Testing the 'speed limits' of quantum computing

Quantum science is all about investigating the unusual properties of life at the smallest scale – and so too did PhD candidate Euan Mendoza’s love for quantum grow when breaking the subject down into its smallest parts. 

“The first time I encountered quantum physics was in high school – first in Year 11 chemistry when we studied the atom, and later in Year 12 physics,” he recalls. 

“At the time, I found quantum mechanics to be vague; I didn’t really understand it… For me to really enjoy it, I had to learn the context and types of questions the researchers were asking – breaking the subject into smaller, more approachable questions.” 

Since acquiring this appreciation of quantum science, Euan hasn’t looked back. He is now undertaking a PhD at UTS under the supervisor of Professor Youming Qiao, supported by a Sydney Quantum Academy (SQA) PhD Scholarship.  

Securing our data in the quantum computing era 

Euan’s research is probing our understanding of one of quantum’s most pressing and well-publicised risks – the data security threats posed by the impending proliferation of incredibly powerful quantum computers. These machines are projected to have the potential to bypass even the most sophisticated encryption in mere minutes, compared to the millions of years it would take for today’s supercomputers to complete the same task. 

The race to protect digital data against future quantum computers is no longer hypothetical, with major technology companies and governments globally (including Australia’s own Australian Signals Directorate) setting strategic plans to brace for the post-quantum cryptography era from 2029-2030 onwards.    

A multifaceted approach to post-quantum cryptography  

Euan’s PhD sits at the nexus of computer science, algebra, geometry, physics and cryptography to offer fresh approaches to tackle this decades-long problem. His research explores how complex mathematical structures can be viewed from different mathematical perspectives to help improve our understanding of how computers can distinguish between two objects, such as quantum states – what Euan refers to as “understanding the ‘speed limits’ of computing”.   

“For our secrets to remain safe on the internet, cryptography relies on mathematical problems we think are hard to compute. The problem however is that we don’t actually know if any mathematical problem is guaranteed to be hard to compute. 

“My research is part of a large collaborative effort for mathematicians, computer scientists and cryptographers to classify certain mathematical problems. This is about understanding how feasible it is to compute a problem on both quantum and classical computers.  

“Getting a better understanding of several techniques in both classical and quantum computing to solve certain problems, and how difficult they are to compute will be important to understand what quantum computers are capable of doing.” 

Opening doors to a broader quantum network  

Opting to study in his home city of Sydney was a no-brainer for Euan, who also completed his undergraduate degree at UTS. While staying put physically, the decision has broadened his horizons across many interdisciplinary and international fields – something that complements his cross-functional research to a tee. 

“UTS is quite well known for contributions to theoretical computer science, quantum software and quantum error correction,” he says.  

“A PhD at UTS I think is one of the most cross-disciplinary opportunities for students… This means that the people who I get the privilege to be mentored by and collaborate with have vastly different understanding of each problem and topic that we tackle.” 

Surrounded by an “empathetic and friendly bunch of researchers and students” during his PhD, Euan is also appreciative of the opportunity to liaise with the broader SQA PhD cohort, helping him establish a wide network of fellow quantum researchers across SQA’s four partner universities and beyond. 

“At SQA there are monthly student catch ups which allow you to get a sense of who your cohort is and what kind of opportunities and jobs exist outside of your field,” he says. 

“SQA has given me the ability to connect with people – industry professionals, academics and students – who I wouldn’t have met otherwise.” 

Making a case for quantum research  

Beyond the exposure to researchers across the multifaced quantum field and the benefits of undertaking coursework options across SQA’s partner universities, Euan praises the seminars he’s completed through SQA’s PhD Experience Program for giving him the confidence to share his knowledge with others, particularly those without a quantum background. 

“Quantum computing is a very technical and challenging area with lots of moving parts and different research areas. SQA gives you a lot of context about what the different areas and applications of quantum computing are – and many different perspectives to explain the theory itself. 

“I think being able to explain the research we do is almost as important as the research itself, so SQA has been really helpful in this regard.” 

Starting early to go the distance in your research career 

And though he’s spent years working on intractable problems, Euan recommends starting as early as possible as his strongest recommendation for students contemplating a PhD scholarship – even exploring having a research paper published before beginning, if possible. 

“It’s a good idea to see what topics you are interested in and then seeing if you can spend time with the researchers working on a project,” he says. 

“I was quite lucky to start my undergraduate research quite early, and this made it a lot easier to learn the basics of presenting and writing mathematical proofs and papers before I started my full PhD.” 

Reflecting on his research career to date, Euan is proud of how far he has grown since his undergraduate studies and enjoys paying it forward by sharing his extensive knowledge with other students with their proofs and notations.  

“It was not too long that I was an undergrad research student,” he says. “These days, when I present and correctly articulate an argument, I’m amazed by how much I have developed. What seemed like very hard and foreign maths back then now feels more basic.” 

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