Skip to main content

Stefano Gogioso

Personal photo - Stefano Gogioso

Dr Stefano Gogioso

Departmental Lecturer

E: stefano.gogioso(a)

Room 416, Wolfson Building, Parks Road, Oxford OX1 3QD
United Kingdom



Stefano Gogioso is a mathematician and computer scientist, focusing on the foundations of quantum theory and the creation of quantum software.

He obtained his doctorate in the Oxford Quantum Group, under the supervision of Bob Coecke, developing pictorial ways to talk about quantum particles and their peculiar behaviour. Since then, he's been working on ways to make the quantum world more accessible to the general public, efforts which culminated in the recent release of "Quantum in Pictures: A New Way to Understand the Quantum World".

He is a Departmental Lecturer at the University of Oxford, teaching applied courses on Quantum Computing to Master's students and professionals from a variety of backgrounds:

He co-founded the start-up Hashberg, where he directs the development of high-level quantum programming tools. He is actively engaged in fundamental research, focusing on the connection between quantum systems and the structure of spacetime. He serves as a Mentor for the AI stream of CDL-Oxford.

Summary of Publications and Presentations

The Topology and Geometry of Causality
Stefano Gogioso and Nicola Pinzani
Presentation available here

In this work, presented at QPL 2022, we provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. Our investigation proceeds from two complementary fronts: a topological one, using tools from sheaf theory, and a geometric one, based on polytopes and linear programming. From the topological perspective, we understand experimental outcome probabilities as bundles of compatible contextual data over certain topological spaces, encoding causality constraints. From the geometric perspective, we understand the same experimental outcome probabilities as points in high-dimensional causal polytopes, which we explicitly construct and fully characterise. Our work is a significant extension of both the established Abramsky-Brandenburger framework for contextuality and the current body of work on indefinite causality. We provide definitions of causal fraction and causal separability for empirical models relative to a broad class of causal constraints: this allows us to construct and characterise novel examples which explicitly connect causal inseparability to non-locality and contextuality. In particular, we clearly demonstrate the existence of "causal contextuality", a phenomenon where causal structure is explicitly correlated to the classical inputs and outputs of local instruments, so that contextuality of the associated empirical model directly implies causal inseparability.

Annealing optimisation of Mixed ZX Phase Circuits
Stefano Gogioso and Richie Yeung
To appear in Electronic Proceedings of Theoretical Computer Science (EPTCS)
Presentation available here

In this work, presented at QPL 2022, we introduce a topology-aware optimisation technique for circuits of mixed ZX phase gadgets, based on conjugation by CX gates and simulated annealing.

Categorical Semantics for Feynman Diagrams
Razin A. Shaikh and Stefano Gogioso

In this work, presented at ACT 2022, we introduce a novel compositional description of Feynman diagrams, with a well-defined interpretation as morphisms in a dagger-compact category. Our chosen setting is suitable for infinite-dimensional diagrammatic reasoning, generalising the ZX calculus and other algebraic gadgets familiar to the categorical quantum theory community. The Feynman diagrams we define look very similar to their traditional counterparts, but are more general: instead of depicting scattering amplitudes, they embody the linear maps from which the amplitudes themselves are computed, for any given initial and final particle states. This shift in perspective reflects into a formal transition from the syntactic, graph-theoretic compositionality of traditional Feynman diagrams to a semantic, categorical-diagrammatic compositionality. Because we work in a concrete categorical setting -- powered by non-standard analysis -- we are able to take direct advantage of complex additive structure in our description. This makes it possible to derive a particularly compelling characterisation for the sequential composition of categorical Feynman diagrams, which automatically results in the superposition of all possible graph-theoretic combinations of the individual diagrams themselves.

