Stefano Gogioso
Dr Stefano Gogioso
Room
204,
Wolfson Building,
Parks Road, Oxford OX1 3QD
United Kingdom
Interests
My main field of research lies between quantum computation, quantum cryptography and quantum foundations. I am mostly interested in problems from theoretical physics and computer science, but my methods come from an area of pure mathematics known as category theory.
Here follow some of my active lines of research:
 Diagrammatic programming languages for quantum computation
 Quantum causality and its applications to quantum computation, communication and cryptography
 Algebraic structures involved in the symmetries and evolution of quantum systems
 Algebraic structures behind the quantum Fourier transform and other forms of quantum advantage
 Nonlocality, causal structure and their application to the security of quantum cryptographic protocols
 Physical methods in computational complexity theory and information theory
 Categorical methods in computational linguistics and natural language processing
 Decoherence, thermodynamics and the quantumclassical interface
In the past, I have also done research in logic, computational geometry and graph theory.
Teaching
I lecture the Physically Based Rendering and Computer Graphics courses jointly with Jassim Happa.
I teach classes for the Department and some Colleges, with the following courses covered in past years: Categorical Quantum Mechanics, Categories Proofs and Processes, Computational Complexity, Computer Graphics, Computer Security, Discrete Mathematics, Information Theory, Lambda Calculus and Types, Linear Algebra, Logic and Proof, Models of Computation, Natural Language Processing, Physically Based Rendering, Probability and Computing, Quantum Computer Science.
I have supervised Master's projects on Natural Language Processing, Machine Learning, Computer Security, Rendering and Quantum Theory.
I currently supervise two DPhil students on the topic of quantum causality, jointly with Bob Coecke.
Summary of Publications and Presentations
In this lecture, aimed at Y10 high school students, we introduce the basic building blocks of quantum computing using diagrams.
In this tutorial we discuss basics of the diagrammatic algebraic approach to the study of quantum causal structures.
Stefano Gogioso
arXiv:1905.13111
To appear in Leibniz International Proceedings in Informatics (LIPIcs) doi:10.4230/LIPIcs.CALCO.2019.16
In this work, presented at CALCO 2019, we introduce a diagrammatic approach to quantum dynamics based on the categorical algebraic structure of strongly complementary observables, with physical semantics provided in terms of quantum clocks and quantisation of time. This is the first in a series of works aimed at bringing quantum dynamics, the driving force behind the processes which underpin the entirety of quantum computation, on a par with information and circuits.
Stefano Gogioso
arXiv:1905.13117
To appear in Electronic Proceedings of Theoretical Computer Science (EPTCS)
In this work, presented at QPL 2019, we show how to reconstruct a process theory of local systems starting from a global theory of reversible processes on a single global system, by using the purification principle. In such a process theory, local systems are not given, but rather `emerge' as the global system is decomposed into subsystems. This marks a significant departure from the traditional compositional approach to process theories, setting the scene for a new decompositional approach which more closely reflects the constraints arising from the physicality of quantum systems. 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.
Nicola Pinzani, Stefano Gogioso and Bob Coecke
arXiv:1902.00032
To appear in the Proceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS'19)
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 speedups. 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.
In this talk we discuss some of the most iconic vulnerabilities from recent years: Heartbleed, Petya/Wannacry/NotPetya, the Mirai botnet, Rowhammer and Meltdown/Spectre.
In this talk we discuss three currently prominent directions of active development for future architectures: Internet of Things, Blockchains and Quantum Cryptography.
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.
In this tutorial we discuss basics of the diagrammatic algebraic approach to the study of quantum field theory.
Stefano Gogioso and Carlo Maria Scandolo
arXiv:1806.00915
To appear in Lecture Notes in Computer Science (LNCS), Springer
Presentation at Quantum Interaction 2018, Nice, available here
In this work, to appear in LNCS, we construct an extension of quantum theory displaying higherorder interference and hyperdecoherence effects. Interference is one of the key features of quantum theory and its study is of fundamental importance to physics and quantum computer science. The study of models displaying altered notions of interference is a necessary step on the way to understanding the physical and computational constraints of quantum theory and, perhaps some day, to overcoming them.
