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. In this work, we extend an alternative computing paradigm which utilizes distributions of microstates to store information in the metastable minima determined by an effective potential energy landscape. These minima serve as mesoscopic memory states which are manipulated by a dynamic landscape to perform information processing. Central to our results is the control erase (CE) protocol, which manipulates the landscape's metastable minima to control whether information is preserved or erased. Importantly, successive executions of this protocol 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 characterize the protocol's robustness by comparing relevant protocol timescales. Due to their superconducting operational temperatures, performing optimized CEs with SQUIDs can serve as a platform for highly energy-efficient universal computation.