Quantum Complexity Science Initiative

Department of Physics – University of Malta

Adiabatic Computing

Universal adiabatic quantum computing and quantum algorithms simulating chemical physics

Quantum Network Science

A ‘Quantum Theory’ of Networked and Complex Systems

Tensor Network States

Graphical calculus representing quantum states, algorithms and invariants

Time-Reversal Symmetry

Time-reversal symmetry breaking in modern quantum information science by ‘chiral quantum walks’

A theory uniting disciplines

One could argue that the fields of quantum information science and complex network theory (a.k.a. complexity science) both address complexity, yet from opposite perspectives. Indeed, the former makes use of a complex system as a computational resource whereas the later generally studies (and often using computer simulations) the scaling, collective behavior and emergent properties of complex system(s).

Accordingly, how the term complexity arises in these two fields is not always interchangeable. So called, computational complexity in quantum information science considers quantifying computational resources whereas complexity science investigates how relationships between parts give rise to collective behaviors of the whole.

And then after closer inspection, these two fields indeed also share some intriguing similarities. By correctly studying information as an entity fundamentally governed by the laws of physics, our development of an emerging common language is already binding certain ideas and mapping some techniques between these a priori distinct fields. What's more, the ubiquitous use of various network and graph theories inside of both disciplines, has allowed us to create a stage for an abstracted comparison of networked systems, recovering both fields as special cases of more general mathematical entities.

And even with these similarities, and other bridges still being built, there seems to be an even vaster host of differences. Pinpointing these similarities and reconciling these differences in increasingly precise terms broadly defines our research initiative aimed at a new theory, uniting the disciplines of quantum information science with the theory of complex and networked systems.

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Why unite the fields of quantum physics and complex systems science?

The independent problems solved in each of these two fields have proven to be reminiscent of each other. And these different solutions to related problems could evidently be made to better apply across disciplines. This seems especially true for contemporary challenges. For example, multi-level (a.k.a. multiplex) networks are a special case of tensor network states - well studied in quantum theory. Additionally, modern experimental breakthroughs in controlling quantum systems have made the state-of-the-art in the size of the state-spaces considered to be roughly the same in both disciplines. As this size of accessible coherent (non-mean field) quantum systems continues to grow, the emergent properties of quantum complex systems will take center stage as a quantum generalization of complex and networked systems science emerges. Note that in particular, we are not concerned with mean-field condensates or distributed quantum communication networks but instead we are making headway towards a full first-principles account of a 'quantum theory' of complex and networked systems. It's a very different challenge.

What are some promising avenues for new research?

Community detection for quantum systems is an area that seems to make a lot of sense for potential applications of complex network theory inside of quantum physics [Physical Review X 4, 041012 (2014)]. Particularly in the areas where quantum effects have been shown to be present in biological systems (here a community might be a region in which a particle might travel which behaves quantum mechanically).

Additionally, chemical reaction networks have been shown to correspond to certain wide classes of non-unitary field theories [Baez and Biamonte]. The bridges here are interesting, a version of coherent states emerged as the steady state solution to a wide class of networks, results related to conserved quantiles have been established by Baez and Fong and much much more. Yet central ideas related to network theory have yet to be mapped to this discipline. I could tell you some really exciting ideas, but then you'd know what we're working on.

And of course, the cross over among quantum tensor networks and multiplex networks is certainly just as interesting as casting the equations of motion for multiplex network evolution into the framework defined in 'quantum techniques for stochastic mechanics'.

What should I read first?

We've written a few blog articles that explain some aspects of 'quantum network theory'.

and of course, we have a page outlining our work as well as some related approaches in the quest to create this new theory.

Jacob Biamonte

Lead of the Quantum Complexity Science Initiative
Jacob-Biamonte
  • Short Biography

    I hold a permanent senior faculty position in 'Theoretical Quantum Physics' at the University of Malta and an appointment at the Institute of Quantum Computing, at the University of Waterloo. I was appointed the 'Shapiro Fellow' in Mathematical Physics at Pennsylvania State University and gave the accompanied lecture series on uniting the fields of quantum information with complexity science. I worked as an early research scientist at D-Wave Systems Inc. 'the quantum computing company' in Vancouver B.C. and completed an award winning doctoral thesis from the University of Oxford. My postdoctoral research was done mainly at Harvard University and at the University of Oxford. I am an elected member of the Foundational Questions Institute (FQXi). In terms of community service, I'm on the editorial boards for several journals, including New Journal of Physics.

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Working Team

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Jacob Biamonte

Principal Investigator
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Jacob Turner

Research Scientist

Postdoctoral and Research Scientist Alumni

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Mauro Faccin

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Ville Bergholm

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Tomi Johnson

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JAMES WHITFIELD

Now Assistant Professor, Dartmouth
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Zoltán Zimborás

Assistant Professor, Wigner Research Centre for Physics, Hungarian Academy of Sciences

PhD and Long-Term Visiting Student Alumni

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David Yudong Cao

Graduated 2016
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JACOB TURNER

Graduated 2015
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PIOTR MIGDAŁ

Graduated 2014
Institut de Ciències Fotòniques, Barcelona

Quantum Colleagues at the University of Malta

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André Xuereb

University of Malta
Faculty Member Research interests: Optomechanics, Laser cooling, Quantum optics, Retarded atom–surface, interactions, Dissipative dipole forces. (active role in science policy and science popularisation in Malta)
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Vittorio Peano

University of Malta
Faculty Member Research interests: Physics of open quantum systems out of equilibrium, quantum optics, optomechanics, photonics, phononics, topological phase transitions, synthetic gauge fields, quantum noise and quantum metrology, physics of rare large fluctuations, ultracold atoms.

Administrative Staff

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Edward Duca

media officer
Dr Edward Duca B.Sc.(Hons.)(Melit.),M.Sc.(Leics.),Ph.D.(Edin.) Communications & Alumni Relations Office Room 127 Administration Building University of Malta Msida contact+356 2340 3451
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Lusa Zeglova

scientific illustrator
webpage design and scientific illustration

External and Collaborative Research Council

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John C. Baez

mathematical network theory
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Mike Mosca

quantum computing
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SETH LLOYD

quantum information

Research Highlights

uniting the fields of quantum information and complexity science

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