Molecular docking (MD) is a crucial task in drug design, which predicts the position, orientation, and conformation of the ligand when it is bound to a target protein. It can be interpreted as a combinatorial optimization problem, where quantum annealing (QA) has shown a promising advantage for solving combinatorial optimization. In this work, we propose a novel quantum molecular docking (QMD) approach based on a QA-inspired algorithm. We construct two binary encoding methods to efficiently discretize the degrees of freedom with an exponentially reduced number of bits and propose a smoothing filter to rescale the rugged objective function. We propose a new quantum-inspired algorithm, hopscotch simulated bifurcation (hSB), showing great advantages in optimizing over extremely rugged energy landscapes. This hSB can be applied to any formulation of an objective function under binary variables. An adaptive local continuous search is also introduced for further optimization of the discretized solution from hSB. Concerning the stability of docking, we propose a perturbation detection method to help rank the candidate poses. We demonstrate our approach on a typical data set. QMD has shown advantages over the search-based Autodock Vina and the deep-learning DIFFDOCK in both redocking and self-docking scenarios. These results indicate that quantum-inspired algorithms can be applied to solve practical problems in drug discovery even before quantum hardware become mature.

How to quickly solve the problem of high-order unconstrained binary optimization (HUBO)? This problem has attracted much attention because of its importance and wide-range applications. Here we present a quantum algorithm and its corresponding quantum-inspired classical algorithm for this problem, and achieve algorithmic speedup by using gauge symmetry. Specifically we map the HUBO problem to quantum Z2 lattice gauge theory defined on the dual graph, and propose the so-called gauged local quantum annealing (gLQA), which is the local quantum annealing (LQA) protected by the gauge symmetry. By running the quantum-inspired classical algorithm, we demonstrate that gLQA reduces the computational time by one order of magnitude from that of LQA.

Conformation generation, also known as molecular unfolding (MU), is a crucial step in structure-based drug design, remaining a challenging combinatorial optimization problem. Quantum annealing (QA) has shown great potential for solving certain combinatorial optimization problems over traditional classical methods such as simulated annealing (SA). However, a recent study showed that a 2000-qubit QA hardware was still unable to outperform SA for the MU problem. Here, we propose the use of quantum-inspired algorithm to solve the MU problem, in order to go beyond traditional SA. We introduce a highly-compact phase encoding method which can exponentially reduce the representation space, compared with the previous one-hot encoding method. For benchmarking, we tested this new approach on the public QM9 dataset generated by density functional theory (DFT). The root-mean-square deviation between the conformation determined by our approach and DFT is negligible (less than about 0.5 Angstrom), which underpins the validity of our approach. Furthermore, the median time-to-target metric can be reduced by a factor of five compared to SA. Additionally, we demonstrate a simulation experiment by MindQuantum using quantum approximate optimization algorithm (QAOA) to reach optimal results. These results indicate that quantum-inspired algorithms can be applied to solve practical problems even before quantum hardware become mature.

Molecular docking is an important tool for structure-based drug design, accelerating the efficiency of drug development. Complex and dynamic binding processes between proteins and small molecules require searching and sampling over a wide spatial range. Traditional docking by searching for possible binding sites and conformations is computationally complex and results poorly under blind docking. Quantum-inspired algorithms combining quantum properties and annealing show great advantages in solving combinatorial optimization problems. Inspired by this, we achieve an improved in blind docking by using quantum-inspired combined with gradients learned by deep learning in the encoded molecular space. Numerical simulation shows that our method outperforms traditional docking algorithms and deep learning-based algorithms over 10%. Compared to the current state-of-the-art deep learning-based docking algorithm DiffDock, the success rate of Top-1 (RMSD<2) achieves an improvement from 33% to 35% in our same setup. In particular, a 6% improvement is realized in the high-precision region(RMSD<1) on molecules data unseen in DiffDock, which demonstrates the well-generalized of our method.

Two classes of quantum-annealing-inspired-algorithms (QAIA), namely different variants of simulated coherent Ising machine and simulated bifurcation, have been proposed for efficiently solving combinatorial optimization problems recently. In order to certify the superiority of these algorithms, standardized comparisons among them and against other physics-based algorithms are necessary. In this work, for Max-Cut problems up to 20,000 nodes, we benchmark QAIA against quantum annealing and other physics-based algorithms. We found that ballistic simulated bifurcation excelled for chimera and small-scale graphs, achieving nearly a 50-fold reduction in time-to-solution compared to quantum annealing. For large-scale graphs, discrete simulated bifurcation achieves the lowest time-to-target and outperforms D-Wave Advantage system when tasked with finding the maximum cut value in pegasus graphs. Our results suggest that QAIA represents a promising means for solving combinatorial optimization problems in practice, and can act as a natural baseline for competing quantum algorithms. One of the most considered applications for quantum-inspired algorithms is solving combinatorial optimization problems. In this manuscript, the authors benchmark several quantum-annealing-inspired algorithms against other state-of-the-art optimizers and quantum annealer, comparing their success probabilities and time-to-solution.