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Quantum Group

We are a group focused on quantum computation and the foundations of quantum theory. The group is led by Professor Jonathan Barrett and Professor Aleks Kissinger. Other faculty in the group are Professor Matty Hoban and Dr Stefano Gogioso.

Some of the research areas we are most intersted in are:

  • Quantum software, compilers, and optimisation
  • Causality in quantum theory and indefinite causal structures
  • Diagrammatic reasoning and the ZX-calculus
  • Generalised/operational probabilistic theories
  • Quantum correlations and self-testing

Also affiliated with the group are it's original founders Professor Bob Coecke (chief scientist at Quantinuum) and Professor Samson Abramsky (professor at UCL), and visiting professor Giulio Chiribella (professor at HKU).

Click here to see a list of past DPhil/PhD and masters theses from the group.

Click here to access the extensive Oxford Quantum Talk Archive, our video archive of research talks.

Quantum software, compilers, and the ZX-calculus

Quantum computers can, in principle, solve computational problems that are far out of reach even for todays most powerful supercomputers. Quantum software refers to the code that runs on those computers. Of central importance in this area is the development of new quantum algorithms to take advantage of these drastically different computational platforms. However, like in classical software development, the field of quantum software is much broader than just the design of new algorithms.

A central research theme in our group is quantum compilation. This is a relatively new field that studies a whole host of theoretical and practical problems involved in translating the high-level description of a quantum algorithm into something that is runnable a quantum hardware.

Examples of such problems are the design of new quantum programming languages, which allow developers to write quantum algorithms in ways that abstract away from distracting details and think about computations in ways that are more fundamentally quantum.

Another example is quantum circuit synthesis and optimisation. Quantum circuits form a de facto "assembly language" for quantum computers, describing computations as sequences of basic physical operations, called gates, which can be implemented on hardware. Gates take time and introduce noise into a computation, hence reducing the number or depth of gates in a circuit can drastically increase the capabilities of todays (very limited) quantum computers.

In addition to abstract optimisation of quantum circuits, there is much to be gained from hardware-aware compilation techniques, which take the specific capabilities and constraints of a hardware platform into account. Ion trap quantum computers have very different characteristics from superconducting ones, and quantum computations based on optics are best described in ways that are totally different from circuits. Hence, one can design compilers that do things like circuit routing to account for connectivity constraints in quantum memories, take advantage of native and global gates available on certain hardware platforms, and translate to/from measurement-based quantum computations (MBQC) which are more well-suited to optical hardware.

Much of this work uses the ZX-calculus, a graph-based "swiss army knife" for reasoning about quantum computations. This theoretical tool was originally developed at Oxford, and now forms the basis of quantum compilation software like PyZX and is being increasingly used in quantum software research teams in industry.

If you are new to this stuff, here's a couple of good places to start:

Here are some recent papers:

We also maintain some open source software projects.

  • PyZX: A Python library for quantum circuit rewriting and optimisation using the ZX-calculus
  • QuiZX: A Rust port of PyZX, for large-scale ZX rewriting and classical simulation of quantum circuits

Quantum foundations and quantum causal structure

Causality is a fundamental concept, both in fundamental physics and our everyday lives. In relativity theory, the causality principle states that information propagates through spacetime at a finite rate (namely, the speed of light). This limitation is what enables us to unambiguously say when events have happened "before" or "after" others and avoid logical paradoxes, even in a universe where time is a relative concept.

On the other hand, in statistical modelling, causality means something quite different. While relativistic causality puts constraints on which events can in principle affect one another, causality in statistics measures how much a single event A does influence another event B. Our work studies the point where these two notions of causality meet, and particularly what happens when quantum processes enter the mix.

While classical functional or statistical causal models are by now well-established, they run in to limitations when trying to make sense situations involving quantum nonlocality. Classical causal models couched in the traditional formulation of Reichenbach's common cause principle don't seem to work any more, as quantum theory predicts correlations between distant events that are simply too strong to be explained by any local, classical common cause. Should we abandon this principle, or should we update it to account for the quantum world? In either case, what should the resulting quantum causal models look like?

In an even more drastic departure from classical notions of causality, recent theoretical work and experiments have suggested the possibility of indefinite causal structures. These are scenarios involving multiple events or agents which cannot be explained by assuming any fixed causal order. Such scenarios can be realised modestly by particles traversing an apparatus in superpositions of paths and might even be possible to realise making use of superpositions of spacetimes as predicted by a quantum theory of gravity.

In the quantum group, our focus is on developing quantum causal models and studying their properties. Along the way, we have developed mathematical and logical tools for studying definite and indefinite causal structures, and reasoning about causal relationships, consistency, and paradox in these frameworks.

We are part of an international consortium on the Quantum Information Structure of Spacetime, which unites experts in quantum information, quantum foundations, and quantum gravity to answer fundamental questions about space, time, and causal structure in the quantum regime.

Here is a selection of some recent papers from the group:

Quantum complexity, self-testing, and non-classicality

Self-testing: this is when we have black-box access to a (potentially quantum) device and by interacting with it, try and determine its quantum characteristics, if that's possible. In a recent paper we showed that we can determine (up to some symmetries) the quantum state of an arbitrary number of systems. 

Resource theories for non-classicality: non-classical phenomena can be seen as a resource in many information processing tasks, so we would like tools to be able to quantify and characterise this resource. In a couple of recent papers we should how to do this for a particular kind of non-classical resource in scenarios related to "Einstein-Podolsky-Rosen steering". 

