Construction of General Quantum Codes
QuantumCode(S) : Code -> CodeQuantum
Example QECC_SimpleQuantConstr (H129E1)
Example QECC_SimpleQuantExtendedConstr (H129E2)
Example QECC_SimpleQuantSelfDualConstr (H129E3)
Example QECC_SimpleQuantAdditiveConstr (H129E4)
QuantumCode(M) : ModMatRngElt -> CodeQuantum
Example QECC_SimpleQuantConstrMat (H129E5)
QuantumCode(G) : Grph -> QuantumCode
Example QECC_HexacodeQuant (H129E6)
Example QECC_DodecacodeQuant (H129E7)
RandomQuantumCode(F, n, k) : FldFin, RngIntElt, RngIntElt -> CodeQuantum
Example QECC_RandomQuantConstr (H129E8)
Subcode(Q, k) : CodeQuantum, RngIntElt -> CodeQuantum
Construction of Special Quantum Codes
Hexacode() : -> CodeQuantum
Dodecacode() : -> CodeQuantum
CSS Codes
CSSCode(C1, C2) : Code, Code -> CodeQuantum
Example QECC_CSSQuantConstr (H129E9)
Cyclic Quantum Codes
QuantumCyclicCode(v) : ModTupFldElt -> CodeAdd
Example QECC_CyclicQuantCodesimple (H129E10)
QuantumCyclicCode(n, f) : RngIntElt, RngUPolElt -> CodeAdd
Example QECC_CyclicQuantCodePoly (H129E11)
QuantumCyclicCode(v4, v2) : ModTupFldElt, ModTupFldElt -> CodeAdd
Example QECC_CyclicQuantCodeGF4GF2 (H129E12)
Quasi-Cyclic Quantum Codes
QuantumQuasiCyclicCode(n, Q) : RngIntElt, SeqEnum[RngUPolElt] -> CodeAdd
QuantumQuasiCyclicCode(Q) : SeqEnum[ModTupFldElt] -> CodeAdd
Example QECC_QuasiCyclicQuantCode (H129E13)
Access Functions
QuantumBasisElement(F) : FldFin -> FldFinElt
StabilizerCode(Q) : CodeQuantum -> CodeAdd
StabilizerMatrix(Q) : CodeQuantum -> ModMatFldElt
NormalizerCode(Q) : CodeQuantum -> CodeAdd
NormalizerMatrix(Q) : CodeQuantum -> ModMatFldElt
Quantum Error Group
QuantumErrorGroup(p, n) : RngIntElt, RngIntElt -> GrpPC
QuantumBinaryErrorGroup(n) : RngIntElt -> GrpPC
Example QECC_quantum-error-group (H129E14)
QuantumErrorGroup(Q) : CodeQuantum -> GrpPC
StabilizerGroup(Q) : CodeQuantum -> GrpPC
StabilizerGroup(Q, G) : CodeQuantum, GrpPC -> GrpPC
Example QECC_quant-stab-group (H129E15)
Example QECC_quant-stab-group-hack (H129E16)
Inner Products and Duals
SymplecticInnerProduct(v1, v2) : ModTupFldElt, ModTupFldElt -> FldFinElt
SymplecticDual(C) : CodeAdd -> CodeAdd
IsSymplecticSelfDual(C) : CodeAdd -> BoolElt
IsSymplecticSelfOrthogonal(C) : CodeAdd -> BoolElt
Example QECC_SymplecticEg (H129E17)
Example QECC_symplecticselforthog (H129E18)
Weight Distribution and Minimum Weight
WeightDistribution(Q) : CodeQuantum -> SeqEnum, SeqEnum, SeqEnum
Example QECC_QuantWeightDist (H129E19)
MinimumWeight(Q) : CodeQuantum -> RngIntElt
Example QECC_QuantMinWeight (H129E20)
IsPure(Q) : CodeQuantum -> BoolElt
Example QECC_QECC-IsPure (H129E21)
New Codes From Old
DirectSum(Q1, Q2) : CodeQuantum, CodeQuantum -> CodeQuantum
ExtendCode(Q) : CodeQuantum -> CodeQuantum
