# Logical and thermodynamical reversibility: optimized experimental implementation of the NOT operation

## TL;DR

This paper demonstrates a physically reversible and energy-efficient implementation of the NOT operation using an underdamped oscillator, achieving low dissipation and high speed, supported by an analytical model and optimization discussion.

## Contribution

It introduces an experimental protocol for a reversible bit-flip with minimal energy dissipation, advancing the physical realization of logically reversible operations.

## Key findings

- Energy dissipation below minimal irreversible cost
- High-speed operation reaching equilibrium in half a period
- Work inversely proportional to system's quality factor

## Abstract

The NOT operation is a reversible transformation acting on a 1-bit logical state, and should be achievable in a physically reversible manner at no energetic cost. We experimentally demonstrate a bit-flip protocol based on the momentum of an underdamped oscillator confined in a double well potential. The protocol is designed to be reversible in the ideal dissipationless case, and the thermodynamic work required is inversely proportional to the quality factor of the system. Our implementation demonstrates an energy dissipation significantly lower than the minimal cost of information processing in logically irreversible operations. It is moreover performed at high speed: a fully equilibrated final state is reached in only half a period of the oscillator. The results are supported by an analytical model that takes into account the presence of irreversibility. The Letter concludes with a discussion of optimization strategies.