Stefano Gogioso
arXiv:1805.12079
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.287.8
In this work, presented at QPL 2018, we define a higherorder generalisation of the Born rule, mixed quantum states and completely positive maps, based on arbitrary finite abelian group symmetries of symmetric monoidal categories. We show that our generalised construction is functorial, i.e. that it is wellbehaved under transformation of physical theories, and that its closure under iteration can be characterised by algebras of a certain monad. We provide examples of new physical theories obtained through this construction, including novel models displaying higherorder interference and hyperdecoherence effects.
Stefano Gogioso and Fabrizio Romano Genovese
arXiv:1805.12087
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.287.9
In this work, presented at QPL 2018, we use tools from nonstandard 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.
Stefano Gogioso, Dan Marsden and Bob Coecke
arXiv:1805.12088
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.287.10
In this work, presented at QPL 2018, we provide a novel unifying categorytheoretic notion of symmetric monoidal structure with local character, which we prove to be a property for a broad spectrum of categorical examples, including the infinitedimensional case of relations over a quantale and the nonfree case of finitely generated modules over a principal ideal domain. Our result is of interest in the foundations of physics, where it shows that the nature of interaction between physical systems is already determined by singlesystem transformations. Our result finds also application in the context of natural language processing, where it shows that linear models for compositional distributional semantics admit an essentially unique compatible pregroup grammar.
Stefano Gogioso
arXiv:1709.09772
Thesis submitted for the degree of Doctor of Philosophy (DPhil) at the University of Oxford
In this thesis, we use strong complementarity to introduce dynamics and symmetries within the framework of CQM, which we also extend to infinitedimensional Hilbert spaces: these were longmissing 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 symmetryobservable 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, theoryindependent 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 nonlocality to the structure of phase groups, within the context of Mermintype nonlocality arguments. Our nonlocality results find further application to quantum cryptography, where we use them to define a quantumclassical secret sharing scheme with provable deviceindependent security guarantees.
Stefano Gogioso and Fabrizio Romano Genovese
arXiv:1703.09594
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.266.22
Presentation at QPL 2017, Nijmegen, available here
In this work, presented at QPL 2017, we use tools from nonstandard analysis to introduce infinitedimensional quantum systems 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 textbook and realworld quantum mechanical systems.
Stefano Gogioso and Carlo Maria Scandolo
arXiv:1701.08075
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.266.23
Presentation at QPL 2017, Nijmegen, available here
In this work, presented at QPL 2017, we devise a simple categorical framework for the treatment of probabilistic theories, with the aim of reconciling the fields of Categorical Quantum Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years, both CQM and OPTs have found successful application to a number of areas in quantum foundations and information theory: they present many similarities, both in spirit and in formalism, but they remain separated by a number of subtle yet important differences. We attempt to bridge this gap, by adopting a minimal number of operationally motivated axioms which provide clean categorical foundations, in the style of CQM, for the treatment of the problems that OPTs are concerned with.
Bob Coecke, Fabrizio Romano Genovese, Stefano Gogioso, Dan Marsden and Robin Piedeleu
arXiv:1803.00708
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.266.17
Presentation at QPL 2017, Nijmegen, available here
In this work, presented at QPL 2018, we derive a uniqueness result for nonCartesian composition of systems in a large class of process theories. Our result is of interest in the foundations of physics, where it shows that the nature of interaction between finitedimensional quantum systems is already determined by singlesystem transformations. Our result also finds application in the context of natural language processing, where it shows that finitedimensional linear models for compositional distributional semantics admit an essentially unique compatible pregroup grammar.
Stefano Gogioso and William Zeng
arXiv:1702.01772
Logical Methods in Computer Science (LMCS), Volume 15, Issue 2 (April 26, 2019) lmcs:5402
In this work, published in LMCS, we broadly generalise Mermintype arguments on GHZ states, and we provide exact grouptheoretic conditions for nonlocality to be achieved. Our results find direct application in quantum foundations, where they yield a new hierarchy of quantumrealisable AllvsNothing arguments, as well as in quantum cryptography, where they provide deviceindependent security guarantees for a broad family of hybrid quantumclassical secret sharing protocols.
Stefano Gogioso and Aleks Kissinger
arXiv:1701.08669
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 speedup (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 lowlevel, and relies heavily on the the interplay between classical group theory and complex vector spaces. Instead, we give a highlevel diagrammatic presentation which showcases the quantum structures truly at play.
