Thermodynamic dissipation bounds on classical and quantum reversible information processing

Presenting Author: Karpur Shukla, Flame University
Contributing Author(s): Michael P. Frank (Sandia National Laboratories)

We describe how to examine systems supporting classical and quantum reversible information processing, and provide bounds on the energy dissipation of reversible information processing operations, by exploiting the thermodynamic uncertainty relations (TURs) for non-equilibrium steady states (NESSs) and the four-corners partition of the Lindbladian with multiple steady states. We briefly review the motivation for reversible computing, and describe the additional constraints that reversible information processing specifically imposes on state Hilbert spaces. We then describe how the dynamics of a system encoding classical and quantum bits with reversible operations, possibly including some sort of dissipative dynamics, can be described using the four-corners partition of Lindbladians. We examine how the requirements of logical reversibility gives rise to a specific class of Lindbladian dynamics, and discuss the dissipation-delay product (DDP), a quantity of interest in reversible computing which characterizes the average energy costs over time of reversible operations. Finally, I discuss TURs for a single NESS, and discuss how this can be extended to TURs for systems with several NESSs by exploiting the geometric properties of Lindbladians with multiple steady states. From this, we provide a preliminary bound on the DDP.

(Session 5 : Saturday from 5:00pm - 7:00pm)


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