Quantum Channel Generators API

Quantum Channel Generators

graphcalc.quantum.channel_generators.amplitude_damping_channel(gamma: float, *, tol: float = 1e-09) → QuantumChannel

Return the qubit amplitude-damping channel.

Parameters:

• gamma (float) – Damping parameter. Must satisfy 0 <= gamma <= 1.

• tol (float, default=1e-9) – Numerical tolerance passed to QuantumChannel.

Notes

This channel models relaxation from |1> to |0> with probability gamma.

A Kraus representation is

K0 = [[1, 0], [0, sqrt(1-gamma)]], K1 = [[0, sqrt(gamma)], [0, 0]].

In particular,

• |0><0| is fixed,

• |1><1| is mapped to gamma |0><0| + (1-gamma) |1><1|.

This channel is trace preserving and completely positive, but in general it is not unital.

graphcalc.quantum.channel_generators.bit_flip_channel(p: float, *, tol: float = 1e-09) → QuantumChannel

Return the qubit bit-flip channel.

Parameters:

• p (float) – Flip probability. Must satisfy 0 <= p <= 1.

• tol (float, default=1e-9) – Numerical tolerance passed to QuantumChannel.

Notes

This channel is defined by

Phi(rho) = (1 - p) rho + p X rho X,

where X is the Pauli X operator.

graphcalc.quantum.channel_generators.bit_phase_flip_channel(p: float, *, tol: float = 1e-09) → QuantumChannel

Return the qubit bit-phase-flip channel.

Parameters:

• p (float) – Flip probability. Must satisfy 0 <= p <= 1.

• tol (float, default=1e-9) – Numerical tolerance passed to QuantumChannel.

Notes

This channel is defined by

Phi(rho) = (1 - p) rho + p Y rho Y,

where Y is the Pauli Y operator.

graphcalc.quantum.channel_generators.depolarizing_channel(p: float, *, dim: int = 2, tol: float = 1e-09) → QuantumChannel

Return the depolarizing channel on a dim-dimensional system.

Parameters:

• p (float) – Mixing parameter. Must satisfy 0 <= p <= 1.

• dim (int, default=2) – Hilbert-space dimension.

• tol (float, default=1e-9) – Numerical tolerance passed to QuantumChannel.

Notes

This implementation uses the convention

Phi(rho) = (1 - p) rho + p * Tr(rho) * I / dim.

For density operators with Tr(rho)=1, this is

Phi(rho) = (1 - p) rho + p I / dim.

A Kraus representation is given by

• K0 = sqrt(1-p) I

• K_{ij} = sqrt(p/dim) E_{ij} for all 0 <= i,j < dim,

where E_{ij} is the matrix unit with a 1 in position (i,j) and zeros elsewhere.

graphcalc.quantum.channel_generators.identity_channel(dim: int, *, tol: float = 1e-09) → QuantumChannel

Return the identity channel on a dim-dimensional system.

graphcalc.quantum.channel_generators.phase_damping_channel(gamma: float, *, tol: float = 1e-09) → QuantumChannel

Return the qubit phase-damping channel.

Parameters:

• gamma (float) – Dephasing parameter. Must satisfy 0 <= gamma <= 1.

• tol (float, default=1e-9) – Numerical tolerance passed to QuantumChannel.

Notes

This channel preserves populations and damps coherences:

[[rho00, rho01], [rho10, rho11]] -> [[rho00, sqrt(1-gamma) rho01], [sqrt(1-gamma) rho10, rho11]].

A Kraus representation is

K0 = diag(1, sqrt(1-gamma)), K1 = diag(0, sqrt(gamma)).

graphcalc.quantum.channel_generators.phase_flip_channel(p: float, *, tol: float = 1e-09) → QuantumChannel

Return the qubit phase-flip channel.

Parameters:

• p (float) – Flip probability. Must satisfy 0 <= p <= 1.

• tol (float, default=1e-9) – Numerical tolerance passed to QuantumChannel.

Notes

This channel is defined by

Phi(rho) = (1 - p) rho + p Z rho Z,

where Z is the Pauli Z operator.