Complexity Geometry: Emergent Gravity and Optimal Algorithms for Quantum Computation

​by Alex Vikoulov [Posted July 1, 2019 3.50 pm PST]

Physicists Paweł Caputa at Kyoto University and Javier Magan at the Instituto Balseiro of Argentina publish their paper on the curious link between quantum computation and gravity

I call it synchronicity -- just days after posting my article "Love is the glue that holds the Universe together, literally" (which was supposed to be a poetic deviation excerpted from The Syntellect Hypothesis), I come across yet another hard theoretical confirmation for the not-so-poetic universal principle related to quantum gravity.

​That was delivered in the new paper "Quantum Computation As Gravity" by physicists Paweł Caputa at Kyoto University and Javier Magan at the Instituto Balseiro, Centro Atómico de Bariloche in Argentina that has been published in a recent issue of Physical Review Letters.
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Information and gravity may seem like completely different things to a layperson, but in the eyes of a physicist they have one important thing in common -- they can both be described in terms of geometry. Basing on this connection, this new paper implies that gravity sets the rules for optimal quantum computation.

Information, be it classical or quantum, is directly related to geometry. In the field of computational complexity, problems are said to be more efficiently solved when the cost, i.e. computational resources, is minimized.

In 2006, Michael Nielsen has shown that computational costs can be estimated by distances in the manifold of allowed unitary operations. This means that minimizing computational costs is equivalent to finding minimal "geodesics," which are the shortest possible distances between two points on a curved surface.

​This geometric approach suggests that gravity could be applied in estimating computational complexity and identifying the most optimal algorithms for solving problems via quantum computation.

Naturally, the work is challenging, and researchers are still trying to propose a universal description of "complexity" in holographic models related to quantum gravity, in particular, conformal field theory.

“This connection between quantum complexity and coadjoint orbit actions is one of the main results of our work and allows for generalizations of our story to coherence groups in arbitrary quantum field theories,” write the authors in their paper.

Currently, there are many other competing proposals, such as the models of Emergence Theory, for laying the foundations in this area.

-Alex Vikoulov

READ MORE: https://phys.org/news/2019-06-optimal-quantum-linked-gravity.html [Phys.org]

References: Paweł Caputa and Javier M. Magan. "Quantum Computation as Gravity." Physical Review Letters. DOI: 10.1103/PhysRevLett.122.231302
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Keywords: Complexity Geometry, Emergent Gravity, Optimal Algorithms, Quantum Computation, Syntellect Hypothesis, Quantum Computation As Gravity, Paweł Caputa, Javier Magan, Physical Review Letters, information, gravity, geometry, optimal quantum computation, quantum information, computational complexity, computational resources, Michael Nielsen, computational costs, geodesics, holographic models, quantum gravity, conformal field theory, quantum complexity, quantum field theories, Emergence Theory, differential geometry.

​Image Credit: Shutterstock

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