About the Efficiency of Loading Density Functions into Quantum States

Author: Gabriel Marín Sánchez
Advisor(s): Mikel Sanz and Yue Ban
Master in Quantum Science and Technology
Publication year: 2021
Abstract: The loading of classical data into a quantum computer represents an essential requirement for emerging quantum computing fields such as quantum machine learning or quantum algorithms. Thus, the lack of protocols for efficient quantum state preparation is a major bottleneck for their applicability. In this Master Thesis, we introduce a quantum state preparation method that addresses this issue and solve it for density functions. Based on the Grover-Rudolph algorithm and assuming an acceptable error emeasured in terms of the fidelity, our proposed protocol reduces the complexity from O(2^n) to O(2^k0(e)) by clustering angles, with n the number of qubits and k0(e) asymptotically independent of n. Our result guarantees a dramatic reduction in the number of two-qubit gates required for the loading discretized density functions. Therefore, the presented algorithm serves as a stepping stone for new applications in quantum machine learning, and in quantum computation in general. Additionally, we present an ansatz for variational models, inspired by our protocol, that is capable of loading functions containing zeros, and thus do not satisfy the necessary conditions of our procedure.
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