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Register a new userQuTiP 2: A Python framework for the dynamics of open quantum systems
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We present version 2 of QuTiP, the Quantum Toolbox in Python. Compared to the preceding version [Comput. Phys. Comm. 183 (2012) 1760], we have introduced numerous new features, enhanced performance, made changes in the Application Programming Interface (API) for improved functionality and consistency within the package, as well as increased compatibility with existing conventions used in other scientific software packages for Python. The most significant new features include efficient solvers for arbitrary time-dependent Hamiltonians and collapse operators, support for the Floquet formalism, and new solvers for Bloch-Redfield and Floquet-Markov master equations. Here we introduce these new features, demonstrate their use, and give a summary of the important backward-incompatible API changes introduced in this version.
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We present an object-oriented open-source framework for solving the dynamics of open quantum systems written in Python. Arbitrary Hamiltonians, including time-dependent systems, may be built up from operators and states defined by a quantum object class, and then passed on to a choice of master equation or Monte-Carlo solvers. We give an overview of the basic structure for the framework before detailing the numerical simulation of open system dynamics. Several examples are given to illustrate the build up to a complete calculation. Finally, we measure the performance of our library against that of current implementations. The framework described here is particularly well-suited to the fields of quantum optics, superconducting circuit devices, nanomechanics, and trapped ions, while also being ideal for use in classroom instruction.
We analyze a class of dynamics of open quantum systems which is governed by the dynamical map mutually commuting at different times. Such evolution may be effectively described via spectral analysis of the corresponding time dependent generators. We consider both Markovian and non-Markovian cases.
We extend the concept of superadiabatic dynamics, or transitionless quantum driving, to quantum open systems whose evolution is governed by a master equation in the Lindblad form. We provide the general framework needed to determine the control strategy required to achieve superadiabaticity. We apply our formalism to two examples consisting of a two-level system coupled to environments with time-dependent bath operators.
A full quantum mechanical treatment of open quantum systems via a Master equation is often limited by the size of the underlying Hilbert space. As an alternative, the dynamics can also be formulated in terms of systems of coupled differential equations for operators in the Heisenberg picture. This typically leads to an infinite hierarchy of equations for products of operators. A well-established approach to truncate this infinite set at the level of expectation values is to neglect quantum correlations of high order. This is systematically realized with a so-called cumulant expansion, which decomposes expectation values of operator products into products of a given lower order, leading to a closed set of equations. Here we present an open-source framework that fully automizes this approach: first, the equations of motion of operators up to a desired order are derived symbolically using predefined canonical commutation relations. Next, the resulting equations for the expectation values are expanded employing the cumulant expansion approach, where moments up to a chosen order specified by the user are included. Finally, a numerical solution can be directly obtained from the symbolic equations. After reviewing the theory we present the framework and showcase its usefulness in a few example problems.
The manipulation of the quantum states of light in linear optical systems has multiple applications in quantum optics and quantum computation. The package QOptCraft gives a collection of methods to solve some of the most usual problems when designing quantum experiments with linear interferometers. The methods include functions that compute the quantum evolution matrix for n photons from the classical description of the system and inverse methods that, for any desired quantum evolution, will either give the complete description of the experimental system that realizes that unitary evolution or, when this is impossible, the complete description of the linear system which approximates the desired unitary with a locally minimal error. The functions in the package include implementations of different known decompositions that translate the classical scattering matrix of a linear system into a list of beam splitters and phase shifters and methods to compute the effective Hamiltonian that describes the quantum evolution of states with n photons. The package is completed with routines for useful tasks like generating random linear optical systems and computing matrix logarithms. The routines are chosen to avoid usual numerical problems when dealing with the unitary matrices that appear in the description of linear systems.
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