Wolfram Computation Meets Knowledge

Your Invitation to Take a Quantum Leap in Education

Your Invitation to Take a Quantum Leap in Education

Learning quantum theory requires dedication and a willingness to challenge classical assumptions. Quantum interference, particularly for massive particles, is a pivotal example in this journey. The Schrödinger equation, inspired by de Broglie’s hypothesis, revolutionized our understanding by revealing the wavelike nature of even massive particles. This phenomenon not only deepens our grasp of nature but also fuels innovations in quantum applications, from quantum sensing to quantum computing. Yet many students don’t have the opportunity to run experiments that require sophisticated hardware. Not anymore!

The Superposition of Wolfram and Infleqtion

We’re proud to announce a strategic partnership in quantum education today by joining forces with Infleqtion, a global leader in quantum information—heralding a new era in quantum education and research that can address both theoretical and experimental aspects. Together, we’re committed to the design and development of educational materials, combining our computational prowess with Infleqtion’s quantum matter service Oqtant.

This collaboration aims to bring classrooms closer to “quantum everywhere,” making advanced learning tools for quantum systems more accessible. We believe that with this collaboration, a unique educational experience is now possible. There is but one more ingredient that is crucial to providing quantum education: academic partners.

A Call to Academia

We are calling upon academic institutions and educators to join this exciting initiative. Joint partnership offers access to Infleqtion’s Oqtant platform and Wolfram Language, providing an unprecedented opportunity to explore quantum mechanics through hands-on experience and interactive learning. Academic partners will receive Wolfram Language licenses and limited sponsored access to Oqtant to foster research and development in quantum education.

Interacting with phenomena is a key component of science education. We envision educational materials where students use Infleqtion’s Oqtant quantum matter service to run experiments with real quantum hardware and analyze the results and theoretical models in an interactive Wolfram Notebook.

We invite academic institutions, researchers and educators passionate about quantum education to partner with us in this venture. Together, we can shape the future of quantum education, making it more interactive and accessible for students around the world.

For academic inquiries and more information on how to get involved, email quantum@wolfram.com.

Letting the Cat out of the Bag

Exploring Experiments with Modern Tools

Let’s try to get a taste of how modeling tools provided in Wolfram Language can help with understanding and modeling the types of experiments students can run using the Oqtant API from Infleqtion. Many students will be familiar with the Schrödinger equation from introductory courses on quantum mechanics. Bose–Einstein condensates (BECs), the system accessible through the Oqtant API from Infleqtion, can be modeled by a nonlinear version of the Schrödinger equation. The source of nonlinearities in the Gross–Pitaevskii equation arises from the interaction term representing the mean-field effects of BECs, and they are not a fundamental correction to the Schrödinger equation.

Unlike the linear version of the Schrödinger equation, numerical techniques are immediately needed to solve the resulting equations. By studying systems like those accessible through Oqtant, students gain practical skills working with real experimental systems, theoretical modeling and numerical simulations.

Utilizing BECs in quantum education is invaluable for several reasons. Firstly, BECs provide a tangible platform for exploring fundamental quantum principles, allowing students to observe and manipulate quantum phenomena firsthand. This hands-on experience fosters a deeper understanding of concepts such as superfluidity, coherence and quantum entanglement, which can be challenging to grasp solely through theoretical study. Additionally, BEC experiments often involve interdisciplinary techniques, exposing students to a range of scientific methodologies and encouraging collaboration across scientific disciplines. Furthermore, by engaging with BECs, students gain practical skills in experimental design, data analysis and problem solving, preparing them for future careers in quantum research and technology development.

Let us start with a simple case of a nonlinear, time-dependent Schrödinger partial differential equation (PDE) operator in 1D:

H1D = SchrodingerPDEComponent

Define the boundary and initial conditions:

bc = {

Compute the solution of the Schrödinger time-dependent equation:

sol1D = NDSolveValue

Plot the absolute value of the solution:


Including a harmonic potential term makes this 1D example qualitatively similar to a 3D BEC. Strictly speaking, BECs cannot exist in one-dimensional systems; nonetheless, the 1D equation can serve as a valuable pedagogical model:

H1D = SchrodingerPDEComponent

Find the solution:

sol1D = NDSolveValue

Plot the absolute value of the solution:


When comparing to the previous case without a harmonic trap, it’s evident that the trap effectively confines particles around its well, demonstrating its clear influence on the system.

Let’s examine a more realistic scenario, where the system exhibits axisymmetric region symmetry, represented by a truncated cylindrical coordinate system that eliminates the angular variable while retaining radial and axial coordinates:

H = SchrodingerPDEComponent

Set the boundary condition and the initial state:

bc = DirichletCondition

Compute the solution:

sol = NDSolveValue

You can see how an initially localized wavefunction spreads out over time when not confined by a trapping potential:

evol = Table[


Let’s change the initial state to a superposition of two Gaussians in order to observe interference patterns that emerge from the overlap of two wave packets:

ic =

Find the solution, given the previous initial condition:

sol2 = NDSolveValue

Even though hardware for creating a BEC is a real 3D system, visualizing the process along just the “main” axis helps make the connection with 1D problems clear for students. As time passes, you can observe interference patterns that emerge:

ListAnimate [

Since the modeling of the system is done in 3D, you can also look at 2D slices through the “middle” of the system:

evol2 = Table


Alternatively, you can show the full 3D picture:


It’s important to note that a full 3D image is quite difficult to achieve in an experimental setting with systems like these. Typically, one would have sensors that look at the 3D phenomena from a particular direction and can give an “integrated picture” of the density.

To Infinity and Beyond!

Of course, this is only the beginning of the interesting modeling one can do. By combining data from numerical simulations and the Oqtant service, educators can give students hands-on experience with skills that will prepare them for the quantum-literate workforce of the future. Not only will students gain strong computational skills using Mathematica, they will also learn details of quantum experiments and using the theory to handle real experimental data.

For more information on how to partner with us and take part in this quantum leap in education, please contact us at quantum@wolfram.com.


Join the discussion

!Please enter your comment (at least 5 characters).

!Please enter your name.

!Please enter a valid email address.