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Computational material science aims to simulate substances to understand their physical properties. Bioelectronics is an interdisciplinary field that studies biological material from the conductivity point of view. In case of proteins, the folding is an important feature that directly influences physical and chemical properties. The folding modelling is a hard task. The enormous number of degrees of freedom makes modelling impossible for classical computation due to resource limits. Quantum computations aim to process multidimensional data with logarithmic growth of quantum bits. Quantum operators (gates) form quantum programs, known as circuits that process the input data. In real quantum computers, the gates are noisy and expensive to execute. Thus, it is essential to reduce the number of quantum gates both for the quality of the result and the cost of computations. This work describes an approach to decrease the number of quantum gates based on their mathematical property. The matrix properties form the first optimization technique. In this case, the optimized quantum circuit predicts precisely the same protein folding as the not optimized circuit predicts. This happens because both of the circuits are mathematically equivalent. The removal of weakly-parametrized gates forms the second optimization technique. In such case the optimized quantum circuit calculates the approximate protein folding. The error depends on parameter’s amplitude of the gates. The first technique allows to decrease the circuit depth from 631 to 629 gates while modelling the part of Azurin peptide. The second technique allows to decrease the depth to 314 gates with the threshold parameter value 0.4 radians.

Researchers have put a lot of effort into reducing the gap between current quantum processing units (QPU) capabilities and their potential supremacy. One approach is to keep supplementary computations in the CPU, and use QPU only for the core of the problem. In this work, we address the complexity of quantum algorithm of arbitrary quantum state initialization, an important building block of quantum data analysis and machine learning. QPUs do not outperform classical machines with existing precise initialization algorithms. Hence, many studies propose an approximate but robust quantum state initialization. Cutting a quantum state into a product of (almost) independent partitions with the help of CPU reduces the number of two-qubit gates, and correspondingly minimizes the loss of state fidelity in the quantum part of the algorithm. To find the least entangled qubits, current methods compute the singular value decomposition (SVD) for each qubit separately with CPU. In this paper, we optimize CPU usage and memory resource bottlenecks. We consider Tucker tensor decomposition as an alternative to the CPU-based SVD in a single low-entangled qubit detection task without the loss of solution quality. Both proposed methods outperform the SVD in time and memory for systems of at least ten qubits. We achieve an order faster implementation and two orders less memory usage for a system of 15 qubits.

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