Xiao, Mingyao: Inverting the Diffusion Equation with Quantum Annealing

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Title: Inverting the Diffusion Equation with Quantum Annealing

Name: Mingyao Xiao

Major: Mathematics/Computer Science/Statistics

School affiliation: School of Arts and Sciences

Programs: Aresty – RA Program

Other contributors: Ruoqian Wang

Abstract: All physical problems can be generally split into two broad kinds of problems. The first is to predict the future, in that given the initial conditions, how will the situation evolve? The second, which concerns this project, deals with the inversion: Given the effect, what was the cause? This project tries to delve into a new computing technology that can help solve the entire range of the inversion problem, by specifically tackling an important concrete case of this, as explained in the title. Inversion problems are often so complex that it is impossible to solve, other than brute forcing a wide range of possible initial conditions, simulating them to their conclusion, and comparing the simulated result to our observed result. However, because the simulations must be run sequentially, often it is still prohibitively time costly. Quantum computing, specifically via D-Wave’s Quantum Annealing system, allows us to simulate all initial conditions in parallel. This project aims to thus reframe a classical approach to the problem into a structure digestible by a quantum annealing system, through a literature review on such a quantum system and on the mathematical and physical details of heat diffusion. Such work will pave the way to reframing other important inversion problems into the domain of quantum computing, and allow the better understanding of physical systems.