**CQE PI Feature – Aram Harrow**

#### Finding unexpected connections between physics and computer science

*Featured in QSEC newsletter in May 2023*

My favorite part of quantum computing is the way it builds connections between fields that, on their face, are distinct. The most famous of these connections is the entire premise of the field: that quantum mechanics radically changes the meaning of computation and information. But many other deep and non-obvious connections exist, such as between quantum error correction and topological order, or the uncertainty principle and cryptography.

In my work, I’ve been happiest building new connections like this. For example, in a recent paper with John Napp, Rolando LaPlaca, Alex Dalzell and Fernando Brandao, we studied a problem that appeared purely computational, namely the complexity of simulating short random quantum circuits in 2D geometries. We chose these because they corresponded to the sorts of quantum computers being currently planned (especially with superconducting qubits) and because they represented the threshold between the known easy and hard cases. It turns out that the computational transition here between easy and hard maps directly onto a physical phase transition between the ordered and disordered phases of the Ising model – a simple classical model of magnetism.

Another example of this sort of connection is in a paper I wrote with Anurag Anshu and Mehdi Soleimanifar where we used communication complexity and quantum algorithms to help understand the scaling of entanglement in many-body quantum systems. This paper connects to a larger theme in my work, which I’ve called “entanglement spread”. Quantum entanglement was originally seen as something ephemeral and experimentally elusive, and early work such as the famous EPR paper viewed it as potentially dispensable. Quantum information theorists from the late 1990s began the study of entanglement through the lens of information theory, as a resource that could be quantified using entropy. The idea of entanglement spread is that in limited-communication settings, entanglement can be viewed as an approximately conserved quantity. This is because the only way to coherently create or destroy entanglement is by using communication. States with entanglement spread have superpositions of varying amounts of entanglement, and share some of the same exotic properties as states with superposition of other conserved properties, such as charges. In this way, physics concepts such as conserved charges can be used to understand information-processing protocols. This proved useful in settings where quantum communication protocols need to consume different amounts of entanglement in different branches of a superposition. An example of this is the task of simulating a noisy quantum channel using an optimal amount of communication, known as the Quantum Reverse Shannon Theorem.

These cases illustrate a few general themes of my work. Quantum information is still a young field, and so the metaphors by which we understand it are still somewhat up for grabs. And a good way to develop these metaphors is often to make a connection to an adjacent field, e.g. entanglement is conserved like electric charge, or algorithmic tools like rejection sampling can be related to physical objects like an optical filter.

I was lucky to start working in quantum information in the summer of 2000, which was relatively early for the field. I first heard about the topic from a Physics colloquium given by John Preskill on quantum error correction. At the time I knew I liked math, physics and CS, and didn’t look forward to the inevitable narrowing of focus that would happen in grad school and beyond. Quantum computing was, then and now, a way of drawing on all of these different areas, and of grappling with topics where the “correct” perspective still hasn’t become clear. I began my quantum computing research in Neil Gershenfeld’s lab, working on experimental NMR quantum computing. I’m still grateful for everything I learned there and the friends and collaborators I met. There I met Ike Chuang, who became my PhD advisor. Ike also connected me to the team at IBM Yorktown Heights led by Charlie Bennett, who became an unofficial second advisor. Grad school for me was a happy time of collaboration alternating with thinking hard about obscure topics, such as entanglement spread or the role of representation theory in quantum information. The small size of the field then made it relatively easy to meet many of the leading theorists, and my collaboration with Andreas Winter was part of what led me to my first job at the University of Bristol, where he worked. Bristol was also a way for me to expand upon my CS interests; although my degrees were in math and physics, I had come to appreciate theoretical computer science, and at Bristol was able to teach in the CS and math departments. I came back to the US 5 years later to join the University of Washington (UW), and about 2 years later joined the MIT faculty where I’ve been ever since. Each of these moves pulled me in different but useful directions. Bristol was a place for me to explore CS and math in more depth, as well as to connect to the QI research in Europe, which had different emphases, such as mathematical physics. At the UW, I began exploring the more applied side of quantum algorithms which today would be called NISQ. And since coming to MIT and teaching in a physics department, my research has connected more concepts from physics to computational applications.

The career paths available to students today look very different than mine. The much larger field means that travel is less critical, and at the same time, it is much harder to get to know a large fraction of the community. The research questions have become more concrete and practical, while at the same time, many of the big questions such as the power of quantum algorithms, are far from resolved. My path has reflected some of my own priorities, like taking my first job out of the US so that I’d be sure to experience living abroad as an adult, or moving to Seattle for a relationship. The only part of my biography which I can confidently advise new students to follow is to have fun and to be open to surprises. Each change of path is a chance to gain new skills and experiences, and to come up with the ingredients for solving old problems by making new connections.