Increasing the clock speed of a thermodynamic computer by adding noise

Abstract

We describe a proposal for increasing the effective clock speed of a thermodynamic computer, by altering the interaction scale of the units within the computer and introducing to the computer an additional source of noise. The resulting thermodynamic computer program is equivalent to the original computer program, but runs at a higher clock speed. This approach offers a way of increasing the speed of thermodynamic computing while preserving the fidelity of computation.

Figures (2)

• Figure 1: Classical digital simulation of a thermodynamic computer program for matrix inversion aifer2024thermodynamicmelanson2025thermodynamic. (a) Probability distribution of the reciprocal of the smallest eigenvalue for $10^7$$4 \times 4$ symmetric positive definite matrices $J$. The values associated with the matrices $J_1$ and $J_2$ are marked by dots. Inset: schematic of the 4-unit thermodynamic computer used to estimate the inverses of $J_1$ and $J_2$, comprising 4 units and 10 connections. (b) Error $E_1$ [Eq. (\ref{['frob']})] in the estimate for $J_1^{-1}$ using the computer program (\ref{['lang1']}) run for time $t_{\rm f}$; here and subsequently we state times in units of $\mu^{-1}$. The program is run $n_{\rm s}=10^4$ times, from which the averages $\langle S_i S_j \rangle$ are calculated. (c) The same for the matrix $J_2^{-1}$. Note that the horizontal scales in (b) and (c) are different. (d) and (e): Estimates of the 10 distinct elements of $J_1^{-1}$ and $J_2^{-1}$, indexed by $k$, for the program times $t_{\rm f}$ indicated. Note that the vertical axes in (d) and (e) have different scales.
• Figure 2: Accelerated matrix inversion program. (a) Error $E_2$ [Eq. (\ref{['frob']})] in the estimate of the matrix $J_2^{-1}$ using the accelerated computer program (\ref{['lang3']}) and (\ref{['sigma']}) run for time $t_{\rm f}=1$, as a function of the clock-acceleration parameter $\lambda$ (black dashed line). This result is overlaid on the data of Fig. \ref{['fig1']}(c), derived from the original program (\ref{['lang1']}) run for time $t_{\rm f}$ (green). We collect $n_{\rm s}=10^4$ samples for each program. As expected from the comparison of (\ref{['lang1']}) and (\ref{['lang4']}), the accelerated program run for time $t_{\rm f}$ is equivalent to the original program run for time $\lambda t_{\rm f}$. (b) Exact elements of $J_2^{-1}$ and those estimated using the accelerated program run for time $t_{\rm f}=1$ at two values of $\lambda$. The case $\lambda=1$ is equivalent to the original program.