# A Summer Project at Oak Ridge National Lab This is a story of the summer research completed by Graduate Student, Ben Clark at the Oak Ridge National Lab.

This summer, I had the opportunity to intern with Oak Ridge National Lab working on quantum communications using photonics. I was a part of the quantum communications group under the quantum science center. My project involved finding a quantum state’s density matrix, the mathematical object that can completely describe a quantum state. This process is known as Quantum State Tomography (QST). Performing QST rigorously can be quite a challenge since quantum states can only be measured once, and the quantum states we were measuring were large, meaning there were many possible states, requiring many measurements. By taking multiple measurements of the state, we could see how likely a state was to collapse into a certain value. Quantum states are made up of multiple classical states, which we call a superposition. Once the state is measured, it collapses into one of these classical states. However, the probability of a quantum state collapsing into a classical state is dependent on how much of the classical state is in this quantum state. Therefore, by measuring these quantum states and recording how frequently we get some classical state, we can reconstruct the quantum state and its density matrix. My contribution to our group this summer was making a massively parallelizable algorithm that can look at these measurements and, given some prior information about the system, infer the quantum state’s density matrix as fast and accurately possible. Many other people that research this problem have figured out algorithms to solve this problem quickly, but in general, they do not quantify error in measurement well. To remedy this, my mentor for the summer, Dr. Joseph Lukens, had the idea to run a Bayesian inference algorithm to quantify the density matrix.

Bayesian inference algorithms serve the same function as any other inference algorithm, they look at the answer to a question and try to figure out what question was asked. Usually, in a basic quantum mechanics class, we are asked how likely a quantum state is to be some classical state upon measurement. We are given the state and want to find the probability. In QST, it is the opposite, we are given a probability and want to find the quantum state. The reason we used a Bayesian inference algorithm specifically is because Bayesian methods give a distribution of answers, quantifying the error that is inherent in finite measurements of quantum systems. In order to implement Bayesian inference for QST, we used the algorithm sequential Monte Carlo sampling (SMC). SMC is appealing because very little must be known about the system to successfully run this algorithm, and it can be easily run in parallel. Parallelization was a huge part of this project because quantifying the density matrix of a complicated quantum system can sometimes take weeks of computing time, but if we could parallelize this algorithm, we could reduce the computing time required, allowing us to quantify larger density matrices with unforeseen rigor. At the end of my internship, we were able to show a decrease in run time with added cores and credible error bars, proving our idea worked. We will publish our results using this algorithm soon, and we plan to test our code using some of the world’s fastest supercomputers at Oak Ridge National Lab.