ExtendCode(Q, m) : CodeQuantum, RngIntElt -> CodeQuantum
PunctureCode(Q, i) : CodeQuantum, RngIntElt -> CodeQuantum
PunctureCode(Q, I) : CodeQuantum, SetEnum -> CodeQuantum
ShortenCode(Q, i) : CodeQuantum, RngIntElt -> CodeQuantum
ShortenCode(Q, I) : CodeQuantum, SetEnum -> CodeQuantum
Example QECC_NonQuantCombs (H129E22)
Best Known Quantum Codes
QECC(F, n, k) : FldFin, RngIntElt, RngIntElt -> CodeQuantum, BoolElt
Example QECC_QECC-egs (H129E23)
Example QECC_QECC-self-dual (H129E24)
Example QECC_QECC-verbose (H129E25)
Best Known Bounds
QECCLowerBound(F, n, k) : FldFin, RngIntElt, RngIntElt -> RngIntElt
QECCUpperBound(F, n, k) : FldFin, RngIntElt, RngIntElt -> RngIntElt
Example QECC_QECCBounds (H129E26)
Automorphism Group
AutomorphismGroup(Q) : CodeQuantum -> GrpPerm
PermutationGroup(Q) : CodeQuantum -> GrpPerm
Example QECC_QuantumAuto (H129E27)
Example QECC_QECC-Auto-stabilizer (H129E28)
Hilbert Spaces
HilbertSpace(F, n) : FldCom, RngIntElt -> HilbSpc
Field(H) : HilbSpc -> FldCom
NumberOfQubits(H) : HilbSpc -> RngIntElt
Dimension(H) : HilbSpc -> RngIntElt
IsDenselyRepresented(H) : HilbSpc -> RngIntElt
H1 eq H2 : HilbSpc, HilbSpc -> BoolElt
H1 ne H2 : HilbSpc, HilbSpc -> BoolElt
Example QECC_HilbertSpaceCreate (H129E29)
Creation of Quantum States
QuantumState(H, v) : HilbSpc, ModTupFldElt -> HilbSpcElt
H ! i : HilbSpc, RngIntElt -> HilbSpcElt
H ! s : HilbSpc, [RngIntElt] -> HilbSpcElt
SetPrintKetsInteger(b) : BoolElt ->
Example QECC_QuantumStateCreate (H129E30)
Example QECC_QuantumStateCreateCoerce (H129E31)
Manipulation of Quantum States
a * e : FldComElt , HilbSpcElt -> HilbSpcElt
- e : HilbSpcElt -> HilbSpcElt
e1 + e2 : HilbSpcElt, HilbSpcElt -> HilbSpcElt
Normalisation(e) : HilbSpcElt -> HilbSpcElt
NormalisaionCoefficient(e) : HilbSpc -> FldComElt
e1 eq e2 : HilbSpcElt, HilbSpcElt -> BoolElt
e1 ne e2 : HilbSpcElt, HilbSpcElt -> BoolElt
Example QECC_QuantumStateNormalisation (H129E32)
Inner Product and Probabilities of Quantum States
InnerProduct(e1, e2) : HilbSpcElt, HilbSpcElt -> HilbSpcElt
ProbabilityDistribution(e) : HilbSpcElt -> Mtrx
Probability(e, i) : HilbSpcElt, RngIntElt -> FldReElt
Probability(e, v) : HilbSpcElt, RngIntElt -> FldReElt
PrintProbabilityDistribution(e) : HilbSpcElt ->
PrintSortedProbabilityDistribution(e) : HilbSpcElt ->
Example QECC_QuantumStateProbabilities (H129E33)
Example QECC_QuantumStateSortedProbabilities (H129E34)
Unitary Transformations on Quantum States
BitFlip(e, k) : HilbSpcElt,RngIntElt -> HilbSpcElt
BitFlip(e, B) : HilbSpcElt, RngIntElt -> HilbSpcElt
PhaseFlip(e, k) : HilbSpcElt,RngIntElt -> HilbSpcElt
PhaseFlip(e, B) : HilbSpcElt, RngIntElt -> HilbSpcElt
ControlledNot(e, B, k) : HilbSpcElt, RngIntElt, RngIntElt -> HilbSpcElt
HadamardTrasformation(e) : HilbSpcElt -> HilbSpcElt