Quantum Natural Language Processing on Near-Term Quantum Computers
Konstantinos Meichanetzidis, Stefano Gogioso, Giovanni De Felice, Nicolò Chiappori, Alexis Toumi and Bob Coecke
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.340.11
Presentation available here

In this work, presented at QPL 2020 (as well as ACT 2020 and other workshops), we describe a full-stack pipeline for natural language processing on near-term quantum computers, aka QNLP. The language modelling framework we employ is that of compositional distributional semantics (DisCoCat), which extends and complements the compositional structure of pregroup grammars. Within this model, the grammatical reduction of a sentence is interpreted as a diagram, encoding a specific interaction of words according to the grammar. It is this interaction which, together with a specific choice of word embedding, realises the meaning (or "semantics") of a sentence. Building on the formal quantum-like nature of such interactions, we present a method for mapping DisCoCat diagrams to quantum circuits. Our methodology is compatible both with NISQ devices and with established Quantum Machine Learning techniques, paving the way to near-term applications of quantum technology to natural language processing.

Giving Operational Meaning to the Superposition of Causal Orders
Nicola Pinzani and Stefano Gogioso
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.340.13
Presentation available here

In this work, presented at QPL 2020, we give rigorous operational meaning to superposition of causal orders. This fits within a recent effort to understand how the standard operational perspective on quantum theory could be extended to include indefinite causality. The mainstream view, that of "process matrices", takes a top-down approach to the problem, considering all causal correlations that are compatible with local quantum experiments. Conversely, we pursue a bottom-up approach, investigating how the concept of indefiniteness emerges from specific characteristics of generic operational theories. Specifically, we pin down the operational phenomenology of the notion of non-classical (e.g. "coherent") control, which we then use to formalise a theory-independent notion of control (e.g. "superposition") of causal orders. To validate our framework, we show how salient examples from the literature can be captured in our framework.

Functorial evolution of quantum fields
Stefano Gogioso, Maria E Stasinou and Bob Coecke
Frontiers in Physics doi:10.3389/fphy.2021.534265
Presentation available here

In this work, under review for publication in a journal, we present a compositional algebraic framework to describe the evolution of quantum fields in discretised spacetimes. We show how familiar notions from Relativity and quantum causality can be recovered in a purely order-theoretic way from the causal order of events in spacetime, with no direct mention of analysis or topology. We formulate theory-independent notions of fields over causal orders in a compositional, functorial way. We draw a strong connection to Algebraic Quantum Field Theory (AQFT), using a sheaf-theoretical approach in our definition of spaces of states over regions of spacetime. We introduce notions of symmetry and cellular automata, which we show to subsume existing definitions of Quantum Cellular Automata (QCA) from previous literature. Given the extreme flexibility of our constructions, we propose that our framework be used as the starting point for new developments in AQFT, QCA and more generally Quantum Field Theory. .

Categorical Semantics for Time Travel
Nicola Pinzani, Stefano Gogioso and Bob Coecke
To appear in the Proceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS'19)
Presentation slides from LICS 2019, Vancouver, available here
Invited talk at University of Calgary, June 2019.

In this work, presented at LICS 2019, we introduce a general categorical framework to reason about quantum theory and other process theories living in spacetimes where Closed Timelike Curves (CTCs) are available, allowing resources to travel back in time and provide computational speed-ups. This work fits within a broader research program on quantum causal structure, aimed at understanding the interaction of quantum theory with relativistic causality and its impact on quantum computation, communication and cryptography.

What are Visual Languages
Stefano Gogioso
Invited talk at the 2nd Statebox Summit, Amsterdam, September 2018.
Presentation available here
Follow-up panel discussion available here (from around 19:00)
Presentation slides available here

In this talk we discuss the use of visual languages in quantum theory and quantum computing, advocating for the broader adoption of compositional and visual programming languages in computer science.

Quantum Field Theory in Categorical Quantum Mechanics
Stefano Gogioso and Fabrizio Romano Genovese
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.287.9
Presentation slides from QPL 2018, Halifax, available here
Presentation slides from QCS 2018, Oxford, available here

In this work, presented at QPL 2018, we use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. This formulation opens the way to the application of categorical methods from classical and quantum computer science to the study of quantum fields and particle physics. This work fits within a broader research program on quantum causal structure, aimed at understanding the interaction of quantum theory with relativistic causality and its impact on quantum computation, communication and cryptography.

