QuTiP: Quantum Toolbox in Python

This documentation contains a user guide and automatically generated API documentation for QuTiP. For more information see the QuTiP project web page. Here, you can also find a collection of tutorials for QuTiP.

• Frontmatter
  • About This Documentation
  • Citing This Project
  • Funding
  • About QuTiP
  • QuTiP Plugins
  • Libraries Using QuTiP
  • Contributing to QuTiP
• Installation
  • Quick Start
  • General Requirements
  • Installing with conda
    • Adding the conda-forge channel
    • New conda environments
  • Installing from Source
    • PEP 517 Source Builds
    • Direct Setuptools Source Builds
  • Installation on Windows
  • Verifying the Installation
  • Checking Version Information
• Users Guide
  • Guide Overview
    • Organization
  • Basic Operations on Quantum Objects
    • First things first
    • The quantum object class
    • Functions operating on Qobj class
  • Manipulating States and Operators
    • Introduction
    • State Vectors (kets or bras)
    • Density matrices
    • Qubit (two-level) systems
    • Gates
    • Expectation values
    • Superoperators and Vectorized Operators
    • Choi, Kraus, Stinespring and \(\chi\) Representations
    • Properties of Quantum Maps
  • Using Tensor Products and Partial Traces
    • Tensor products
    • Example: Constructing composite Hamiltonians
    • Partial trace
    • Superoperators and Tensor Manipulations
  • Superoperators, Pauli Basis and Channel Contraction
    • Superoperator Representations and Plotting
    • Reduced Channels
  • Time Evolution and Quantum System Dynamics
    • Introduction
    • Dynamics Simulation Results
    • Lindblad Master Equation Solver
    • Monte Carlo Solver
    • Krylov Solver
    • Stochastic Solver
    • Solving Problems with Time-dependent Hamiltonians
    • Solver Class Interface
    • Bloch-Redfield master equation
    • Floquet Formalism
    • Monte Carlo for Non-Markovian Dynamics
    • Setting Options for the Dynamics Solvers
    • Computing propagators
  • Hierarchical Equations of Motion
    • Introduction
    • Bosonic Environments
    • Fermionic Environments
    • Previous implementations
    • References
  • Solving for Steady-State Solutions
    • Introduction
    • Steady State solvers in QuTiP
    • Using the Steadystate Solver
    • Additional Solver Arguments
    • Example: Harmonic Oscillator in Thermal Bath
  • Permutational Invariance
    • Permutational Invariant Quantum Solver (PIQS)
  • Two-time correlation functions
    • Steadystate correlation function
    • Emission spectrum
    • Non-steadystate correlation function
  • Plotting on the Bloch Sphere
    • Introduction
    • The Bloch Class
    • Configuring the Bloch sphere
    • Animating with the Bloch sphere
  • Visualization of quantum states and processes
    • Fock-basis probability distribution
    • Quasi-probability distributions
    • Visualizing operators
    • Quantum process tomography
  • Saving QuTiP Objects and Data Sets
    • Storing and loading QuTiP objects
    • Storing and loading datasets
  • Generating Random Quantum States & Operators
    • Random objects with a given eigen spectrum
    • Composite random objects
    • Controlling the random number generator
    • Internal matrix format
  • Modifying Internal QuTiP Settings
    • User Accessible Parameters
    • Example: Changing Settings
  • Measurement of Quantum Objects
    • Introduction
    • Performing a basic measurement (Observable)
    • Performing a basic measurement (Projective)
    • Obtaining measurement statistics(Observable)
    • Obtaining measurement statistics(Projective)
  • Quantum Optimal Control
    • Introduction
    • Closed Quantum Systems
    • The GRAPE algorithm
    • The CRAB Algorithm
    • Optimal Quantum Control in QuTiP
• Gallery
• API documentation
  • Classes
    • Qobj
    • QobjEvo
    • Bloch sphere
    • Distributions
    • Solvers
    • Monte Carlo Solvers
