A Josephson Parametric Oscillator-Based Ising Machine

Abstract

Ising machines 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, Ising machines can effectively complement CPUs in tackling optimization challenges. To realize these Ising machines, a bi-stable 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 Ising machines. Leveraging the bi-stable nature of JPOs, which are superconductor-based oscillators, the proposed machine can operate at frequencies of 7.5GHz while consuming significantly less power (by three orders of magnitude) than CMOS-based systems. Furthermore, the compatibility of the proposed tile structure with the Lechner-Hauke-Zoller (LHZ) 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 Ising machines, opening new avenues for efficient and scalable combinatorial optimization in quantum computing.

Figures (10)

• Figure 1: A general structure of the JPO-based tile. $S_1$ to $S_4$ are the JPO-based spin nodes that are coupled together, and $S_{a1}$ and $S_{a2}$ are JPO-based ancilla spins which are used to impose the constraint $C_l$. $C_{cnst}$ is the offset value added to ensure that $C_l$ is always negative in the tile structure.
• Figure 2: Circuit schematic of the Josephson parametric oscillator used as a cell to emulate the spin resonance. For symmetry we assume that $L_1 = L_2 = 7.5pH$, $I_{C1} = I_{C2} = 80\mu A$ with 15 $\Omega$ shunt resistances, and the $C_S = 4.5pF$. The resonator frequency is at 7.5 GHz.
• Figure 3: Resonator frequency calculation result with different applied DC currents. The material is Nb, and the characteristics are chosen to match the MIT LL SFQee5 process.
• Figure 4: A tile for the scalable architecture of IM. The structure has six JPOs, four as the logic and two as the ancilla. The coupler connects all JPO cells and provides interaction between them.
• Figure 5: Analytical modeling result of a tile that will be used for large-scale integration of IM. Here, the penalty term is positive, and the external field values are swiped so that the circuit can show all the possible states.