An On-Chip Control and Readout Circuit Design for an Ising Annealer

In this work, we propose a novel methodology for on-chip control and readout circuits for the Lechner-Hauke-Zoller (LHZ) based superconductor Ising machines (IMs). By enabling the precise mapping of weight values on each spin realized by the Josephson parametric oscillator (JPO), we solve combinatorial optimization problems (COPs) efficiently. Our approach overcomes key challenges in mapping weighted Non-deterministic Polynomial Complete (NPC) problems. We demonstrate 3-bit weight resolution by dynamically modulating the phase of the pump current, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$I_{pump}$</tex-math></inline-formula>, in JPOs using integrated control circuits. For the readout, we designed a Quasi One Junction SQUID (QOS) circuit capable of detecting 0 and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pi$</tex-math></inline-formula> phase differences at the output of the JPOs. Finally, we validate our methodology by solving two weighted NPC problems by simulation.