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IEEE Transactions on Applied Superconductivity

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

Beyza Zeynep Ucpinar, Mustafa Altay Karamuftuoglu, Sasan Razmkhah, Mehdi Kamal, Massoud Pedram

Published Feb 7, 2025• 0 citations
Publisher

Abstract

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,$I_{pump}$, in JPOs using integrated control circuits. For the readout, we designed a Quasi One Junction SQUID (QOS) circuit capable of detecting 0 and$\pi$phase differences at the output of the JPOs. Finally, we validate our methodology by solving two weighted NPC problems by simulation.

DOI
10.1109/tasc.2025.3540049

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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,IpumpI_{pump}Ipump​, in JPOs using integrated control circuits. For the readout, we designed a Quasi One Junction SQUID (QOS) circuit capable of detecting 0 andπ\piπphase differences at the output of the JPOs. Finally, we validate our methodology by solving two weighted NPC problems by simulation.
Ising machines (IMs) have emerged as a promising solution for rapidly solving NP-complete combinatorial optimization problems, surpassing the capabilities of traditional computing methods. By efficiently determining the ground state of the Hamiltonian during the annealing process, IMs can effectively complement CPUs in tackling optimization challenges. To realize these IMs, a bistable oscillator is essential to emulate the atomic spins and interactions of the Ising model. This study introduces a Josephson parametric oscillator (JPO) based tile structure, serving as a fundamental unit for scalable superconductor-based IMs. Leveraging the bistable nature of JPOs, which are superconductor-based oscillators, the proposed machine can operate at frequencies of $\ensuremath{\sim}7.5$ GHz while consuming significantly less power (by three orders of magnitude) than complementary metal-oxide semiconductor based systems. Furthermore, the compatibility of the proposed tile structure with the Lechner-Hauke-Zoller architecture ensures its viability for large-scale integration. We conducted simulations of the tile in a noisy environment to validate its functionality. We verified its operational characteristics by comparing the results with the analytical solution of its Hamiltonian model. This verification demonstrates the feasibility and effectiveness of the JPO-based tile in implementing IMs, opening new avenues for efficient and scalable combinatorial optimization in quantum computing.
Complex combinatorial optimization problems serve as the foundation for various real-world applications. The time required to identify the optimal solutions to these problems escalates dramatically as the problem grows. Nevertheless, transforming these problems into another NP-complete problem, like the Ising model with a representation as a physical phenomenon, can be efficiently approximated. In this work, we use a system of bistable Josephson parametric oscillators (JPO) as artificial spins to realize the Ising model on a superconductor fabric. By integrating these JPOs based on the Lechner, Zoller, and Hauke (LHZ) architecture, we design a superconductor-based scalable Ising machine (IM). We develop a framework to automatically create the IM circuit and tune its parameters. The circuit functionality is assessed by simulating an IM designed for solving four-, six-, and ten-node unweighted Max-Cut problems.
We theoretically present new unit circuits of Kerr parametric oscillators (KPOs) with four-body interactions, which enable the scalable embedding of all-to-all connected logical Ising spins using the Lechner-Hauke-Zoller (LHZ) scheme. These unit circuits enable four-body interactions using linear couplers, making the circuit fabrication and characterization much simpler than those of conventional unit circuits with nonlinear couplers. Numerical calculations indicate that the magnitudes of the coupling constants can be comparable to those in conventional circuits. On the basis of this theory, we designed a four-KPO circuit and experimentally confirmed the four-body correlation by measuring the pump-phase dependence of the parity of the four-KPO states. We show that the choice of the pump frequencies are important not only to enable the four-body interaction, but to cancel the effects of other unwanted interactions. Using the circuit, we demonstrated the quantum annealing based on the LHZ scheme, where the strength of the interaction between the logical Ising spins is mapped to the local field and controlled by a coherent drive applied to each KPO.
This paper presents a CMOS-compatible Lechner-Hauke-Zoller (LHZ)--based analog tile structure as a fundamental unit for developing scalable analog Ising machines (IMs). In the designed LHZ tile, the voltage-controlled oscillators are employed as the physical Ising spins, while for the ancillary spins, we introduce an oscillator-based circuit to emulate the constraint needed to ensure the correct functionality of the tile. We implement the proposed LHZ tile in 12nm FinFET technology using the Cadence Virtuoso. Simulation results show the proposed tile could converge to the results in about 31~ns. Also, the designed spins could operate at approximately 13~GHz.
Abstract Josephson parametric oscillators (JPOs) have potential as fundamental building blocks for large-scale quantum annealing systems. To scale up such systems, both readout and control circuits need to be implemented at cryogenic temperatures. Adiabatic quantum flux parametron (AQFP) circuits are well suited for such environments due to their ultra-low power consumption. This paper proposes a phase-state readout scheme for JPOs based on AQFP circuits, which enables real-time digitization of oscillation phases. A JPO was fabricated, and the concept was experimentally validated at 4.2 K. After confirming stable oscillations in the JPO, a digital readout method using AQFP circuits was demonstrated. Analysis of the probability of obtaining a logical ‘1’ at the output revealed a clear phase-dependent behavior. Furthermore, our simulations predicted a readout fidelity of nearly 100% at millikelvin temperatures, demonstrating the feasibility of AQFP-based phase-state readout for future large-scale quantum annealing systems.
There is a significant ongoing effort in realizing quantum annealing with different physical platforms. The challenge is to achieve a fully programmable quantum device featuring coherent adiabatic quantum dynamics. Here we show that combining the well-developed quantum simulation toolbox for Rydberg atoms with the recently proposed Lechner-Hauke-Zoller (LHZ) architecture allows one to build a prototype for a coherent adiabatic quantum computer with all-to-all Ising interactions and, therefore, a platform for quantum annealing. In LHZ an infinite-range spin-glass is mapped onto the low energy subspace of a spin-1/2 lattice gauge model with quasi-local four-body parity constraints. This spin model can be emulated in a natural way with Rubidium and Caesium atoms in a bipartite optical lattice involving laser-dressed Rydberg-Rydberg interactions, which are several orders of magnitude larger than the relevant decoherence rates. This makes the exploration of coherent quantum enhanced optimization protocols accessible with state-of-the-art atomic physics experiments.