Arnold's Bifurcation Principle for Anticipating Electro-Thermal Quench in Josephson-Junction Control Electronics for Quantum Computers
Year: 2026
Type: preprint
Abstract: Superconducting quantum computers depend on classical control electronics that sit in the same cold refrigerator as the qubits. One such technology, Single Flux Quantum (SFQ) logic, is built entirely out of current-biased Josephson junctions. A junction that carries current and switches does not stay perfectly cold: it dissipates a little heat every time it switches. If that heat is not carried away fast enough, the junction's own local temperature can creep upward. Since a junction's critical current falls as its temperature rises, this creates a feedback loop: more heat, less critical current, more of the junction's operating margin used up, more heat again. Taken far enough, this loop does not stop at a mistimed pulse. It ends with the junction, andpossibly its neighbors, losing superconductivity altogether: a true quench. This is a different and more serious failure than the pulse-timing errors we studied in our earlier work. This paper asks whether the same idea we used before, watching a system's leading eigenvalue drift toward zero as it nears a bifurcation, can also give an early warning of this kind of thermal quench, in time for the control system to shunt current away from the affected channel before superconductivity is actually lost. We build a simple, two-variable model of a single current-biased junction with self-heating, grounded entirely in physics already established in the literature. We show that this model has exactly the same kind of fold, the same kind of eigenvalue-goes-to-zero signature, as the switching problem we studied before. We are honest about what we cannot do here: this quench process depends on real thermal noise, real materialdisorder, and real cooling-power limits that cannot be faithfully invented in a simulation. We do not attempt to validate this framework on synthetic data. We explain why, and we describe exactly what a real hardware team, such as the groups already building SFQ-controlled quantum processors, would need to do to test it.
Author: VAITHYANATHAN, PRAKASH
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204050215
Cites:
Cited by:
Related to: