We introduce the Control Erasure (CE) protocol, which generalizes the Landauer information erasure protocol to an effective two-dimensional potential energy landscape.

Performing a CE involves dynamically changing the landscapes' energy minima---corresponding to the landscape's darker purple colors---in order to control what information is erased or stored. An example CE involves erasing the yellow particle into the cyan particle's location, while storing the silver and pink particles within their respective minima.

Executing successive CEs can lead to performing a NAND gate---an irreversible universal logic gate that is commonly used to construct modern computing architectures. We show how to carry out a NAND gate with a device created by inductively coupling two superconducting quantum interference devices (SQUIDs): This device can serve as a computationally fast and energy efficient universal computing substrate!

Previously, the network theory approach to analyzing superconducting circuits had limitations, such as only being able to consider at most one linear inductor per circuit loop. We void this assumption and address its consequences, and by doing so, we extended this approach to be able to handle more complicated superconducting circuits.

As an example, we derived the potential energy potential surface generated by a device constructed from two inductively-coupled SQUIDs. This landscape will serve as a test-bed for constructing energy efficient universal logic gates, and investigating their thermodynamic performance.