The description of gene interactions that constantly occur in the cellular environment is an extremely challenging task due to an immense number of degrees of freedom and incomplete knowledge about microscopic details. Hence, a coarse-grained and rather powerful modeling of such dynamics is provided by Boolean Networks (BNs). BNs are dynamical systems composed of Boolean agents and a record of their possible interactions over time. Stable states in these systems are called attractors which are closely related to the cellular expression of biological phenotypes. Identifying the full set of attractors is, therefore, of substantial biological interest. However, for conventional high-performance computing, this problem is plagued by an exponential growth of the dynamic state space. Here, we demonstrate a novel quantum search algorithm inspired by Grover's algorithm to be implemented on quantum computing platforms. The algorithm performs an iterative suppression of states belonging to basins of previously discovered attractors from a uniform superposition, thus increasing the amplitudes of states in basins of yet unknown attractors. This approach guarantees that a new attractor state is measured with each iteration of the algorithm, an optimization not currently achieved by any other algorithm in the literature. Tests of its resistance to noise have also shown promising performance on devices from the current Noise Intermediate Scale Quantum Computing (NISQ) era.

翻译：由于自由度数量巨大且微观细节知识不完整，描述细胞环境中持续发生的基因相互作用是一项极具挑战性的任务。因此，布尔网络（BNs）为此类动力学提供了粗粒度且相当强大的建模方法。布尔网络是由布尔智能体及其随时间可能发生的相互作用记录组成的动态系统。这些系统中的稳定状态被称为吸引子，它们与生物表型的细胞表达密切相关。因此，识别完整的吸引子集合具有重要的生物学意义。然而，对于传统高性能计算而言，该问题因动态状态空间的指数级增长而备受困扰。本文展示了一种受Grover算法启发的新型量子搜索算法，可在量子计算平台上实现。该算法通过迭代抑制来自均匀叠加态中已发现吸引子盆地的状态，从而增大未知吸引子盆地中状态的振幅。该方法保证了算法的每次迭代都能测量到一个新的吸引子状态，这是目前文献中其他算法尚未实现的优化。其在噪声环境下的测试也表明，在当前噪声中等规模量子计算（NISQ）时代的设备上表现出良好的性能。