Momentum-Driven Reversible Logic Accelerates Efficient Irreversible Universal Computation

TL;DR

The paper tackles the energy efficiency of universal computation by introducing momentum-based computing with coupled quantum flux parametrons (CQFPs). It compares two NAND implementations: Controlled Erasure (CE), which stores information in positional degrees and faces speed/fidelity limits, and Erasure-Flip (EF), which leverages momentum to perform both reversible and irreversible logic in different subspaces, achieving higher speed and fidelity at similar energy costs. Through Langevin-dynamics simulations, the authors quantify work, fidelity, and speed for CE and EF, showing that EF significantly outperforms CE and enabling a complete NAND with a single EF cycle; CE can be improved but remains thermodynamically constrained. The results demonstrate a promising momentum-based computing paradigm with potential experimental realization and broad implications for energy-efficient, high-fidelity computing architectures that blend reversible and irreversible operations across memory subspaces.

Abstract

We present implementations of two physically-embedded computation-universal logical operations using a 2-bit logical unit composed of coupled quantum flux parametrons -- Josephson-junction superconducting circuits. To illustrate universality, we investigate NAND gates built from these two distinct elementary operations. On the one hand, Controlled Erasure (CE) is designed using fixed-point analysis and assumes that information must be stored in locally-metastable distributions. On the other, Erasure-Flip (EF) leverages momentum as a computational resource and significantly outperforms the metastable approach, simultaneously achieving higher fidelity and faster computational speed without incurring any additional energetic cost. Notably, the momentum degree of freedom allows the EF to achieve universality by using both nontrivial reversible and irreversible logic simultaneously in different logical subspaces. These results not only provide a practical, high-performance protocol ripe for experimental realization but also underscore the broader potential of momentum-based computing paradigms.

Figures (19)

• Figure 1: CQFP Circuit: Boxed diagrams (dashed lines) represent the Josephson junctions modeled as RCSJs. Table \ref{['table:circuit_parameters']} in the Appendix explains the symbols.
• Figure 2: (a) Truth tables for the three operations: NAND, Controlled Erasure (CE), and Erasure-Flip (EF). (b) Schematic illustration of the initial and final logical-state distributions for CE (top) and EF (bottom) operations. The four 2-bit digits at the corners indicate the coarse-graining label for the potential wells and the colored boxes represent the particles. The initial state (left) represents the thermal equilibrium distribution of particles within the four-well potential, corresponding to the logical inputs. The final state (right) depicts the particle distribution after the respective operations, which should be compared with the truth table to determine the logical output.
• Figure 3: Snapshots illustrating the evolution of the CE protocol are presented at four distinct time points. The first row of the figure contains the contour plots of the potential energy landscape in the $\varphi_{1}\text{-}\varphi_{2}$ state space, where the colored circles mark the instantaneous distributions of the four particle types (00, 01, 10, and 11). The second and third rows depict the corresponding potential energy graphs along the blue and red cutlines, respectively, as indicated on the contour plots. (https://drive.google.com/file/d/1dn8LQAMVQNqLFT4am6F1jOUtWKFEmted/view?usp=sharing).
• Figure 4: (a) Contour graph of the four-well potential. The diamonds indicate critical points of the potential. Number 0 to 3 are the local minima and number 4 to 7 are saddle points. (b) Potential contour at the moment of saddle point bifurcation happens. $\Delta U_{ij}$ indicate the potential differences between the critical points. The first index and second index in the subscript indicate the the local minimum and saddle point refering to. At the bifurcation point, stable point 2 and saddle point 5 merge together. (c) The left (right) potential plots trace the potential along the red (blue) line in (b). (d) Reducing the potential barrier height $\Delta U_{05}$ leads to a decrease in the overall work cost of the CE protocol. These two graphs illustrate the potential energy profile along the respective cutlines when a significantly lower barrier height is employed.
• Figure 5: (a) Total work distribution of the CE protocol. The red dashed line indicates the average work, which is $53.6 ~k_BT$. (b) Work distributions for each particle type: The average works for each particle type are also shown in the figure. A signature of this protocol is that the particles moving from a high potential well to a low potential well involve significantly more work compared to other particle types. Details of the protocol are shown in Figure \ref{['table:protocol_table']}(a) in Appendix \ref{['appendix:detail_of_protocols']}.