A Novel Quantum Algorithm for Efficient Attractor Search in Gene Regulatory Networks

Mirko Rossini, Felix M. Weidner, Joachim Ankerhold, Hans A. Kestler
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Abstract

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.
用于基因调控网络中高效吸引子搜索的新型量子算法
由于自由度极大且对微观细节的了解不全面,描述细胞环境中不断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(Boolean Networks,BNs)为此类动力学提供了一个粗粒度且相当强大的模型。布尔网络是由布尔代理和它们在一段时间内可能发生的相互作用记录组成的动力系统。系统中的稳定状态称为吸引子,与生物表型的细胞表达密切相关。因此,识别全套吸引子具有重要的生物学意义。然而,对于传统的高性能计算来说,这个问题受到动态状态空间指数级增长的困扰。在这里,我们展示了一种受格罗弗算法启发的新型量子搜索算法,该算法可在量子计算平台上实现。该算法从均匀叠加中对属于先前发现的吸引子盆地的状态进行迭代抑制,从而增加未知吸引子盆地中状态的振幅。这种方法保证了算法的每次迭代都能测出一个新的吸引子状态,这是目前文献中其他算法无法实现的优化。对其抗噪声能力的测试也表明,它在当前噪声中等规模量子计算(NISQ)时代的设备上具有良好的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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