Výpočet vlastních čísel pomocí metod kvantového počítání

Abstract

This bachelor thesis deals with the calculation of eigenvalues using quantum counting methods. The main goal is to understand the basic concepts of quantum mechanics and apply them to quantum computation. The thesis also focuses on learning about the Python language and the Qiskit package for implementing the solution. An eigenvalue problem solver (eigen-solver) is implemented and the calculation of potential overfaces for H2 molecules is performed.

The first part of the thesis is devoted to the study of quantum mechanics and its basic concepts such as quantum state, qubits, quantum gates and quantum circuits. It also deals with the principle of superposition and quantum algorithms such as the quantum Fourier transform (QFT) and quantum phase approximation (QPE), which are crucial for the computation of eigenvalues.

In the next part of the paper, the eigen-solver is implemented using the Qiskit package. A quantum circuit for QPE is created and it is shown how to use it for eigenvalue computation. Subsequently, the calculation of the potential superplanes of the molecule H2 is performed by constructing a linear system and implementing it in Qiskit.

Important aspects of quantum computation such as decoherence and mitigation are also discussed. It is shown that decoherence limits the stability of quantum systems and contributes to computational errors. Various mitigation methods are described, including the addition of noise to quantum circuits and the use of error mitigation to increase the accuracy of results.

Finally, the future of quantum computing and its applications are discussed. The need for further development of quantum technologies and the limitations of current Noisy Intermediate-Scale Quantum(NISQ) systems are mentioned. The use of hybrid algorithms such as Variational Quantum Eigensolver(VQE), which combine quantum and classical computation to offload part of the computation to quantum processors, is proposed.