simulate

boulderopal.superconducting.simulate(transmons, cavities, interactions, gate_duration, sample_count=128, cutoff_frequency=None, initial_state=None)

Simulate a system composed of transmons and cavities.

This function builds a graph describing the Hamiltonian (see the note part for details) of a superconducting system, and calls execute_graph to simulate its dynamics.

Parameters:

  • transmons (list[Transmon]) – List of objects containing the physical information about the transmons. It must not contain any optimizable coefficients. It can be an empty list, but at least one transmon or cavity must be provided.

  • cavities (list[Cavity]) – List of objects containing the physical information about the cavities. They must not contain any optimizable coefficients. It can be an empty list, but at least one transmon or cavity must be provided.

  • interactions (list[TransmonTransmonInteraction or TransmonCavityInteraction or CavityCavityInteraction]) – List of objects containing the physical information about the interactions in the system. They must not contain any optimizable coefficients. It can be an empty list.

  • gate_duration (float) – The duration of the gate to be simulated, \(t_\mathrm{gate}\). It must be greater than zero.

  • sample_count (int, optional) – The number of times between 0 and gate_duration (included) at which the evolution is sampled. Defaults to 128.

  • cutoff_frequency (float or None, optional) – The cutoff frequency of a linear sinc filter to be applied to the piecewise-constant signals you provide for the coefficients. If not provided, the signals are not filtered. If the signals are filtered, a larger sample count leads to a more accurate numerical integration. If the signals are not filtered, the sample count has no effect on the numerical precision of the integration.

  • initial_state (np.ndarray or None, optional) – The initial state of the system, \(|\Psi_\mathrm{initial}\rangle\), as a 1D array of length D = np.prod([system.dimension for system in transmons + cavities]). If not provided, the function only returns the system’s unitary time-evolution operators.

Returns:

The result of the execute_graph call. Its output item is a dictionary containing information about the evolution of the system, with the following keys:

sample_times

The times at which the system’s evolution is sampled, as an array of shape (T,).

unitaries

The system’s unitary time-evolution operators at each sample time, as an array of shape (T, D, D).

state_evolution

The time evolution of the initial state at each sample time, as an array of shape (T, D). This is only returned if you provide an initial state.

Return type:

dict

See also

boulderopal.superconducting.optimize

Find optimal pulses or parameters for a system composed of transmons and cavities.

Notes

The Hamiltonian of the system is of the form

\[H = \sum_i H_{\mathrm{transmon}_i} + \sum_i H_{\mathrm{cavity}_i} + \sum_{i,j} H_{\mathrm{transmon}_i-\mathrm{transmon}_j} + \sum_{i,j} H_{\mathrm{transmon}_i-\mathrm{cavity}_j} + \sum_{i,j} H_{\mathrm{cavity}_i-\mathrm{cavity}_j}\]

where i and j mark the i-th and j-th transmon or cavity. For their definition of each Hamiltonian term, see its respective class.

The Hilbert space of the system is defined as the outer product of all the transmon Hilbert spaces (in the order they’re provided in transmons) with the cavity Hilbert spaces (in the order they’re provided in cavities), that is:

\[\mathcal{H} = \mathcal{H}_{\mathrm{transmon}_1} \otimes \mathcal{H}_{\mathrm{transmon}_2} \otimes \ldots \otimes \mathcal{H}_{\mathrm{cavity}_1} \otimes \mathcal{H}_{\mathrm{cavity}_2} \otimes \ldots\]

The system dimension D is then the product of all transmon and cavity dimensions.