Extracting equations of motion from superconducting circuits

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-principles circuit design 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 and practical circuit prototyping, as well as accessing scalable circuit architectures. The analytical efficiency is demonstrated by reproducing the potential energy landscape generated by a SQUID. We then show how inductively coupling two SQUIDs produces a device that is capable of executing two-bit computations via its composite potential energy landscape. More generally, the synthesized methods detailed here provide a basis for constructing universal logic gates and investigating their thermodynamic performance.

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