# 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=None, **kwargs)

Performs 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.

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

qctrl.dynamic.types.coherent_simulation.Result

Warning

You must provide at least one term (in drives, shifts, or drifts).

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.

Examples

See the Simulation user guide.