Stefano Gogioso
arXiv:1605.04013
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.221.3
Presentation at SLPCS 2016, Glasgow, available here
The categorical compositional distributional (DisCoCat) model of meaning rigorously connects distributional semantics and pregroup grammars, and has found a variety of applications in computational linguistics. From a more abstract standpoint, the DisCoCat paradigm predicates the construction of a mapping from syntax to categorical semantics. In this work, presented at SLPCS 2016, we describe a concrete construction of one such mapping, from a toy model of syntax for corpora annotated with constituent structure trees, to categorical semantics taking place in a category of free Rsemimodules over an involutive commutative semiring R.
Stefano Gogioso and Fabrizio Romano Genovese
arXiv:1605.04305
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.236.4
Presentation at QPL 2016, Glasgow, available here
Presentation at Categories Logic and Physics Scotland, Glasgow Apr 2017, available here
In this work, presented at QPL 2016, we use tools from nonstandard analysis to introduce infinitedimensional quantum systems within the framework of categorical quantum mechanics: this was a longmissing feature for the formalism, which opens the way to the application of categorical methods from classical and quantum computer science to the study of textbook and realworld quantum mechanical systems.
Stefano Gogioso and William Zeng
arXiv:1506.02675
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.195.17
Presentation at QPL 2015, Oxford, available here
The study of nonlocality is fundamental to the understanding of quantum mechanics. The past 50 years have seen a number of nonlocality proofs, but its fundamental building blocks, and the exact role it plays in quantum protocols, has remained elusive. In this paper, presented at QPL 2015, we focus on a particular flavour of nonlocality, generalising Mermin's argument on the GHZ state. Using strongly complementary observables, we provide necessary and sufficient conditions for Mermin nonlocality in abstract process theories. We show Mermin nonlocality to be the key resource ensuring the deviceindependent security of the HBB CQ (N,N) family of Quantum Secret Sharing protocols. We challenge the unspoken assumption that the measurements involved in Mermintype scenarios should be complementary (like the pair X,Y), opening the doors to a much wider class of potential experimental setups than currently employed.
Stefano Gogioso
arXiv:1506.05025
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.195.16
Presentation at QPL 2015, Oxford, available here
Building on established literature and recent developments in the graphtheoretic characterisation of its CPM category, we provide a treatment of pure state and mixed state quantum mechanics in the category fRel of finite sets and relations. On the way, we highlight the wealth of exotic beasts that hide amongst the extensive operational and structural similarities that the theory shares with more traditional arenas of categorical quantum mechanics, such as the category fdHilb. We conclude our journey by proving that fRel is local, but not without some unexpected twists.
Stefano Gogioso
arXiv:1501.06489
Presentation at QPL 2015, Oxford, available here
In this work, presented at QPL 2015, we provide a novel toolbox for the simulation of finitedimensional quantum dynamics within the framework of categorical quantum mechanics. The material in this work will be developed into the author's DPhil Thesis and a large part of it will appear in the CALCO 2019 paper.
Stefano Gogioso
arXiv:1405.3558
Thesis submitted for the degree of MASt in Mathematics at the University of Cambridge
The aim of this review paper is to give a panoramic of the impact of spin glass theory and statistical physics in the study of the Ksat problem. The introduction of spin glass theory in the study of the random Ksat problem has indeed left a mark on the field, leading to some groundbreaking descriptions of the geometry of its solution space, and helping to shed light on why it seems to be so hard to solve.
Biography
OXFORD UNIVERSITY   Departmental Lecturer   2019  Present 
ORIEL COLLEGE   College Lecturer   2016  Present 
OXFORD UNIVERSITY   Postdoctoral 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 
See also
Selected Publications

Generalised Mermin−type non−locality arguments
Stefano Gogioso and William Zeng
In Logical Methods in Computer Science‚ arXiv:1702.01772. 2017.
Details about Generalised Mermin−type non−locality arguments  BibTeX data for Generalised Mermin−type non−locality arguments

A Diagrammatic Approach to Quantum Dynamics
Stefano Gogioso
In CALCO 2019. 2019.
Details about A Diagrammatic Approach to Quantum Dynamics  BibTeX data for A Diagrammatic Approach to Quantum Dynamics

Categorical Semantics for Time Travel
Nicola Pinzani‚ Stefano Gogioso and Bob Coecke
In LICS 2019. 2019.
Details about Categorical Semantics for Time Travel  BibTeX data for Categorical Semantics for Time Travel