Santa Fe Institute Collaboration Platform

Thermodynamics of Computation

Karpur Shukla

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Biography: I'm currently a PhD student at the School of Engineering at Brown University. My interests lie at the intersection of geometric phenomena in quantum systems, conformal field theory, quantum thermodynamics, and condensed matter theory. In particular, I'm deeply interested in geometric properties of Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) dynamics and their applications to condensed matter systems, quantum information processing, and classical information processing. I'm also interested in the properties of conformal field theories (CFTs) out of equilibrium, and the ways by which nonequilibrium CFT phenomena manifest in condensed matter models. Finally, I'm interested in the consequences that renormalisation group transformations have for resource theories.

At present, my work focuses on applications of Gorini-Kossakowski-Lindblad-Sudarshan (GKSL) dynamics with multiple steady states, resource theories, and shortcuts-to-adiabaticity to physical models for reversible computing and conformally invariant systems. Reversible computing is a paradigm of computing that relies on preserving and unwinding correlations, which allows us to avoid the energy cost resulting from irretrievably ejecting information stored in memory devices into the environment. Although systems implementing reversible logic were first proposed as early as 1978 by Fredkin and Toffoli; designing a model of fast, fully adiabatic, and scalable classical reversible operations remains an ongoing and active area of interest. Here, the language of GKSL dynamics, shortcuts-to-adiabaticity, resource theories, and quantum speed limits are especially suited to helping us design our desired models for reversible computing. I'm currently working alongside several others to develop these models.

My other work focuses on the consequences that conformal invariance can have for resource theories, as well as the lessons resource theories can have for conformally invariant systems. Recent results by Bernamonti et al. for holographic second laws, Guarnieri et al. for relationships between stochastic quantum work techniques and resource theories, and Faist and Renner on new information measures for the work cost of quantum processes, and Albert et al. on the geometric properties of Lindbladians themselves have substantial implications for systems described by CFTs. My interest here is in examining what lessons these results have for CFTs: in particular, understanding whether stochastic quantum work techniques can be expressed for CFTs via the holographic second laws, where an extension to the holographic second laws can be developed using this new information measure, and what lessons we may derive for CFTs out of equilibrium with degenerate steady states.

Before my current appointment, I was a research fellow and visiting faculty member at the Department of Applied Mathematics at Flame University. I received my M.Sci. in physics from Carnegie Mellon University in 2016, and my B.Sci. in physics from Carnegie Mellon University in 2014. There, I worked under Di Xiao on optoelectronic phenomena on the surfaces of topological insulators, in particular examining properties of the photogalvanic effect on the surfaces of topological insulators at zero and finite temperature. I also had the brief opportunity to work on curve fitting for experimental soft condensed matter physics under Stephanie Tristram-Nagle, as well as on analytic analysis of the dynamical RG flow of the Ising model under Robert Swendsen.

Field(s) of Research: General Non-equilibrium Statistical Physics, Stochastic Thermodynamics, Logically Reversible Computing, Quantum Thermodynamics and Information Processing

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