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Welcome to the toqito wiki!

Mission: Enable scientists to discover new results in quantum information theory via sophisticated software.

Objective: To act as the primary software arsenal for tackling numerical problems pertaining to quantum states, channels, and measurements in quantum information theory.

Contributing: Consult the contribution guide for instructions on how to help improve the toqito project and accelerate our numerical tools for this field.

Project ideas for GSoC 2025 are available here.

2024 - 2025 Roadmap

Goals

• Port cvxquad from MATLAB to functions within channels/*.

  • lieb_ando.m
  • matrix_geo_mean_epi_cone.m
  • matrix_geo_mean_hypo_cone.m
  • op_rel_entr_epi_cone.m
  • quantum_cond_entr.m
  • quantum_entr.m
  • quantum_rel_entr.m
  • rel_entr_quad.m
  • trace_logm.m
  • trace_mpower.m
  • cq_channel_capacity.m
  • degradable_channels_capacity.m
  • entanglement_assisted_capacity.m
  • nearest_correlation_matrix.m
  • rel_entr_entanglement.m
  • rel_entr_recovery.m

• Port QETLAB functions from MATLAB to functions within toqito:

  • AbsPPTConstraints.m
  • AntisymmetricProjection.m (perms/antisymmetric_projection.py)
  • ApplyMap.m (channel_ops/apply_channel.py)
  • BCSGameLB.m (nonlocal_games/nonlocal_game.py)
  • BCSGameValue.m (nonlocal_games/nonloca_game.py)
  • Bell.m (states/bell.py)
  • BellInequalityMax.m
  • BellInequalityMaxQubits.m
  • BrauerStates.m (states/brauer.py)
  • BreuerStates.m (states/breuer.py)
  • CBNorm.m (channel_metrics/completely_bounded_trace_norm.py)
  • ChannelDistinguishability.m
  • ChessboardState.m (states/chessboard.py)
  • ChoiMap.m (channels/choi.py)
  • ChoiMatrix.m
  • CliqueNumber.m
  • Commutant.m
  • ComplementaryMap.m
  • Concurrence.m (state_props/concurrence.py)
  • CopositivePolynomial.m
  • DephasingChannel.m (channels/dephasing_channel.py)
  • DepolarizingChannel.m (channels/depolarizing_channel.py)
  • DiamondNorm.m (channel_props/diamond_norm.py)
  • DickeState.m
  • Distinguishability.m
  • DualMap.m (channel_ops/dual_channel.py)
  • EntFormation.m (state_props/entanglement_of_formation.py)
  • EntangledSubspace.m
  • Entropy.m (state_props/von_neumann_entropy.py)
  • Fidelity.m (state_metrics/fidelity.py)
  • FilterNormalForm.m
  • FourierMatrix.m (matrices/fourier_matrix.py)
  • GHZState.m (states/ghz_state.py)
  • GellMann.m (matrices/gell_mann.py)
  • GenGellMann.m (matrices/gen_gell_mann.py)
  • GenPauli.m (matrices/gen_pauli.py)
  • GisinState.m (states/gisin_state.py)
  • HorodeckiState.m (states/horodecki_state.py)
  • InSeparableBall.m (state_props/in_separable_ball.py)
  • InducedMatrixNorm.m
  • InducedSchattenNorm.m
  • IsAbsPPT.m
  • IsBlockPositive.m (matrix_props/is_block_positive.py)
  • IsCP.m (channel_props/is_completely_positive.py)
  • IsCopositive.m
  • IsEntanglingGate.m
  • IsHermPreserving.m (channel_props/is_herm_preserving.py)
  • IsPPT.m (state_props/is_ppt.py)
  • IsPSD.m (matrix_props/is_positive_semidefinite.py)
  • IsProductOperator.m (state_props/is_product.py)
  • IsProductVector.m (state_props/is_product.py)
  • IsSeparable.m (state_props/is_separable.py)
  • IsTotallyNonsingular.m
  • IsTotallyPositive.m (matrix_props/is_totally_positive.py)
  • IsUPB.m (state_props/is_unextendible_product_basis.py)
  • IsotropicState.m (states/isotropic_state.py)
  • KrausOperators.m (channel_ops/kraus_to_choi.py) and (channel_ops/choi_to_kraus.py)
  • KyFanNorm.m
  • L1NormCoherence.m (matrix_props/l1_norm_coherence.py)
  • LocalDistinguishability.m
  • Majorizes.m (state_props/majorizes.py)
  • MatsumotoFidelity.m (state_metrics/matsumoto_fidelity.py)
  • MaxEntangled.m (states/max_entangled.py)
  • MaximumOutputFidelity.m
  • MinUPBSize.m
  • NPAHierarchy.m (helper/npa_hierarchy.py)
  • Negativity.m (state_props/negativity.py)
  • NonlocalGameLB.m (nonlocal_games/nonlocal_game.py)
  • OperatorSchmidtDecomposition.m (state_ops/schmidt_decomposition.py)
  • OperatorSchmidtRank.m (state_props/schmidt_rank.py)
  • OperatorSinkhorn.m
  • ParallelRepetition.m (nonlocal_games/nonlocal_game.py)
  • PartialMap.m (channels/partial_channel.py)
  • PartialTrace.m (channels/partial_trace.py)
  • PartialTranspose.m (channels/partial_transpose.py)
  • Pauli.m (matrices/pauli.py)
  • PauliChannel.m
  • PermutationOperator.m (perms/permutation_operator.py)
  • PermuteSystems.m (perms/permutate_systems.py)
  • PolynomialAsMatrix.m
  • PolnyomialOptimize.m
  • PolynomialSOS.m
  • Purity.m (state_props/purity.py)
  • RandomDensityMatrix.m (rand/random_density_matrix.py)
  • RandomGraph.m
  • RandomPOVM.m (rand/random_povm.py)
  • RandomPPTState.m
  • RandomProbabilities.m
  • RandomStateVector.m (rand/random_state_vector.py)
  • RandomSuperoperator.m
  • RandomUnitary.m (rand/random_unitary.py)
  • Realignment.m (channels/realignment.py)
  • ReductionMap.m (channels/reduction.py)
  • RelEntCoherence.m
  • RobustnessCoherence.m
  • SchattenNorm.m
  • SchmidtDecomposition.m (state_ops/schmidt_decomposition.py)
  • SchmidtRank.m (state_props/schmidt_rank.py)
  • SkOperatorNorm.m (matrix_props/sk_norm.py)
  • SkVectorNorm.m (state_props/sk_vec_norm.py)
  • Swap.m (perms/swap.py)
  • SwapOperator.m (perms/swap_operator.py)
  • SymmetricExtension.m (state_opt/symmetric_extension_hierarchy.py)
  • SymmetricInnerExtension.m
  • SymmetricProjection.m (perms/symmetric_projection.py)
  • Tensor.m (matrix_ops/tensor.py)
  • TensorSum.m
  • TraceDistanceCoherence.m
  • TraceNorm.m (state_props/trace_norm.py)
  • Twirl.m
  • UPB.m
  • UPBSepDistinguishable.m
  • WState.m (states/w_state.py)
  • WernerState.m (states/werner.py)
  • XORGameValue.m (nonlocal_games/xor_game.py)
  • kpNorm.m (matrix_props/kp_norm.py)
  • kpNormDual.m