Computational hardness of estimating entropy and entanglement: not only do we want to identify non-classicality such as "quantum entanglement", we would like to identify it efficiently. One way of doing this is through estimating the entropy produced by sub-systems of an entangled system (called the entanglement entropy). Current quantum technologies typically allow for quite low-depth quantum circuits before the quantum systems become noisy and useless. Thus we are interested in determining the non-classicality of low-depth quantum circuits. With Andru Gheorghiu we showed that this problem is hard even for a quantum computer assuming learning with errors is hard for a quantum computer (an assumption underpinning many schemes in post-quantum cryptography). 

Here are some recent papers:

Joining the group

If you'd like more information about joining the group, as a postdoctoral researcher or as a DPhil student, please contact Professor Jonathan Barrett, Professor Aleks Kissinger, and/or Professor Matty Hoban. We have supported postdoctoral fellowship applications for strong applicants. The Engineering and Physical Sciences Research Council and the Royal Society have annual postdoctoral fellowship competitions, some of which are open to non-British nationals. The department also awards DPhil scholarships each year to the strongest UK and overseas applicants.

If you're already doing a Masters degree in Oxford and might be interested in doing your project with a member of our group, please get in touch as soon as possible with one of the group members listed above.

We regularly supervise masters dissertation projects from students doing the MSc in Advanced Computer Science, the MSc in Mathematics and the Foundations of Computer Science, and various other masters degrees, e.g. in Maths, Physics, or Materials.

Mailing lists

We run international mailing lists on quantum computing and quantum foundations.

We also have a separate list to announce local events related to our group's activities; to subscribe, send a blank email to To prevent too much spam, this list is mostly restricted to people in or near Oxford. Requests from Oxford email addresses will be approved automatically, but if you are from elsewhere and would like to join (e.g. because you are visiting us for a while), send an email to introducing yourself. If you are looking for a general-purpose quantum computing or foundations list, join one of the two lists above instead.


We gratefully acknowledge support from the Airforce Office of Scientific Research, the John Templeton Foundation, and the Engineering and Physical Sciences Research Council.


Engineering and Physical Sciences Research Council (EPSRC) – UKRI

Head of Activity


Visiting Professors

Giulio Chiribella
(CIFAR-Azrieli Global Scholar)



Past Members

Sivert Aasnaess
Andrei Akhvlediani
Yaared Al-Mehairi
John-Mark Allen
Philip Atzemoglou
Alexandru Baltag
(University of Amsterdam)
Krzysztof Bar
Karen Barnes
Jacob Biamonte
(ISI Foundation)
Ed Blakey
(University of Bristol)
Rick Blute
(University of Ottawa)
Josef Bolt
Giovanni Carù
Eric Cavalcanti
Destiny Chen
Cole Comfort
Carmen Constantin
Oscar Cunningham
Christopher Dean
(Dalhousie University)
Niel de Beaudrap
Giovanni de Felice
Nadish de Silva
Andreas Doering
Maximilian Doré
Ross Duncan
(Free University of Brussels)
William Edwards
(Perimeter Institute)
Brendan Fong
Fabrizio Romano Genovese
Dan Ghica
(University of Birmingham)
Edward Grefenstette
Amar Hadzihasanovic
(RIMS, Kyoto University)
Lucien Hardy
(Perimeter Institute)
Vojtech Havlicek
Jules Hedges
James Hefford
Chris Heunen
(University of Edinburgh)
Peter Hines
(University of York)
Matty Hoban
Matthias Hofer
Mathieu Huot
Ben Jackson
Bart Jacobs
Nal Kalchbrenner
Ohad Kammar
Elham Kashefi
(University of Edinburgh)
Alex Kavvos
Kohei Kishida
Hlér Kristjánsson
Alex Lang
Ciaran Lee
JS Pacaud Lemay
Martha Lewis
Robin Lorenz
Leon Loveridge
Fotini Markopoulou
(Perimeter Institute)
Owen Maroney
Dan Marsden
Keye Martin
(Naval Research Laboratory)
Yoshihiro Maruyama
Konstantinos Meichanetzidis
Alex Merry
Hector Miller-Bakewell
Hugo Nava Kopp
Kang Feng Ng
Ognyan Oreshkov
Thomas Paine
Prakash Panangaden
(McGill University)
Eric Paquette
Vaia Patta
Karl Paulsson
Dusko Pavlovic
(Royal Holloway)
Simon Perdrix
(University of Grenoble)
Robin Piedeleu
Nicola Pinzani
Matthew Pusey
(University of York)
David Quick
Luca Reggio
Irene Rizzo
Subhayan Roy Moulik
Ondrej Rypacek
Sina Salek
Carlo Maria Scandolo
Phil Scott
(University of Ottawa)
John Selby
Marni Sheppeard
Rui Soares Barbosa
Sam Speight
Maria Stasinou
Colin Stephen
Sean Tull
Nikos Tzevelekos
(Queen Mary, University of London)
Sander Uijlen
Matthijs Vákár
Dominic Verdon
Jamie Vicary
Nathan Walk
Quanlong Wang
Olivia Waring
Linde Wester
Matthew Wilson
Norihiro Yamada
Woongseon  Yoo
Vladimir Zamdzhiev
Yu Zhang
Jonathan Zvesper
Maaike Zwart

Selected Publications

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