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mindquantum.core.gates.ThermalRelaxationChannel

class mindquantum.core.gates.ThermalRelaxationChannel(t1: float, t2: float, gate_time: float, **kwargs)

Thermal relaxation channel.

The thermal relaxation channel describes the thermal decoherence and dephasing of qubit when a quantum gate is applied, and is determined by T1, T2 and gate time.

The Choi-matrix representation of this channel is as below:

$$\begin{array}{r}\begin{array}{c}ϵ(\rho )={\text{tr}}_1\left[\mathrm{\Lambda }({\rho }^T\otimes I)\right],\mathrm{\Lambda }=\left(\begin{array}{cccc}{ϵ}_{T_1}& 0& 0& {ϵ}_{T_2}\\ 0& 1-{ϵ}_{T_1}& 0& 0\\ 0& 0& 0& 0\\ {ϵ}_{T_2}& 0& 0& 1\end{array}\right)\\ \text{where}{ϵ}_{T_1}=e^{-T_g/T_1},{ϵ}_{T_2}=e^{-T_g/T_2}\end{array}\end{array}$$

Where $\rho$ is quantum state as density matrix type; $\mathrm{\Lambda }$ is Choi matrix, $T_1$ is thermal relaxation time of qubit, $T_2$ is dephasing time of qubit, $T_g$ is gate time.

Parameters

• t1 (int, float) – T1 of the qubit.

• t2 (int, float) – T2 of the qubit.

• gate_time (int, float) – time of the quantum gate.

Examples

>>> from mindquantum.core.gates import ThermalRelaxationChannel
>>> from mindquantum.core.circuit import Circuit
>>> t1 = 100000
>>> t2 = 50000
>>> gate_time = 35
>>> circ = Circuit()
>>> circ += ThermalRelaxationChannel(t1, t2, gate_time).on(0)
>>> print(circ)
      ╔═══════════════════════════════╗
q0: ──╢ TRC(t1=100000,t2=50000,tg=35) ╟───
      ╚═══════════════════════════════╝

get_cpp_obj()

Get underlying C++ object.

matrix()

Kraus operator of the quantum channel.

Returns

list, contains all Kraus operators of this quantum channel.