Reality's quantum nature is its most inexplicable feature. The outcome of every observation we make can ultimately be written on classical pieces of paper. Why would understanding this classical data merit non-classical logic? This puzzle has pushed a heated search for fundamental physical principles to justify why reality is quantum mechanical.

**The Quantum Epsilon Project** has been formed through the auspices of the John Templeton Foundation to explain this paradox.
We seek to isolate quantum theory from philosophical principles, that arise from a novel interplay of the foundational ideas in computational mechanics and quantum theory.
The former to capture the ideal of *Occam's Razor* – the preference for understanding reality through the least extraneous causes.
The latter to understand exactly how this notion of ‘least extraneous causes’ depends on what sort of information theory we use.
Together these concepts suggest an intriguing new line of inquiry: could the desire for simplicity isolate quantum theory as the ideal way to understand reality?

January 8th – 12th 2017

We are pleased to announce our first international workshop to explore the intersection between quantum and complexity science. For full details, please visit the workshop webpage at http://qcomplexity.quantumlah.org/.

- Provably unbounded memory advantage in stochastic simulation using quantum mechanics. September 2016
- Using quantum theory to reduce the complexity of input-output processes January 2016
- The classical-quantum divergence of complexity in the Ising spin chain November 2015
- When is simpler thermodynamically better? October 2015

Project leader

Project co-leader

Research fellow

Research fellow

PhD student, CQT

PhD student, NTU

PhD student, NTU

Workshop on the interdisciplinary frontiers of quantum and complexity science,

Singapore,
Jan 8 - Jan 12 2017

Asia-Pacific Conference & Workshop on Quantum Information Sciences,

Auckland, New Zealand,
Nov 30 - Dec 4 2015

Asia-Pacific Conference & Workshop on Quantum Information Sciences,

Auckland, New Zealand,
Nov 30 - Dec 4 2015

It has been established that quantum models can provide a simpler description of most processes than the best possible classical model. However, the extent to which the quantum model can outperform the classical was an open question. Here, we answer this question and demonstrate that quantum theory's advantage can be made unboundedly large. We consider digital simulations of a continuous processes, and show that whereas increasing the precision on a classical simulator always increases the memory requirement, when running a quantum simulation, the memory requirement saturates at some finite maximum value. Any gains in precision beyond this comes at no additional memory cost.

We understand all natural things around us by their input-response behavior, for example we perceive neurological networks as transducing sensory inputs to electrical impulses known as spike trains, meanwhile photosynthesis is a mechanism for converting electro-magnetic energy to chemical energy. Here we ask how does our understanding of such phenomena depend on the information theory we use to describe them? We show that in general the simplest explanation of how such systems behave, the one which posits the least causes to inform future expectations of how the process will behave, are in general quantum mechanical. Such that the processes look remarkably simpler when viewed through the lens of quantum theory. In answering this question, we establish a much broader class of processes where it is simpler to be quantum. This gives a much greater imperative to nature processes to privilege the laws of quantum mechanics.

At the heart of complexity and complex systems is the manipulation of patterns – predictable structures – using an internal memory, but the exact structure of this memory is not uniquely defined. Here, we consider the thermodynamics involved in this manipulation, such as by living things which exploit patterns in their surroundings, and use the energy released to generate new structure. We physically substantiate the intuition of Occam's razor by identifying the thermodynamic consequences of using a complicated memory.

To do this, we introduce a general framework for the manipulation of patterns, consisting of generators that use energy to produce patterns, and extractors that release energy by destroying patterns. Both must contain internal memory about what has happened in the pattern so far, in order that they can accurately generate (or anticipate) the upcoming parts of the pattern. When it comes to generating a pattern, updating the internal memory incurs an energy cost. This cost is lowest when the memory contains no more information than required to accurately generate the pattern. We thus identify that simpler is better when it comes to producing patterns, providing a physical motivation to support Occam's razor.

Can quantum information fundamentally change the way we perceive what is complex? Here, we generalize a widely-used measure of complexity – the statistical complexity – to the quantum regime. Statistical complexity quantifies the minimal classical information we must store about a process to simulate its future behaviour. We construct a quantum variant of this measure, which allows for simulation using quantum mechanical systems instead. The resulting complexity measure – quantum statistical complexity – exhibits drastically different qualitative behaviour closer in line to our intuition. This indicates to us that for a better understanding of nature, we must examine it through the lens of quantum information theory.

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Selected publications

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