Digital-analog quantum computing and algorithms

Author: Ana Martín Fenández
Advisor(s): Mikel Sanz
Departamento de Química Física Facultad de Ciencia y Tecnología
Publication year: 2023
Abstract: The field of quantum computing has experienced significant growth in recent years, driven by breakthroughs in the development of new algorithms, the discovery of novel quantum phenomena, and the construction of increasingly larger and more stable quantum systems. Despite these advances, the implementation of quantum algorithms on real hardware remains a significant challenge, as quantum systems are prone to errors and decoherence that can limit their computational power. In this context, the digital-analog quantum computational paradigm has emerged as a promising approach to building large-scale quantum computers and implementing quantum algorithms for practical applications. The digital-analog paradigm combines the strengths of both digital and analog quantum computing, allowing for efficient implementation of quantum algorithms with improved accuracy and error mitigation. The digital-analog paradigm is particularly well-suited for implementing quantum algorithms that require a large number of quantum gates and measurements or that involve complex entanglement structures. By leveraging the robustness of analog quantum simulation and the flexibility of digital quantum computation, the digital-analog paradigm provides a powerful framework for designing and implementing quantum algorithms on real hardware. In this thesis, we provide a detailed analysis of the digital-analog quantum computational paradigm and its application to the implementation of quantum algorithms. We first present a comprehensive overview of the digital-analog paradigm, including a toolkit for Hamiltonian simulation that enables the implementation of quantum algorithms with improved efficiency and accuracy. In addition, we present a noise model to compare the performance of the digital and digital-analog quantum computation frameworks. Next, we focus on the implementation of four relevant quantum algorithms using both the digital and digital-analog quantum computational frameworks. These algorithms include the quantum Fourier transform, the quantum phase estimation, the Harrow-Hassidim-Lloyd algorithm for solving linear systems of equations, and the quantum approximate optimization algorithm. By comparing the performance of these algorithms using both frameworks, we demonstrate that the digital-analog paradigm offers significant advantages over the digital approach, particularly in terms of reduced error rates and improved scalability. Finally, we explore how the cross-resonance effect present in superconducting circuits can be used for digital analog quantum simulations. Our results show that this effect can be leveraged to implement Hamiltonian simulations with high accuracy and efficiency, further demonstrating the potential of the digital-analog paradigm for practical quantum computing applications. In conclusion, our thesis demonstrates the promise of the digital-analog quantum computational paradigm for implementing quantum algorithms on real hardware. The digital-analog paradigm offers significant advantages over the purely digital approach, including improved scalability, reduced error rates, and greater flexibility in circuit design. We believe that this work will contribute to ongoing efforts to develop practical quantum computing technologies and pave the way for future research in the field. As the field of quantum computing continues to evolve, the exploration of new methods for improving the accuracy and efficiency of quantum computations will be crucial for advancing our understanding of quantum computing and identifying new approaches for implementing quantum algorithms.
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