Categorical Quantum Dynamics
Stefano Gogioso
Thesis submitted for the degree of Doctor of Philosophy (DPhil) at the University of Oxford
Leibniz International Proceedings in Informatics (LIPIcs) doi:10.4230/LIPIcs.CALCO.2019.16
Presentation slides from CALCO 2019, London, available here
Presentation slides from SYCO 3, Oxford, available here

In this thesis, we use strong complementarity to introduce dynamics and symmetries within the framework of CQM, which we also extend to infinite-dimensional Hilbert spaces: these were long-missing features, which open the way to a wealth of new applications. The coherent treatment presented in this work also provides a variety of novel insights into the dynamics and symmetries of quantum systems: examples include the extremely simple characterisation of symmetry-observable duality, the connection of strong complementarity with the Weyl Canonical Commutation Relations, the generalisations of Feynman's clock construction, the existence of time observables and the emergence of quantum clocks. Furthermore, we show that strong complementarity is a key resource for quantum algorithms and protocols. We provide the first fully diagrammatic, theory-independent proof of correctness for the quantum algorithm solving the Hidden Subgroup Problem, and show that strong complementarity is the feature providing the quantum advantage. In quantum foundations, we use strong complementarity to derive the exact conditions relating non-locality to the structure of phase groups, within the context of Mermin-type non-locality arguments. Our non-locality results find further application to quantum cryptography, where we use them to define a quantum-classical secret sharing scheme with provable device-independent security guarantees.

Generalised Mermin-type non-locality arguments
Stefano Gogioso and William Zeng
Logical Methods in Computer Science (LMCS), Volume 15, Issue 2 (April 26, 2019) lmcs:5402

In this work, published in LMCS, we broadly generalise Mermin-type arguments on GHZ states, and we provide exact group-theoretic conditions for non-locality to be achieved. Our results find direct application in quantum foundations, where they yield a new hierarchy of quantum-realisable All-vs-Nothing arguments, as well as in quantum cryptography, where they provide device-independent security guarantees for a broad family of hybrid quantum-classical secret sharing protocols.

Fully graphical treatment of the quantum algorithm for the Hidden Subgroup Problem
Stefano Gogioso and Aleks Kissinger
Accepted for publication in Quantum
Presentation at Categories Logic and Physics Scotland, Edinburgh May 2016, available here

In this work, accepted for publication in Quantum, we provide the first fully diagrammatic proof of correctness for the abelian HSP protocol, showing that strongly complementary observables are the key ingredient to its success. The abelian Hidden Subgroup Problem (HSP) is extremely general, and many problems with known quantum exponential speed-up (such as integers factorisation, the discrete logarithm and Simon's problem) can be seen as specific instances of it. The traditional presentation of the quantum protocol for the abelian HSP is low-level, and relies heavily on the the interplay between classical group theory and complex vector spaces. Instead, we give a high-level diagrammatic presentation which showcases the quantum structures truly at play.


Oxford University | Departmental Lecturer | 2019 - Present
Kellogg College | Fellow | 2021 - Present
Hashberg Ltd | Director | 2019 - Present
Oriel College | College Lecturer | 2016 - 2021
Oxford University | Post-doctoral Researcher | 2017 - 2019
Oxford University | DPhil in Computer Science  | 2013 - 2017 
Cambridge University | MASt in Mathematics (Part III)  | 2012 - 2013 
Cambridge University | BA in Mathematics (Tripos)  | 2009 - 2012 
ISICT Consortium | ICT and Management  | 2006 - 2009 
University of Genova | MSc in Computer Science  | 2009 - 2009
University of Genova | BSc in Computer Science  | 2006 - 2009

Selected Publications

View AllManage publications


Past Students

Nicola Pinzani
Maria Stasinou