Supplementary Information from Designing the optimal bit: balancing energetic cost, speed and reliability

We consider the challenge of operating a reliable bit that can be rapidly erased. We find that both erasing and reliability times are non-monotonic in the underlying friction, leading to a trade-off between erasing speed and bit reliability. Fast erasure is possible at the expense of low reliability at moderate friction, and high reliability comes at the expense of slow erasure in the underdamped and overdamped limits. Within a given class of bit parameters and control strategies, we define ‘optimal’ designs of bits that meet the desired reliability and erasing time requirements with the lowest operational work cost. We find that optimal designs always saturate the bound on the erasing time requirement, but can exceed the required reliability time if critically damped. The non-trivial geometry of the reliability and erasing time-scales allows us to exclude large regions of parameter space as suboptimal. We find that optimal designs are either critically damped or close to critical damping under the erasing procedure.

本研究聚焦于可快速擦除的可靠比特（bit）的运行挑战。我们发现，擦除时长与可靠时长均随底层摩擦系数呈现非单调变化，由此在擦除速度与比特可靠性之间形成权衡关系。在中等摩擦系数条件下，可通过牺牲可靠性实现快速擦除；而在欠阻尼与过阻尼区间内，若要获得高可靠性则需以降低擦除速度为代价。在给定的比特参数与控制策略类别内，我们将以最低运行功耗满足既定可靠性与擦除时长要求的比特设计定义为"最优"设计。我们发现，最优设计始终满足擦除时长要求的边界条件，但在临界阻尼工况下，其可靠时长可能超出既定要求。可靠性与擦除时长尺度所具备的非平凡几何特性，使得我们能够将大量参数空间区域判定为次优解并予以排除。我们还发现，在擦除过程中，最优设计要么处于临界阻尼状态，要么接近临界阻尼状态。