Controlled Erasure as a Building Block for Universal Thermodynamically-Robust Superconducting Computing

Reducing the energy inefficiency of conventional CMOS-based computing devices -- which rely on logically irreversible gates to process information -- remains both a fundamental engineering challenge and a practical social challenge of increasing importance. We extend an alternative computing paradigm that manipulates microstate distributions to store information in the metastable minima determined by an effective potential energy landscape. These minima serve as mesoscopic memories that are manipulated by a dynamic landscape to perform information processing. Central to our results is the control erase (CE) protocol that controls the landscape's metastable minima to determine whether information is preserved or erased. Importantly, successive protocol executions can implement a NAND gate -- a logically-irreversible universal logic gate. We show how to practically implement this in a device created by two inductively-coupled superconducting quantum interference devices (SQUIDs). We identify circuit parameter ranges that give rise to effective CEs and establish the device's robustness against logical errors. These SQUID-based logical devices are capable of operating above GHz frequencies and at the $k_\text{B} T$ energy scale. Due to this, optimized devices and associated protocols provide a universal-computation substrate that is both computationally fast and energy efficient.