Abstract Iris The power of quantum computing lies in its ability to perform certain calculations and solve complex problems exponentially faster than classical computers. This potential has profound implications for a wide range of fields, including particle physics. This thesis lays a fundamental foundation for understanding quantum computing. Particular emphasis is placed on the intricate process of quantum gate decomposition, an elementary lynchpin that underpins the development of quantum algorithms and plays a crucial role in this research. In particular, this concerns the implementation of quantum algorithms designed to simulate the dynamic evolution of multiparticle quantum systems  socalled Hamiltonian simulations. The concept of quantum gate decomposition is introduced and linked to quantum circuit optimisation. The decomposition of quantum gates plays a crucial role in faulttolerant quantum computing in the sense that an optimal implementation of a quantum gate is essential to efficiently perform a quantum simulation, especially for nearterm quantum computers. Part of this thesis aims to propose a new explicit tensorial notation of quantum computing. Two notations are commonly used in the literature. The first is the Dirac notation and the other standard formalism is based on the socalled computational basis. The main disadvantage of the latter is the exponential growth of vector and matrix dimensions and the fact that it hides some relevant quantum properties of the operations by increasing the apparent number of independent variables. A third possible notation is introduced here, which describes qubit states as tensors and quantum gates as multilinear or quasimultilinear maps. Some advantages for the detection of separable and entangled systems and for measurement techniques are also shown. Finally, this thesis demonstrates the advantage of quantum computing in the description of multiparticle quantum systems by proposing a quantum algorithm to simulate collective neutrino oscillations. Collective flavour oscillations of neutrinos due to forward neutrinoneutrino scattering provide an intriguing manybody system for time evolution simulations on a quantum computer. These phenomena are of particular interest in extreme astrophysical settings such as corecollapse supernovae, neutron star mergers and the early universe. A detailed description of the physical phenomena and environments in which collective flavor oscillations occur is first reported, and the derivation of the Hamiltonian governing the evolution of flavor oscillations is detailed. The aim is to reproduce this evolution using a quantum algorithm. To manage the computational complexity, we use the Trotter approximation of the time evolution operator, which mitigates the exponential growth of circuit complexity. The quantum algorithm was designed to work on a trappedion based testbed (the theory of which is presented in detail). After machineaware optimisation, the quantum circuit implementing the algorithm was run on the real quantum machine 'Quantinuum', and the results are presented and discussed.
Digital Quantum Computing for ManyBody Simulations / Amitrano, Valentina.  (2023 Dec 13), pp. 1150. [10.15168/11572_398733]
Digital Quantum Computing for ManyBody Simulations
Amitrano, Valentina
20231213
Abstract
Abstract Iris The power of quantum computing lies in its ability to perform certain calculations and solve complex problems exponentially faster than classical computers. This potential has profound implications for a wide range of fields, including particle physics. This thesis lays a fundamental foundation for understanding quantum computing. Particular emphasis is placed on the intricate process of quantum gate decomposition, an elementary lynchpin that underpins the development of quantum algorithms and plays a crucial role in this research. In particular, this concerns the implementation of quantum algorithms designed to simulate the dynamic evolution of multiparticle quantum systems  socalled Hamiltonian simulations. The concept of quantum gate decomposition is introduced and linked to quantum circuit optimisation. The decomposition of quantum gates plays a crucial role in faulttolerant quantum computing in the sense that an optimal implementation of a quantum gate is essential to efficiently perform a quantum simulation, especially for nearterm quantum computers. Part of this thesis aims to propose a new explicit tensorial notation of quantum computing. Two notations are commonly used in the literature. The first is the Dirac notation and the other standard formalism is based on the socalled computational basis. The main disadvantage of the latter is the exponential growth of vector and matrix dimensions and the fact that it hides some relevant quantum properties of the operations by increasing the apparent number of independent variables. A third possible notation is introduced here, which describes qubit states as tensors and quantum gates as multilinear or quasimultilinear maps. Some advantages for the detection of separable and entangled systems and for measurement techniques are also shown. Finally, this thesis demonstrates the advantage of quantum computing in the description of multiparticle quantum systems by proposing a quantum algorithm to simulate collective neutrino oscillations. Collective flavour oscillations of neutrinos due to forward neutrinoneutrino scattering provide an intriguing manybody system for time evolution simulations on a quantum computer. These phenomena are of particular interest in extreme astrophysical settings such as corecollapse supernovae, neutron star mergers and the early universe. A detailed description of the physical phenomena and environments in which collective flavor oscillations occur is first reported, and the derivation of the Hamiltonian governing the evolution of flavor oscillations is detailed. The aim is to reproduce this evolution using a quantum algorithm. To manage the computational complexity, we use the Trotter approximation of the time evolution operator, which mitigates the exponential growth of circuit complexity. The quantum algorithm was designed to work on a trappedion based testbed (the theory of which is presented in detail). After machineaware optimisation, the quantum circuit implementing the algorithm was run on the real quantum machine 'Quantinuum', and the results are presented and discussed.File  Dimensione  Formato  

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