Minimum energy dissipation required for a logically irreversible operation

Abstract

According to Landauer's principle, the minimum heat emission required for computing is linked to logical entropy, or logical reversibility. The validity of Landauer's principle has been investigated for several decades and was finally demonstrated in recent experiments by showing that the minimum heat emission is associated with the reduction in logical entropy during a logically irreversible operation. Although the relationship between minimum heat emission and logical reversibility is being revealed, it is not clear how much free energy is required to be dissipated for a logically irreversible operation. In the present study, in order to reveal the connection between logical reversibility and free energy dissipation, we numerically demonstrated logically irreversible protocols using adiabatic superconductor logic. The calculation results of work during the protocol showed that, while the minimum heat emission conforms to Landauer's principle, the free energy dissipation can be arbitrarily reduced by performing the protocol quasistatically. The above results show that logical reversibility is not associated with thermodynamic reversibility, and that heat is not only emitted from logic devices but also absorbed by logic devices. We also formulated the heat emission from adiabatic superconductor logic during a logically irreversible operation at a finite operation speed.

Adiabatic Quantum-Flux-Parametron: A Tutorial Review

“…These demonstrations indicate that the RQFP is a practical reversible logic gate and can be used as a building block for making reversible computers. We also verified Landauer's principle [21] in a numerical simulation to reveal the energy dissipation for data erasure [91]. It is noteworthy that whereas a single AQFP can operate reversibly via adiabatic switching, conventional AQFP logic gates, such as MAJ, AND, and OR gates, operate irreversibly and dissipate energy via non-adiabatic processes due to logical and physical irreversibility [44], which causes an inappropriate interaction between AQFPs and lead to non-adiabatic operations.…”

“…AQFP logic can perform stochastic operations using thermal fluctuations [91]. Imagine a potential energy shape during adiabatic switching (Fig.…”

Superconductor Amoeba-Inspired Problem Solvers for Combinatorial Optimization

“…1(c), where the color strength of the particles represents the probability of being in each state. In this case, the AQFP gate absorbs heat Q from the thermal bath, and the logical entropy of the gate changes by ΔH = βQ (> 0) [21]. In this way, stochastic processes can be introduced to AQFP gates through heat absorption.…”

“…We have also conducted research on information thermodynamics [20], which studies information processing from a thermodynamics perspective, by the calculation of the heat emitted from and absorbed by AQFP logic. In previous work [21], we demonstrated Landauer's principle [22] numerically by showing that the probability distribution of logic states (logical entropy H) in AQFP gates is associated with thermodynamic entropy S and that the change in logical entropy ΔH is accompanied by heat absorption Q such that ΔH = βQ in the quasi-static limit, where β is the inverse temperature.…”

Scalable true random number generator using adiabatic superconductor logic

“…The AQFP is an energy-efficient logic device based on the quantum flux parametron 19 , 20 that can operate with extremely small energy dissipation near the thermodynamic limit 21 due to an energy-efficient switching scheme, adiabatic switching 22 – 24 . Moreover, the AQFP can easily perform stochastic operations by thermal fluctuations 25 , 26 . As part of our effort, we have developed a true random number generator (TRNG) using AQFP logic and demonstrated the generation of a low-autocorrelation random bitstream 27 .…”