Quantum-Inspired Ising Machines for Quantum Chemistry Calculations

TL;DR

The paper investigates quantum-inspired Ising solvers (CIM variants and Simulated Bifurcation) as scalable alternatives to gate-based quantum chemistry calculations on NISQ hardware. By mapping molecular Hamiltonians to Ising form and applying steepest-descent post-processing, the authors demonstrate rapid reconstruction of H2 and H2O energy profiles with accuracy comparable to traditional methods. The results show that the Chaotic Feedback Control (CFC) variant, combined with GPU-accelerated sampling, yields efficient convergence and substantial speed-ups over typical quantum hardware runtimes. These findings suggest a practical pathway for scalable quantum chemistry calculations and hybrid quantum–classical workflows applicable to larger molecular systems and materials science problems.

Abstract

Four decades after Richard Feynman's famous remark, we have reached a stage at which nature can be simulated quantum mechanically. Quantum simulation is among the most promising applications of quantum computing. However, like many quantum algorithms, it is severely constrained by noise in near-term hardware. Quantum-inspired algorithms provide an attractive alternative by avoiding the need for error-prone quantum devices. In this study, we demonstrate that the coherent Ising machine and simulated bifurcation algorithms can accurately reproduce the electronic energy profiles of H_2 and H_2O, capturing their essential energetic features. Notably, we obtain computational times of 1.2 s and 2.4 s for the H_2 and H_2O profiles, respectively, representing a substantial speed-up compared to gate-based quantum computing approaches, which typically require at least 6 s to compute a single molecular geometry with comparable accuracy. These results highlight the potential of quantum-inspired approaches for scaling to larger molecular systems and for future applications in chemistry and materials science.

Figures (5)

• Figure 1: Schematic presentation of the hybrid quantum–inspired algorithm used to determine the ground-state energy profiles of $H_2$ and $H_2O$. (a) Conversion of the molecular Hamiltonian into Ising form. (b) Feeding sampled data into quantum-inspired algorithms. (c) Applying the steepest descent method for result refinement.
• Figure 2: Schematic of the hybrid algorithm employed in this study, extending and refining the framework originally introduced by Alán Aspuru-Guzik Areview2019.
• Figure 3: Calculated ground-state energy of the hydrogen molecule as a function of internuclear distance using four quantum-inspired algorithms based on a single computational sample. The subfigures correspond to: (a) Separated Feedback Control (SFC), (b) Chaotic Feedback Control (CFC), (c) Discrete Simulated Bifurcation (dSB), and (d) Chaotic Amplitude Control (CAC). In each plot, the different colored lines represent variations in the key algorithm parameter $r$ (ranging from $r = 2$ to $r = 6$), illustrating its influence on the energy estimation.
• Figure 4: Performance of solving the hydrogen Hamiltonian for $r = 2$ and $r = 6$. Two experimental approaches are presented: increasing the number of Ising machine samples up to $100$, which allows the algorithms to reach the true global minimum, and using a single-shot execution of the Ising machines combined with a steepest descent algorithm, which achieves the same result.
• Figure 5: Energy profile of the water molecule computed using the CFC variant of the CIM, selected for its superior performance. The energy was evaluated over the bond-length range $r=[2,6]$.