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Stefano Gogioso

Personal photo - Stefano Gogioso

Dr Stefano Gogioso

Departmental Lecturer

College Lecturer, Oriel College

E: stefano.gogioso(a)cs.ox.ac.uk

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:

  1. Diagrammatic programming languages for quantum computation
  2. Quantum causality and its applications to quantum computation, communication and cryptography
  3. Algebraic structures involved in the symmetries and evolution of quantum systems
  4. Algebraic structures behind the quantum Fourier transform and other forms of quantum advantage
  5. Non-locality, causal structure and their application to the security of quantum cryptographic protocols
  6. Physical methods in computational complexity theory and information theory
  7. Categorical methods in computational linguistics and natural language processing
  8. Decoherence, thermodynamics and the quantum-classical 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

Quantum Computing with Diagrams
Stefano Gogioso
Invited speaker for Royal Institution Masterclass in Computer Science, University of Oxford, July 2019.
Presentation slides available soon

In this lecture, aimed at Y10 high school students, we introduce the basic building blocks of quantum computing using diagrams.

Diagrammatic Causality
Stefano Gogioso
Invited tutorial at Quantum Causal Structures 2019.
Presentation slides available here

In this tutorial we discuss basics of the diagrammatic algebraic approach to the study of quantum causal structures.

A Diagrammatic Approach to Quantum Dynamics
Stefano Gogioso
arXiv:1905.13111
To appear in 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 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.

A Process-Theoretic Church of the Larger Hilbert Space
Stefano Gogioso
arXiv:1905.13117
To appear in Electronic Proceedings of Theoretical Computer Science (EPTCS)
Presentation slides from QPL 2019, Orange CA, available here
Invited talk at University of Calgary, June 2019.

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.

Categorical Semantics for Time Travel
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)
Presentation slides from LICS 2019, Vancouver, available here
Invited talk at University of Calgary, June 2019.
Presented also at QPL 2019, Quantum Causal Structures 2019 and Applied Category Theory 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.

A Zoo of Vulnerabilities
Stefano Gogioso
Invited presentation for Security Architectures, CDT in Cyber Security, University of Oxford, November 2018.
Presentation slides available here

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.

Future of Security Architectures
Stefano Gogioso
Invited presentation for Security Architectures, CDT in Cyber Security, University of Oxford, November 2018.
Presentation slides available here

In this talk we discuss three currently prominent directions of active development for future architectures: Internet of Things, Blockchains and Quantum 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 Fields with Diagrams
Stefano Gogioso
Presentation at Quantum Causal Structures 2018, Oxford.
Presentation slides available here

In this tutorial we discuss basics of the diagrammatic algebraic approach to the study of quantum field theory.

Density Hypercubes, Higher Order Interference and Hyper-Decoherence: a Categorical Approach
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
Presentation slides from Quantum Interaction 2018, Nice, available here

In this work, to appear in LNCS, we construct an extension of quantum theory displaying higher-order interference and hyper-decoherence 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.

Higher-order CPM Constructions
Stefano Gogioso
arXiv:1805.12079
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.287.8
Presentation slides from QPL 2018, Halifax, available here

In this work, presented at QPL 2018, we define a higher-order 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 well-behaved 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 higher-order interference and hyper-decoherence effects.

Quantum Field Theory in Categorical Quantum Mechanics
Stefano Gogioso and Fabrizio Romano Genovese
arXiv:1805.12087
Electronic Proceedings in Theoretical Computer Science (EPTCS) doi:10.4204/EPTCS.287.9
Presentation slides from QPL 2018, Halifax, 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.

Symmetric Monoidal Structure with Local Character is a Property
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 category-theoretic notion of symmetric monoidal structure with local character, which we prove to be a property for a broad spectrum of categorical examples, including the infinite-dimensional case of relations over a quantale and the non-free 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 single-system 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.

Categorical Quantum Dynamics
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 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.

Towards Quantum Field Theory in Categorical Quantum Mechanics
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 non-standard analysis to introduce infinite-dimensional 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 real-world quantum mechanical systems.

Categorical Probabilistic Theories
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.

Uniqueness of Composition in Quantum Theory and Linguistics
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 non-Cartesian 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 finite-dimensional quantum systems is already determined by single-system transformations. Our result also finds application in the context of natural language processing, where it shows that finite-dimensional linear models for compositional distributional semantics admit an essentially unique compatible pregroup grammar.

Generalised Mermin-type non-locality arguments
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 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
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 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.

A Corpus-based Toy Model for DisCoCat
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 R-semimodules over an involutive commutative semiring R.

Infinite-dimensional Categorical Quantum Mechanics
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 non-standard analysis to introduce infinite-dimensional quantum systems within the framework of categorical quantum mechanics: this was a long-missing 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 real-world quantum mechanical systems.

Mermin Non-Locality in Abstract Process Theories
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 non-locality is fundamental to the understanding of quantum mechanics. The past 50 years have seen a number of non-locality 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 non-locality, generalising Mermin's argument on the GHZ state. Using strongly complementary observables, we provide necessary and sufficient conditions for Mermin non-locality in abstract process theories. We show Mermin non-locality to be the key resource ensuring the device-independent security of the HBB CQ (N,N) family of Quantum Secret Sharing protocols. We challenge the unspoken assumption that the measurements involved in Mermin-type scenarios should be complementary (like the pair X,Y), opening the doors to a much wider class of potential experimental setups than currently employed.

A Bestiary of Sets and Relations
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 graph-theoretic 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.

Categorical Semantics for Schrödinger's Equation
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 finite-dimensional 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.

Aspects of Statistical Physics in Computational Complexity
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 K-sat problem. The introduction of spin glass theory in the study of the random K-sat 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 | 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

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