calculate_coherent_simulation
- static FunctionNamespace.calculate_coherent_simulation(*, duration, sample_times=None, drives=None, shifts=None, drifts=None, initial_state_vector=None, target=None, result_scope='ALL', **kwargs)
Perform the evolution of a closed quantum system.
Use this function to simulate the dynamics of a system under a Hamiltonian expressed as a sum of piecewise-constant terms. The function calculates the resulting unitary evolution operator. It can also calculate the infidelity with respect to a given target operator and the evolution of a given initial state.
When using this function, you must provide at least one term in drives, shifts, or drifts.
- Parameters:
duration (float) – The duration of the simulation, \(\tau\). Must be positive and match the duration of each control in drives and shifts.
sample_times (List[float], optional) – The times at which you want to sample the simulation. If provided, it must contain at least one element, be increasing, and each element must be between 0 and \(\tau\) (inclusive). Defaults to a singleton array containing duration.
drives (List[qctrl.dynamic.types.coherent_simulation.Drive], optional) – The list of complex control terms in the system’s Hamiltonian. Each term has the form \(\gamma_{j}(t) C_{j} + \mathrm{H.c.}\), where \(C_{j}\) is a non-Hermitian operator and \(\gamma_{j}(t)\) is a complex piecewise-constant function between 0 and \(\tau\). Defaults to an empty list.
shifts (List[qctrl.dynamic.types.coherent_simulation.Shift], optional) – The list of real control terms in the system’s Hamiltonian. Each term has the form \(\alpha_{k}(t) A_{k}\), where \(A_{k}\) is a Hermitian operator and \(\alpha_{k}(t)\) is a real piecewise- constant function between 0 and \(\tau\). Defaults to an empty list.
drifts (List[qctrl.dynamic.types.coherent_simulation.Drift], optional) – The list of static terms in the system’s Hamiltonian. Each term has the form of a constant Hermitian operator \(D_{l}\). Defaults to an empty list.
initial_state_vector (ndarray, optional) – The initial state vector to be evolved, \(|\psi(0)\rangle\). If provided, the function calculates its evolution at the sample times.
target (qctrl.dynamic.types.TargetInput, optional) – The target partial isometry, \(V\). If provided, the function calculates the infidelity with respect to it at the sample times.
result_scope (qctrl.dynamic.types.coherent_simulation.ResultScope, optional) – Configuration for the scope of the returned data. Use this to select which data you want returned and which you want to omit.
- Returns:
The result of the coherent simulation. It includes the values, at the sample times, of the unitary evolution operator \(U(t)\), the target operation infidelity \(\mathcal{I}(t)\) (if requested), and the evolved state \(|\psi(t)\rangle\) (if requested).
- Return type:
Warning
This is a legacy function that will be removed in the future. The recommended way of running simulations is through the calculate_graph function. You can read about how to use the calculate_graph function for coherent simulations in the How to simulate quantum dynamics for noiseless systems using graphs user guide.
See also
calculate_graphEvaluate generic functions.
Notes
This function integrates the time-dependent Schrödinger equation,
\[i \frac{d U(t)}{d t} = H(t) U(t),\]with a control Hamiltonian
\[H(t) = \sum_{j = 1}^{N_\mathrm{drives}} \left( \gamma_{j}(t) C_{j} + \mathrm{H.c.} \right) + \sum_{k = 1}^{N_\mathrm{shifts}} \alpha_{k}(t) A_{k} + \sum_{l = 1}^{N_\mathrm{drifts}} D_{l} ,\]and returns the unitary evolution operator \(U(t)\) for each \({t}\) in sample_times.
If you provide target, the function also returns the infidelity at each sample time, calculated as
\[\mathcal{I}(t) = 1 - \left| \frac{\mathrm{Tr} \left(V^\dagger U(t)\right)} {\mathrm{Tr} \left(V^\dagger V\right)} \right|^2 .\]If you provide initial_state_vector, the function also returns the evolved state \(|\psi(t)\rangle = U(t)|\psi(0)\rangle\) at each sample time.