Energy-Time-Accuracy Tradeoffs in Thermodynamic Computing

TL;DR

This paper explores the fundamental energy, time, and accuracy trade-offs in thermodynamic computing, deriving bounds and proposing control schemes to optimize performance without prior knowledge of solutions.

Contribution

It provides the first theoretical bounds on energy, time, and accuracy trade-offs in thermodynamic computing and introduces quasi-optimal control methods for practical implementation.

Findings

Derived bounds on energy-delay-deficiency product (EDDP) in thermodynamic computing.

Developed quasi-optimal control schemes requiring no prior solution knowledge.

Demonstrated the approach on matrix inversion in overdamped quadratic systems.

Abstract

In the paradigm of thermodynamic computing, instead of behaving deterministically, hardware undergoes a stochastic process in order to sample from a distribution of interest. While it has been hypothesized that thermodynamic computers may achieve better energy efficiency and performance, a theoretical characterization of the resource cost of thermodynamic computations is still lacking. Here, we analyze the fundamental trade-offs between computational accuracy, energy dissipation, and time in thermodynamic computing. Using geometric bounds on entropy production, we derive general limits on the energy-delay-deficiency product (EDDP), a stochastic generalization of the traditional energy-delay product (EDP). While these limits can in principle be saturated, the corresponding optimal driving protocols require full knowledge of the final equilibrium distribution, i.e., the solution itself. To overcome this limitation, we develop quasi-optimal control schemes that require no prior information of the solution and demonstrate their performance for matrix inversion in overdamped quadratic systems. The derived bounds extend beyond this setting to more general potentials, being directly relevant to recent proposals based on non-equilibrium Langevin dynamics.