Wolfram Computation Meets Knowledge

Wolfram Summer School


Jacob Marks

Science and Technology

Class of 2017


Jacob Marks received his bachelor of science from Yale University, majoring in intensive physics, math and philosophy. As an undergraduate, Jacob conducted particle physics research at CERN, interned as a software engineer at Reservoir Labs and immersed himself in quantum information research at both the Yale Quantum Institute and the Institute for Quantum Computing in Waterloo, Ontario, Canada. In the fall, he will be beginning his PhD in theoretical physics at Stanford. His current areas of interest include quantum computing, atomic physics, artificial intelligence and operations research. In his free time, Jacob loves to play basketball, rock climb and strum his acoustic guitar.

Computational Essay

Introduction to Quantum Interference »

Project: Quantum Computing Framework

Goal of the project:

Create an efficient framework for simulating quantum circuits in Mathematica.

Summary of work:

This quantum computing package enables the simulation of quantum circuits for qudits (generalized d-level quantum systems). Using sparse arrays and lookup tables, this package efficiently stores quantum states, maintaining a unified structure for pure, mixed and entangled quantum states. The user can create an initial quantum state and generate a quantum circuit—either out of individual gate operations or by concatenating other circuits. The crux of the framework is quantum circuit compilation: the circuit is not evaluated until it acts on an input quantum state, and using pattern matching, I implement a variety of algebraic simplification rules to minimize the number of matrix multiplications.

Once the quantum state has passed through the quantum circuit, you can query to find out if the resulting state is pure, mixed or entangled. Moreover, you can discard ancillary wires and measure observables.

Results and future work:

Obviously, there are a plethora of quantum computing features I would have liked to implement had I had more time. In the future, I hope to add functionality for combining quantum states, as well as incorporating a wider variety of multi-qudit operations. In addition, I would like to include functions for well-known quantum algorithms such as Deutsch’s, Grover’s and Shor’s algorithms so that the user can apply them directly to a quantum state.

Wolfram Summer School | Champaign, IL, USA | July 3 29–July 22, 2022