Lorenza Viola is a Professor of Physics and the Director of the Quantum Information Science Initiative at Dartmouth. She is a theoretical physicist specialising in quantum information processing and quantum statistical mechanics, and a 2014 Fellow of the American Physical Society. Her work, as she describes below, falls broadly into two areas: quantum control and engineering; quantum correlations and many-body physics.

We are delighted that Lorenza joined the editorial board of Journal of Physics A: Mathematical and Theoretical earlier this year.

**Your work broadly covers quantum information theory. What led you to this area of research?**

Long story, also because the field of *“quantum information science”* as we know it today is not something that existed when I took my first professional steps back in Italy… In a way, my career path has been far from mainstream (whatever that means!).

I started research as a physics undergraduate in Trento (Italy), applying methods from Lie algebras and dynamical symmetries to roto-vibrational spectroscopy of complex molecules. As a PhD student in Padua (Italy), I then worked in mathematical physics, on topics that would nowadays fall under “quantum foundations” – namely, by seeking a rigorous formulation of Nelson’s stochastic quantization in relativistic settings. While this was my ‘official*’* work, I also became more and more fascinated by (at the time) emerging ideas related to quantum measurement and decoherence, the transition from quantum-to-classical, and open quantum systems in general. So I also ‘unofficially*’* started doing some research in those directions.

After completing my PhD in theoretical physics in 1996, I spent a semester as a visiting scholar at MIT (USA), while waiting to hear back from a Marie-Curie postdoctoral fellowship application in mathematical physics (at the ‘BiBoS’ Research Center in Bielefeld, Germany). I soon found myself at a career crossroad, when in 1997 I was both awarded the Marie Curie fellowship and offered the possibility to join MIT as a postdoc in the Mechanical Engineering Department to work on control open quantum systems…

I ended up declining the (three-year long and better paid!) Marie Curie award in favour of the (one-year) MIT postdoc. I view that as my ‘turning point*’* for entering the field of quantum information… to be sure, in 1997 (just two years after Peter Shor’s landmark discovery) it was still a very small field, with very few people actively and openly pursuing it (especially in Physics Departments!). Small, yet loaded with fresh energy and enthusiasm, and cross-disciplinary to a level I had never experienced before. I did not look back. The rest… has been another chapter in my adventure, taking me from the Mechanical Engineering Department at MIT to the Computer & Computational Sciences Division in Los Alamos (where I was a J.R. Oppenheimer fellow from 2000-2004), then finally back east to a physics department – here at Dartmouth where I have been since.

**What kind of problems appeal to you?**

Looking back at the problems I have worked on throughout the years, they do touch upon a variety of questions and technical approaches, thus my interests are probably broader than I can succinctly attempt to categorize.

That said, I especially enjoy problems which are directly motivated by (quantum) physics, and where mathematical and physical tools can be seamlessly integrated together to produce (at least on paper!) rigorous answers – ideally, also offering a ‘simple*’* higher-level understanding, and a unified perspective not manifest otherwise. After many years of investigations, I remain deeply fascinated by the formal apparatus of quantum mechanics, especially in relationship to *‘*complexity*’* aspects that emerge in the presence of many degree of freedom, competing interactions and correlations, randomness and irreversibility.

**What are you currently working on?**

My current research falls roughly into two broad areas: quantum control and engineering; quantum correlations and many-body physics. In quantum control, I do both fairly rigorous, ‘system-theoretic’ work, as well as more phenomenological work of direct relevance to existing qubit devices, in collaboration with experimental colleagues. A common theme is *control of open quantum system dynamics*, where non-unitary decoherence and dissipation effects may either be seen as an issue to overcome, or a resource to harness – basically depending on the type and level of control involved. For instance, two concrete problems I am working on right now are:

- The characterization of open-system dynamics which has a desired quantum state (in particular, a multi-partite entangled state) as its
*unique equilibrium state*, subject to physical locality constraints; - The construction of quantum-control protocols that may be used for
*noise spectroscopy*, that is, to gather detailed spectral information about the noise processes responsible for qubit decoherence dynamics.

In many-body physics, I have a long-standing interest in obtaining a deeper physical understanding of multi-partite entanglement, especially for degrees of freedom obeying non-trivial quantum statistics (e.g. indistinguishable fermions, or anyons!) This also ties in with recent work I have done on ‘*quantum extension problems*’, where we ask whether (and when) given reduced quantum states or channels may consistently arise from a same, valid global one. Another current direction I am very interested in is *topological quantum matter* – in particular, topological superconductors and Majorana fermions, for both fundamental physics and (perhaps) quantum-information applications. For instance, I am quite excited by the on-going work we are doing on exact solutions of a paradigmatic class of non-interacting topological models, whereby I hope to gain a deeper understanding of fundamental issues – such as ‘*bulk-boundary correspondence’*.

**What would you say has been your career highlight to date/ biggest achievement to date?**

I am not particularly good (nor comfortable!) in talking about my own achievements and in any case I feel that this would be best done by other people in my field over time. In terms of personal satisfaction, something I can say is that I would have never expected that methods for dynamical decoherence suppression in open quantum systems (such as *‘dynamical decoupling’*), that I started working on at MIT in 1997, would become so important both theoretically and experimentally within the quantum information community – basically representing a *‘method-of-choice’* for physical-layer decoherence control in many settings. Likewise, I feel fortunate in having had the opportunity to push some pretty mathematical ideas and constructions all the way to experimental validation – most notably in the case of a “noiseless subsystem code” for protecting quantum information.

**What are the challenges facing researchers in mathematics and theoretical physics?**

I feel that challenges have always existed to some extent, and they have varied (and still do vary) a lot depending on several different factors including historical, social, and cultural ones. That being acknowledged, perhaps one of the distinctive challenges that many researchers working in mathematics and theoretical physics often face today is to strike a healthy balance between the competing demands of application-driven, ‘*programmatic’* research, versus higher-risk, curiosity-driven investigation. The latter being something that I believe is at the very core of both disciplines and should as such be treasured.

**Where do you think your research will take you next? Are there any other fields you are interested in exploring?**

Hard to say where exactly I will be led next in my research. Leaving the immediate future aside, and extrapolating from my experience thus far, many of the questions I ended up working on and enjoying the most seem to have come up in quite an unpredictable (and often interesting) way. Perhaps I will come full circle, getting back to relativistic physics and exploring some aspects of relativistic quantum information. Or maybe I will dig deeper into mathematical and foundational aspects of quantum theory. Whatever research problems I will end up tackling, almost certainly it will indeed be something having to do with quantum mechanics! Beyond that, however, I would welcome and like to leave plenty of room for improvisation…

I would like to say a huge thank you to Lorenza for taking the time to answer the questions and for providing such as wonderful, honest insight into her career so far. Welcome to JPhysA!

This work is licensed under a Creative Commons Attribution 3.0 Unported License. Image courtesy of Lorenza Viola.

Categories: Journal of Physics A: Mathematical and Theoretical