Ph.D. Dissertation Defense
Computer Science and Electrical Engineering

Solving Mathematical Problems in Quantum Regime

Omar Shehab

2:00pm Thursday, 7 July 2016, ITE 325b

In this dissertation, I investigate a number of algorithmic approaches in quantum computational regime to solve mathematical problems. My problems of interest are the graph isomorphism and graph automorphism problems, and the complexity of memory recall of Hopfield network. I show that the hidden subgroup algorithm, quantum Fourier sampling, always fails, to construct the automorphism group for the class of the cycle graphs. I have discussed what we may infer for a few non-trivial classes of graphs from this result. This raises the question, which I have discussed in this dissertation, whether the hidden subgroup algorithm is the best approach for these kinds of problems. I have given a correctness proof of the Hen-Young quantum adiabatic algorithm for graph isomorphism for cycle graphs. To the best of my knowledge, this result is the first of its kind. I also report a proof-of-concept implementation of a quantum annealing algorithm for the graph isomorphism problem on a commercial quantum annealing device. This is also, to the best of my knowledge, the first of its kind. I have also discussed the worst-case for the algorithm. Finally, I have shown that quantum annealing helps us achieve exponential capacity for Hopfield networks.

Committee: Drs. Samuel J Lomonaco Jr. (Chair), Milton Halem, Yanhua Shih, William Gasarch and John Dorband

A short book reflection by Shira Devorah 

Just a few moments ago I finished Janet Mock’s memoir, Redefining Realness, My Path to Womanhood, Identity, Love & So Much More. I’m still stunned. I’m not much of a memoir reader, but I’m pretty sure this book has changed that.

here’s a link to buy the book on Amazon!

Thanks to a generous donation from UMBC’s LGBTQ Faculty & Staff Association, I was able to snatch up this book from the Women’s Center’s very own lending library! Over the past couple of days, I have been relishing every moment of Janet Mock and her story. Mock, a trans woman of color, takes her readers through her life from early childhood until now. In a whirlwind of wit and poignancy, she shares herself with us.

I am not ashamed to admit that I cried a whole bunch throughout this book. Mock fought tooth and nail to become the woman she is today, and though she has been through a lot of pain and oppression, she never falters in her stance as an activist. Every personal recollection comes with a lesson Mock has for her readers. She challenges us to be better people, to see others more complexly, to  be critical of systems of inequality and injustice that exist all around us. Mock allows her readers to peak into incredibly sensitive parts of her, and trusts us to learn from the barriers she faced in her girlhood and adolescence.

I think this memoir is a wonderful introduction to intersectional identities and social justice. Any person who picks up this book will be gently introduced to many concepts that they might not have been privy to beforehand.  While I feel like I know a bit about many issues touched upon in this book, I have been changed  by her discussions. Mock pushes readers to confront poverty, trans issues, multiculturalism, drug use, sexual abuse and sex work. White, middle-class people like me  are made to confront our privilege and come out of this book with a better understanding of other’s lives. I am so lucky to get a chance to grow with Janet through the pages of her self discovery.

I highly suggest this book to anyone and everyone. As a trigger warning, Mock discusses her personal experiences of sexual abuse and sex work, so please practice self care if you plan to borrow this book from the Women’s Center after I return it.

If you’ve already read Redefining Realness and need more Janet Mock in your life, check out her awesome blog!

If you want more  info about the book itself, here’s a quick interview she did with Slate back in 2014.

I first learned about Janet Mock through Her Story, an awesome web-series  written by and starring trans women, so you should totally check that out.  Here’s an Interview with Janet and Jen Richards, co-creator of HerStory.

So go out there and read, friends! I’ll be updating periodically on the rest of my summer reading books from my summer reading challenge. Happy Reading!