| | ▪The bit-flip channel is represented by the quantum channel QuantumChannel[{p QuantumOperator["X"],1-p QuantumOperator["I"]}] . In this channel, a qubit undergoes a bit-flip operation with probability p and remains unchanged with probability 1 - p. | ▪The phase-flip channel is represented by the quantum channel QuantumChannel[{p QuantumOperator["Z"],1-p QuantumOperator["I"]}] . In this channel, a qubit undergoes a phase-flip operation with probability p and remains unchanged with probability 1 - p. | ▪The bit-phase-flip channel is represented by the quantum channel QuantumChannel[{p QuantumOperator["Y"],1-p QuantumOperator["I"]}] . In this channel, a qubit undergoes a combined bit and phase-flip operation with probability p and remains unchanged with probability 1 - p. | ▪The depolarizing channel is represented by the quantum channel QuantumChannel[{p/4 QuantumOperator["X"],p/4 QuantumOperator["Y"],p/4 QuantumOperator["Z"],1-3p/4 QuantumOperator["I"]}] . In this channel, a qubit undergoes a random Pauli operation (X, Y, or Z) with equal probability p/4 or remains unchanged with probability 1 - 3p/4. | ▪The amplitude damping channel is represented by the quantum channel QuantumChannel[{QuantumOperator[{{1,0},{0,1-γ }}],QuantumOperator[{{0,γ },{0,0}}]}] . This channel models the energy relaxation of a qubit, where γ is the damping rate. | ▪The generalized amplitude damping channel is represented by the quantum channel QuantumChannel[{p QuantumOperator[{{1,0},{0,1-γ }}],p QuantumOperator[{{0,γ },{0,0}}],1-p QuantumOperator[{{1-γ ,0},{0,1}}],1-p QuantumOperator[{{0,0},{γ ,0}}]}] . This channel models the energy relaxation of a qubit in the presence of a thermal environment, where p is the probability of the qubit being excited and γ is the damping rate. | ▪The phase damping channel is represented by the quantum channel QuantumChannel[{QuantumOperator[{{1,0},{0,1-λ }}],QuantumOperator[{{0,0},{0,λ }}]}] . This channel models the dephasing of a qubit, where λ is the dephasing rate. |
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