Terminologyï
This is a short terminology glossary for the solver and related classes. See the rest of the guide for more in depth information.
- Quantum system
Set of operators and physical parameters used to build the dynamic equations. Common components are the Hamiltonian, collapse or jump operators, bath coupling operators and environment/spectral noise configurations.
- method
The identifier string used to select the numerical integration technique for a time-evolution run. May refer to an ODE or SDE integration algorithm, depending on the solver.
- ODE
Ordinary Differential Equation.
$$ frac{dX}{dt} = f(t, X) $$
- SDE
Stochastic Differential Equation:
$$ dX = f(t, X) dt + sum_i g_i(t, X) dW_i $$
where $dW_i$ represents an independent Wiener processes modeling Gaussian white noise.
- RHS
Right-Hand Side. The representation describing the derivative in a differential equation (i.e., the $f(t, X)$ term in an ODE).
- Feedback
The term we use for quantum dynamics where the underlying quantum system parameters depend explicitly on the instantaneous state of the system, introducing a form of non-linearity. For example, when its Hamiltonian depends on the expectation value of an operator or the state itself: $H = H(t, rho)$. Different
Solversub-classes may provide different feedback formats.- Deterministic / Non-deterministic
A categorization based on whether randomness is involved in the time-evolution.
Deterministic evolution algorithms (like standard master equations or Schrödinger equations) always yield identical results (up to numerical imprecision) across separate runs given identical initial conditions.
Non-deterministic evolution introduces pseudo-random variables, yielding structurally unique trajectories on successive invocations.
- Stochastic
While broadly synonymous with non-deterministic behavior, in this section, âstochasticâ specifically denotes simulations driven by true Stochastic Differential Equations (SDEs) containing Gaussian noise channels (e.g.,
SMESolver). Conversely, while Monte Carlo simulations (MCSolver) are non-deterministic due to discrete, random quantum jumps, their trajectories are piecewise-deterministic and are typically excluded when discussing âstochastic evolutionâ.- Trajectory
A single, continuous realization of a non-deterministic quantum evolution process. For instance, an individual run of a Monte Carlo simulation contains a unique sequence of jump events and timings that defines one distinct trajectory.