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Proceedings of the Python in Science Conferences

QuTiP: A framework for the dynamics of open quantum systems using SciPy and Cython

Robert Johansson, Paul D. Nation

Published Jan 1, 2012• 2 citations
Publisher

Abstract

We present QuTiP (http://www.qutip.org),an object-oriented, opensource framework for solving the dynamics of open quantum systems.Written in Python, and using a combination of Cython, NumPy, SciPy, and matplotlib, QuTiP provides an environment for computational quantum mechanics that is both easy and efficient to use.Arbitrary quantum systems, including timedependent systems, may be built up from operators and states defined by a quantum object class, and then passed on to a choice of unitary or dissipative evolution solvers.Here we give an overview of the basic structure for the framework, and the techniques used in its implementation.We also present a few selected examples from current research on quantum mechanics that illustrate the strengths of the framework, as well as the types of calculations that can be performed.This framework is particularly well suited to the fields of quantum optics, superconducting circuit devices, nanomechanics, and trapped ions, while also being ideal as an educational tool.

DOI
10.25080/majora-54c7f2c8-00a

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We present QuTiP (http://www.qutip.org),an object-oriented, opensource framework for solving the dynamics of open quantum systems.Written in Python, and using a combination of Cython, NumPy, SciPy, and matplotlib, QuTiP provides an environment for computational quantum mechanics that is both easy and efficient to use.Arbitrary quantum systems, including timedependent systems, may be built up from operators and states defined by a quantum object class, and then passed on to a choice of unitary or dissipative evolution solvers.Here we give an overview of the basic structure for the framework, and the techniques used in its implementation.We also present a few selected examples from current research on quantum mechanics that illustrate the strengths of the framework, as well as the types of calculations that can be performed.This framework is particularly well suited to the fields of quantum optics, superconducting circuit devices, nanomechanics, and trapped ions, while also being ideal as an educational tool.
QuTiP, the Quantum Toolbox in Python (Johansson et al., 2012, Johansson et al., 2013), has been at the forefront of open-source quantum software for the past 13 years. It is used as a research, teaching, and industrial tool, and has been downloaded millions of times by users around the world. Here we introduce the latest developments in QuTiP v5, which are set to have a large impact on the future of QuTiP and enable it to be a modern, continuously developed and popular tool for another decade and more. We summarize the code design and fundamental data layer changes as well as efficiency improvements, new solvers, applications to quantum circuits with QuTiP-QIP, and new quantum control tools with QuTiP-QOC. Additional flexibility in the data layer underlying all “quantum objects” in QuTiP allows us to harness the power of state-of-the-art data formats and packages like JAX, CuPy, and more. We explain these new features with a series of both well-known and new examples. The code for these examples is available in a static form on GitHub ( https://github.com/qutip/qutip-paper-v5-examples ) and as continuously updated and documented notebooks in the qutip-tutorials package ( https://github.com/qutip/qutip-tutorials ).
The study of the impact of noise on quantum circuits is especially relevant to guide the progress of Noisy Intermediate-Scale Quantum (NISQ) computing. In this paper, we address the pulse-level simulation of noisy quantum circuits with the Quantum Toolbox in Python (QuTiP). We introduce new tools in qutip-qip , QuTiP's quantum information processing package. These tools simulate quantum circuits at the pulse level, leveraging QuTiP's quantum dynamics solvers and control optimization features. We show how quantum circuits can be compiled on simulated processors, with control pulses acting on a target Hamiltonian that describes the unitary evolution of the physical qubits. Various types of noise can be introduced based on the physical model, e.g., by simulating the Lindblad density-matrix dynamics or Monte Carlo quantum trajectories. In particular, the user can define environment-induced decoherence at the processor level and include noise simulation at the level of control pulses. We illustrate how the Deutsch-Jozsa algorithm is compiled and executed on a superconducting-qubit-based processor, on a spin-chain-based processor and using control optimization algorithms. We also show how to easily reproduce experimental results on cross-talk noise in an ion-based processor, and how a Ramsey experiment can be modeled with Lindblad dynamics. Finally, we illustrate how to integrate these features with other software frameworks.
The dynamics of open quantum systems is governed by the Lindblad master equation, which provides a consistent framework for incorporating environmental effects into the evolution of the system. Since exact solutions are rarely available, numerical methods become essential tools for analyzing such systems. This article presents a step-by-step implementation of the fourth-order Runge-Kutta method in Python to solve the Lindblad equation for a single quantized field mode subject to decay. A coherent state is used as the initial condition, and the time evolution of the average photon number is investigated. The proposed methodology enables transparent and customizable simulations of dissipative quantum dynamics, emphasizing a pedagogical approach that helps readers understand the numerical structure without relying on external libraries such as QuTiP. This standalone implementation offers full control over each integration step, making it particularly suitable for educational contexts and for exploring non-standard dynamics or introducing custom modifications to the Liouvillian.
Abstract We present an open-source software package called “Hamiltonian Open Quantum System Toolkit" (HOQST), a collection of tools for the investigation of open quantum system dynamics in Hamiltonian quantum computing, including both quantum annealing and the gate-model of quantum computing. It features the key master equations (MEs) used in the field, suitable for describing the reduced system dynamics of an arbitrary time-dependent Hamiltonian with either weak or strong coupling to infinite-dimensional quantum baths. We present an overview of the theories behind the various MEs and provide examples to illustrate typical workflows in HOQST. We present an example that shows that HOQST can provide order of magnitude speedups compared to “Quantum Toolbox in Python" (QuTiP), for problems with time-dependent Hamiltonians. The package is ready to be deployed on high performance computing (HPC) clusters and is aimed at providing reliable open-system analysis tools for noisy intermediate-scale quantum (NISQ) devices.