jump_trajectory_evolution_pwc
Graph.jump_trajectory_evolution_pwc(initial_state_vector, hamiltonian, lindblad_terms, max_time_step, trajectory_count, sample_times=None, seed=None, *, name=None)
Calculate the state evolution of an open system described by the GKS–Lindblad master equation using a jump-based trajectory method.
This function calculates multiple pure-state trajectories starting from an initial pure state and returns the average density matrix over all trajectories.
Note that regardless of their original formats, both hamiltonian and lindblad_terms are internally converted to a dense representation, so there is no computational advantage in using a sparse representation with this method.
Parameters
- initial_state_vector (np.ndarray or Tensor) – The initial state vector
(D,)
array or Tensor, or batch of initial state vectors as a(B, D)
array or Tensor. - hamiltonian (Pwc or SparsePwc) – A piecewise-constant function representing the system Hamiltonian,
- lindblad_terms (list [ tuple [ float , np.ndarray or Tensor or scipy.sparse.spmatrix ] ]) – A list of pairs, , representing the positive decay rate and the Lindblad operator for each coupling channel
- max_time_step (float) – The maximum time step to use in the integration. Each PWC segment will be subdivided into steps that are, at most, this value. A smaller value for the maximum time step will more accurately sample the jump processes, but also lead to a slower computation.
- trajectory_count (int) – The number of quantum trajectories to run.
- sample_times (np.ndarray or None , optional) – A 1D array like object of length specifying the times
- seed (int or None , optional) – A seed for the random number generator. Defaults to None, in which case a random value for the seed is used.
- name (str , optional) – The name of the node.
Returns
The time-evolved density matrix, with shape (D, D)
or (T, D, D)
,
depending on whether you provided sample times.
If you provide a batch of initial states, the shape is (B, T, D, D)
or (B, D, D)
.
Return type
SEE ALSO
Graph.density_matrix_evolution_pwc
: State evolution of an open quantum system.
Graph.steady_state
: Compute the steady state of open quantum system.
Notes
Under the Markovian approximation, the dynamics of an open quantum system can be described by the GKS–Lindblad master equation 1 2
where
for any system operator
This function solves the GKS–Lindblad master equation with an initial pure state , by calculating multiple quantum trajectories performing quantum jumps,
References
[1] V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, J. Math. Phys. 17, 821 (1976).