Protein structure prediction (PSP) predicts the native conformation for a given protein sequence. Classically, the problem has been shown to belong to the NP-complete complexity class. Its applications range from physics, through bioinformatics to medicine and quantum biology. It is possible however to speed it up with quantum computational methods, as we show in this paper. Here we develop a fast quantum algorithm for PSP in three-dimensional hydrophobic-hydrophilic model on body-centered cubic lattice with quadratic speedup over its classical counterparts. Given a protein sequence of n amino acids, our algorithm reduces the temporal and spatial complexities to, respectively, O(2\frac n2) and O(n2 logn). With respect to oracle-related quantum algorithms for the NP-complete problems, we identify our algorithm as optimal. To justify the feasibility of the proposed algorithm we successfully solve the problem on IBM quantum simulator involving 21 and 25 qubits. We confirm the experimentally obtained high probability of success in finding the desired conformation by calculating the theoretical probability estimations.

中文翻译：

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蛋白质结构预测的量子加速


蛋白质结构预测 (PSP) 可预测给定蛋白质序列的天然构象。经典问题已被证明属于 NP 完全复杂性类别。其应用范围从物理学、生物信息学到医学和量子生物学。然而，正如我们在本文中所示，可以通过量子计算方法来加速它。在这里，我们为体心立方晶格的三维疏水-亲水模型中的 PSP 开发了一种快速量子算法，其加速比经典算法的二次方快。给定 n 个氨基酸的蛋白质序列，我们的算法将时间和空间复杂性分别降低到 O(2\frac n2) 和 O(n2 logn)。对于 NP 完全问题的预言机相关量子算法，我们认为我们的算法是最优的。为了证明所提出算法的可行性，我们在 IBM 量子模拟器上成功解决了涉及 21 和 25 个量子位的问题。通过计算理论概率估计，我们确认了通过实验获得的成功找到所需构象的高概率。