    n::Int64,
    k::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return the Napp and Preskill 3D, modifed Bacon-Shor code.

NappPreskill4DCode(
    x::Int64,
    y::Int64,
    z::Int64,
    w::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return the Napp and Preskill 4D, modifed Bacon-Shor code.

PlanarSurfaceCode(d_x::Int, d_z::Int)
PlanarSurfaceCode(d::Int)

Return the [[d_x * d_z + (d_x - 1) * (d_z - 1), 1, d_x/d_z]] planar surface code.

The top and bottom boundaries are "smooth" (Z) and the left and right are "rough" (X).

PlanarSurfaceCode3D(d::Int64) -> StabilizerCodeCSS

Return the 3D planar surface code of distance d.

Q1513() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[15, 1, 3]]$ quantum Reed–Muller code.

Q1573() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the [[15, 7, 3]] quantum Hamming code.

Q15RM() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[15, 1, 3]]$ quantum Reed–Muller code.

Q412() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[4, 1, 2]]$ CSS stabilizer code generated by $XXXX$, $ZZII$, and $IIZZ$.

Q422() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[4, 2, 2]]$ stabilizer code $C_4$ defined by Knill.

Q511() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[5, 1, 1]]$ stabilizer code generated by translates of $ZXIII$.

Q513() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[5, 1, 3]]$ perfect qubit stabilizer code.

Q713() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[7, 1, 3]]$ Steane code.

Q823() -> Union{StabilizerCode, StabilizerCodeCSS}

Return an $[[8, 2, 3]]$ qubit stabilizer code.

Q832() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[8, 3, 2]]$ qubit stabilizer code known as the smallest interesting color code.

Q913() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[9, 1, 3]]$ Shor code.

Q9143() -> Union{SubsystemCode, SubsystemCodeCSS}

Return the $[[9, 1, 4, 3]]$ gauged Shor subsystem code.

QC4() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[4, 2, 2]]$ stabilizer code $C_4$ defined by Knill.

QC6() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the C_6 stabilizer code defined by Knill.

QuantumGolayCode() -> StabilizerCodeCSS

Return the [[23, 1, 7]] quantum Golay CSS code.

QuantumRepetitionCode(
    d::Int64;
    error_type
) -> Union{StabilizerCode, StabilizerCodeCSS}

Return the [[d, 1, d]] quantum repetition code. error_type can be :phase_flip (X stabilizers) or :bit_flip (Z stabilizers).

RotatedSurfaceCode(
    d::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS}

Return the [[d^2, 1, d]] rotated surface code.

This is the surface-13/17 configuration found in "Low-distance surface codes under realistic quantum noise" by Tomita and Svore. The standard planar surface code is equivalent to their surface-25 configuration, which can be seen by viewing the stabilizers of PlanarSurfaceCode as an adjacency matrix.

ShorCode() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[9, 1, 3]]$ Shor code.

SmallestInterestingColorCode(

) -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[8, 3, 2]]$ qubit stabilizer code known as the smallest interesting color code.

SteaneCode() -> Union{StabilizerCode, StabilizerCodeCSS}

Return the $[[7, 1, 3]]$ Steane code.

SubsystemSurfaceCode(
    m::Int64,
    n::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return the subsystem surface code on a rectangular lattice with m rows and n columns of squares.

SubsystemSurfaceCode(
    d::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return the subsystem surface code on a square lattice with d rows and d columns of squares.

SubsystemToricCode(
    m::Int64,
    n::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return the subsystem toric code on a rectangular lattice with m rows and n columns of squares.

SubsystemToricCode(
    d::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS, SubsystemCode, SubsystemCodeCSS}

Return the subsystem toric code on a square lattice with d rows and d columns of squares.

ToricCode(d::Int64) -> StabilizerCodeCSS

Return the [[2d^2, 2, d]] toric code.

The lattice orientation used here follows the picture at https://errorcorrectionzoo.org/c/surface.

ToricCode3D(d::Int64) -> StabilizerCodeCSS

Return the 3D toric code of distance d.

Function returning the stabilizers and logicals of periodic 4d surface codes of linear size l >= 2. Constructions taken from J. Math. Phys. 43, 4452-4505 (2002).

ToricColorCode666(L::Int64) -> StabilizerCodeCSS

Return the Toric 6.6.6 Color Code on a periodic lattice of size L. L must be a multiple of 3 for the lattice to be 3-colorable. Generates a [[2L^2, 4, d]] CSS code.

TriangularSurfaceCode(L::Int64) -> StabilizerCodeCSS

Return the periodic triangular-lattice CSS code obtained from the generated $X$ and $Z$ check matrices after omitting the final row of each.

TwistDefectSurfaceCode(
    d::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS}

Return a distance d planar surface code containing a single twist defect in the bulk. The defect increases the logical dimension k by merging an X and Z stabilizer.

XCubeModel(L::Int64) -> StabilizerCodeCSS

Return the X-Cube model on a cubic lattice of linear size L with periodic boundaries. The X-Cube model is a 3D fracton stabilizer code with parameters [[3L^3, 6L - 3, L]].

XYSurfaceCode(d_x::Int, d_z::Int)
XYSurfaceCode(d::Int)

Return the [[d_x * d_y + (d_x - 1) * (d_y - 1), 1, d_x/d_y]] XY surface code of "Ultrahigh Error Threshold for Surface Codes with Biased Noise" by Tuckett, Bartlett, and Flammia.

The top and bottom boundaries are "smooth" (Y) and the left and right are "rough" (X).

XZZXSurfaceCode(
    d::Int64
) -> Union{StabilizerCode, StabilizerCodeCSS}

Return the [[d^2, 1, d]] XZZX surface code.

TriangularColorCode488(d::Int)

Return the 4.8.8 triangular color code of distance d, whose qubits are numbered in trellis order.

Note

• Run using JLD2 to activate this extension. The stabilizers and logicals are loaded from stored data, which currently covers odd $3 \leq d \leq 19$.

TriangularColorCode666(d::Int)

Return the 6.6.6 triangular color code of distance d, whose qubits are numbered in trellis order.

Note

• Run using JLD2 to activate this extension. The stabilizers and logicals are loaded from stored data, which currently covers odd $3 \leq d \leq 21$.

PlanarSurfaceCode3D_X(d::Int)

Return the $X$-check, $X$-logical, and $X$-metacheck matrices of the three-dimensional planar surface code of distance d.

Note

• Run using JLD2 to activate this extension. The matrices are loaded from stored data, which currently covers $3 \leq d \leq 9$.

ToricCode3D_X(d::Int)

Return the $X$-check, $X$-logical, and $X$-metacheck matrices of the three-dimensional toric code of distance d.

Note

• Run using JLD2 to activate this extension. The matrices are loaded from stored data, which currently covers $2 \leq d \leq 13$.