qat.quops

This module regroups classes and functions to create and manipulate quantum channels, also called quantum operations, quantum maps or quantum process. They describe the generalized dynamics of quantum systems when coupled to an external environment.

Quantum Channels

Here are classes related to describing a generic quantum channel.

`qat.quops.ChannelRepresentations`	Identifiers for quantum channel representations
`qat.quops.ParametricGateNoise`	Applies noise channel based on gate time
`qat.quops.ParametricQuantumChannel`	Abstract class for parametric quantum channels
`qat.quops.QuantumChannel`	Abstract class for quantum channels
`qat.quops.QuantumChannelChi`	Quantum channel in the chi matrix representation
`qat.quops.QuantumChannelChoi`	Quantum channel in the Choi-Jamiolkowski representation
`qat.quops.QuantumChannelKraus`	Quantum channel in the Kraus representation
`qat.quops.QuantumChannelPTM`	Quantum channel in the Pauli Transfer Matrix (PTM) representation

All quantum channels derive from the abstract class QuantumChannel. Different representations are available: namely Kraus operators, Pauli Transfer Matrix (PTM), Choi-Jamiolkowski mapping and \(\chi\)-matrix. They can be converted into one another through dedicated methods, for example to_chi(). Channels that depend on a parameter, for instance a duration that represents the exposition time to an environment, are called parametric quantum channels and derive from ParametricQuantumChannel.

The following functions allows to check for important properties of a QuantumChannel. Be aware that they are not defined for all representations.

`qat.quops.is_completely_positive()`	Check if a channel is completely positive
`qat.quops.is_trace_preserving()`	Check if a channel is trace preserving
`qat.quops.is_trace_reducing()`	Check if a channel is trace reducing
`qat.quops.is_unital()`	Check if a channel is unital

Predefined quantum channels

The following commonly used channels are already defined in Qaptiva:

`qat.quops.make_avg_fid_equiv_depol_channel()`	Quantum channel for depolarizing noise (alternative)
`qat.quops.make_depolarizing_channel()`	Quantum channel for depolarizing noise
`qat.quops.make_generalized_amplitude_damping()`	Quantum channel for generalized amplitude damping noise
`qat.quops.ParametricAmplitudeDamping`	Parametric quantum channel for amplitude damping noise
`qat.quops.ParametricPureDephasing`	Parametric quantum channel for pure dephasing noise

Metrics

qat.quops.metrics regroups functions related to metrics of the space of density matrices and of the space of quantum maps (also called processes in this context), i.e. distances, norms and fidelities.

`qat.quops.metrics.get_average_process_fidelity()`	Average process fidelity between two quantum channels
`qat.quops.metrics.get_diamond_norm()`	Diamond norm of a quantum channel
`qat.quops.metrics.get_entanglement_process_fidelity()`	Entanglement process fidelity between two quantum channels
`qat.quops.metrics.get_process_distance()`	Trace distance between Choi representations of two quantum channels
`qat.quops.metrics.get_state_fidelity()`	Fidelity between two states
`qat.quops.metrics.get_trace_distance()`	Trace distance between two density matrices

Operator basis

The \(\chi\)-matrix representation depends on the choice of operator basis. Here are functions to define such basis.

`qat.quops.math_util.convert_density_mat_to_pauli_vec()`	Convert matrix from canonical to Pauli
`qat.quops.math_util.convert_pauli_vec_to_density_mat()`	Convert matrix from Pauli to canonical
`qat.quops.math_util.make_pauli_matrix_basis()`	Pauli matrix basis
`qat.quops.math_util.make_standard_matrix_basis()`	Canonical matrix basis
`qat.quops.math_util.make_standard_vector_basis()`	Canonical vector basis

Mathematical utilities

Some useful functions related to the manipulation of quantum channels.

`qat.quops.math_util.are_equal_up_to_phase()`	Check equality of states up to a global phase
`qat.quops.math_util.multikron()`	Kronecker product of a list of matrices
`qat.quops.math_util.partial_trace()`	Partial trace of a matrix