    • Non-Markovian HEOM Solver
    • Stochastic Solver
    • Integrator
    • Stochastic Integrator
    • Solver Options and Results
    • Permutational Invariance
    • Distribution functions
  • Functions
    • Manipulation and Creation of States and Operators
    • Functions acting on states and operators
    • Measurement
    • Dynamics and Time-Evolution
    • Visualization
    • Non-Markovian Solvers
    • Utility Functions
• Change Log
  • QuTiP 5.0.3 (2024-06-20)
    • Bug Fixes
    • Documentation
    • Miscellaneous
  • QuTiP 5.0.2 (2024-05-16)
    • Bug Fixes
    • Documentation
    • Miscellaneous
  • QuTiP 5.0.1 (2024-04-03)
  • QuTiP 5.0.0 (2024-03-26)
    • Contributors
    • Qobj changes
    • QobjEvo changes
    • Solver changes
    • QuTiP core
    • QuTiP settings
    • Visualization
    • Package reorganization
    • Miscellaneous
    • Feature removals
    • Changes from QuTiP 5.0.0b1:
    • Features
    • Miscellaneous
  • QuTiP 5.0.0b1 (2024-03-04)
    • Features
    • Bug Fixes
    • Miscellaneous
  • QuTiP 5.0.0a2 (2023-09-06)
    • Features
    • Bug Fixes
    • Removals
    • Documentation
    • Miscellaneous
    • Contributors
    • Qobj changes
    • QobjEvo changes
    • Solver changes
    • QuTiP core
    • QuTiP settings
    • Package reorganization
    • Miscellaneous
    • Feature removals
  • QuTiP 4.7.5 (2024-01-29)
    • Bug Fixes
  • QuTiP 4.7.4 (2024-01-15)
    • Bug Fixes
    • Miscellaneous
  • QuTiP 4.7.3 (2023-08-22)
    • Bug Fixes
    • Miscellaneous
  • QuTiP 4.7.2 (2023-06-28)
    • Bug Fixes
    • Miscellaneous
    • Features
    • Bug Fixes
    • Documentation
    • Miscellaneous
    • Improvements
    • Bug Fixes
    • Documentation Improvements
    • Developer Changes
    • Improvements
    • Bug Fixes
    • Documentation Improvements
    • Developer Changes
    • Improvements
    • Bug Fixes
    • Developer Changes
    • Improvements
    • Bug Fixes
    • Developer Changes
    • Improvements
    • Bug Fixes
    • Deprecations
    • Developer Changes
    • Improvements
    • Improvements
    • Bug Fixes
    • Developer Changes
    • Improvements
    • Bug Fixes
    • Deprecations
    • Developer Changes
    • Improvements
    • Bug Fixes
    • Improvements
    • Bug Fixes
    • Improvements
    • Bug Fixes
    • Improvements
    • Bug Fixes
    • Improvements
    • Bug Fixes
    • Improvements
    • Bug Fixes
    • Bug Fixes
    • Improvements
    • Bug Fixes
    • New Features
    • Improvements
    • Bug Fixes
    • New Features
    • Bug Fixes
    • Bug Fixes
    • New Features
    • Improvements
    • New Features
    • Bug Fixes
    • New Features
    • Bug Fixes
    • New Features
    • Bug Fixes
    • New Functions
    • Bug Fixes
    • Bug Fixes
    • New Functions
    • Bug Fixes
    • New Functions
    • Bug Fixes
• Developers
  • Lead Developers
  • Past Lead Developers
  • Contributors
• Development Documentation
  • Contributing to QuTiP Development
    • Quick Start
    • Core Library: qutip/qutip
    • Documentation: qutip/qutip (doc directory)
  • QuTiP Development Roadmap
    • Preamble
    • Library package structure
    • Development Projects
    • Completed Development Projects
    • QuTiP major release roadmap
  • Ideas for future QuTiP development
    • QuTiP Interactive
    • Pulse level description of quantum circuits
    • Quantum Error Mitigation
    • GPU implementation of the Hierarchical Equations of Motion
    • Google Summer of Code
    • Completed Projects
  • Working with the QuTiP Documentation
    • Directives
  • Release and Distribution
    • Preamble
    • Setting Up The Release Branch
    • Build Release Distribution and Deploy
    • Making a Release on GitHub
    • Website
    • Conda Forge
• Bibliography
• Copyright and Licensing
  • License Terms for Documentation Text
  • License Terms for Source Code of QuTiP and Code Samples

Indices and tables

• Index

• Module Index

• Search Page