Extracting Equations of Motion from Superconducting Circuits

TL;DR

This paper introduces a method to efficiently derive equations of motion for superconducting circuits, enabling scalable design and analysis of complex quantum devices like QFPs for classical computation.

Contribution

It develops specialized derivation techniques and optimization methods for superconducting circuits, simplifying the process of modeling their energetics and dynamics.

Findings

Successfully reproduces the potential energy landscape of QFPs

Demonstrates coupling of two QFPs for 2-bit computation

Provides a foundation for designing universal logic gates

Abstract

Alternative computing paradigms open the door to exploiting recent innovations in computational hardware to probe the fundamental thermodynamic limits of information processing. One such paradigm employs superconducting quantum interference devices (SQUIDs) to execute classical computations. This, though, requires constructing sufficiently complex superconducting circuits that support a suite of useful information processing tasks and storage operations, as well as understanding these circuits' energetics. First-principle circuit design, though, leads to prohibitive algebraic complications when deriving the effective equations of motion -- complications that to date have precluded achieving these goals, let alone doing so efficiently. We circumvent these complications by (i) specializing our class of circuits and physical operating regimes, (ii) synthesizing existing derivation techniques to suit these specializations, and (iii) implementing solution-finding optimizations which facilitate physically interpreting circuit degrees of freedom that respect physically-grounded constraints. This leads to efficient, practical circuit prototyping and access to scalable circuit architectures. The analytical efficiency is demonstrated by reproducing the potential energy landscape generated by the quantum flux parametron (QFP). We then show how inductively coupling two QFPs produces a device that is capable of executing 2-bit computations via its composite potential energy landscape. More generally, the synthesis methods detailed here provide a basis for constructing universal logic gates and investigating their thermodynamic performance.