Brandin Farris

Brandin Farris

PhD student studying TDA and data science under Chad Giusti at Oregon State University.

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publications

Paper Title Number 4

Published in GitHub Journal of Bugs, 2024

This paper is about fixing template issue #693.

Recommended citation: Your Name, You. (2024). "Paper Title Number 3." GitHub Journal of Bugs. 1(3).
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talks

Characterizing Root Nodule-Host Interactions using Image Analysis

Published:

When performing analysis on images of the root systems of hundreds of plants, it is useful to have a high throughput method for gathering directly observed and inferred data from the roots. In this talk we introduce our methods for converting the collection of images into data for analysis. Nodule Analysis is a set of two Fiji (ImageJ2) plugins (Nodule Segmentation and Nodule Distances) that provides a method for computing counts, areas, and pair-wise distances along the root system of all of the nodules on an image of a root system using various data gathering methods. The plugin utilizes part of Weka’s FIJI plugin, particularly their unsupervised color clustering method to segment the nodules and the root system separately.

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Simulating Quantum Circuits with Non-Clifford Noise using Stabilizer Formalism

Published:

Quantum computing is an active area of research which has the potential to revolutionize fields such as cryptography, optimization, and simulation of quantum systems. In order to verify the correctness and performance of new quantum algorithms, researchers have turned to the classical simulation of quantum systems. However quantum systems are highly susceptible to noise and decoherence, both of which are expensive processes to classically simulate . So in an effort to develop computationally efficient methods to simulate quantum noise we explore three methods that leverage the Gottesman-Knill theorem, which provides efficient simulation of circuits containing only Clifford gates. First, we explore methods to decompose a noise operator into a sum of Clifford gates via mixed integer linear programming, using these decompositions to classically simulate noisy quantum circuits within the stabilizer formalism first proposed by Aaronson and Gottesman (2004). We find that the a Clifford decomposition is not guaranteed to have low rank decompositions and that at best the runtime of simulating noise using Clifford decompositions would be $O(2^k)$, where $k$ is the number of Kraus operators applied. Second, we explore the process of dilating our noise operators into a higher dimensional Hilbert space. Specifically we formailze two unitary dilation based algorithms for simulating noise; Sz.-Nagy and Stinespring’s dilation algorithms. The two algorithms yield respective run-times of $O\left(\dfrac{1}{\delta \Delta^2} s n^3 \eta^{-2} 1.17^t\right)$ and $O\left(n^2 \prod_{i=1}^k \lvert\xi_i\rvert + n^3 \sum_{i=1}^k \lvert\xi_i\rvert^3\right)$. Third we propose a theoretical “K-gadget” framework for generalizing the T-Gadget approach developed by Bravyi and Gosset (2016). Through numerical simulation, we show that the K-gadget approach provides an exponential speed up over traditional approaches when simulating certain quantum circuits. In particular, we show empirically that one can simulate over ten thousand non-Clifford amplitude dampening channels using the K-gadget method on a 29TB system. This generalized approach can be used to simulate noisy circuits with significantly more efficient runtime and space complexity then previously proposed methods.

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Persistent Simplicial Homology and its Computation

Published:

We will start with an introduction to simplicial homology and some examples where it is used in data analysis, followed by persistent homology and some more examples. Then I will talk about computing these objects over \Z_2 using a standard algorithm and explain some optimizations for said algorithm. 

The Structure Abused in Computing Persistent Homology

Published:

The notion of Persistent Homology originates from Zoromodian’s PhD thesis in 2001. Shortly after, in 2004, Carlson and Zoromodian further formalized the idea and provided an algorithm for its computation. This talk will describe that algorithm and one of its quirks, comparing it to the modern algorithms used. Time permitting, we will talk about why it’s restricted to field coefficients and a recent paper that generalizes further.

A Topological Approach to Conditional Causality

Published:

Causality is notoriously difficult to study because determining the true orientation of correlation is difficult to gaurantee. In this talk we will introduce Fujitsu Causal Discovery, an algorithm designed by Fujitsu to conver large quantities of data into a large quantity of conditional causal graphs, or causal graphs that occur given some conditions on the data set. We will then introduce three methods we develoepd to analyze these conditional causal graphs, with the goal being to understand how different conditions can alter causality.

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teaching