Determining probability density functions with adiabatic quantum computing
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913637273174016 |
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| author | Robbiati, Matteo Cruz-Martinez, Juan M. Carrazza, Stefano |
| author_facet | Robbiati, Matteo Cruz-Martinez, Juan M. Carrazza, Stefano |
| contents | The two main approaches to quantum computing are gate-based computation and analog computation, which are polynomially equivalent in terms of complexity, and they are often seen as alternatives to each other. In this work, we present a method for fitting one-dimensional probability distributions as a practical example of how analog and gate-based computation can be used together to perform different tasks within a single algorithm. In particular, we propose a strategy for encoding data within an adiabatic evolution model, which accomodates the fitting of strictly monotonic functions, as it is the cumulative distribution function of a dataset. Subsequently, we use a Trotter-bounded procedure to translate the adiabatic evolution into a quantum circuit in which the evolution time t is identified with the parameters of the circuit. This facilitates computing the probability density as derivative of the cumulative function using parameter shift rules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11346 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Determining probability density functions with adiabatic quantum computing Robbiati, Matteo Cruz-Martinez, Juan M. Carrazza, Stefano Quantum Physics High Energy Physics - Phenomenology The two main approaches to quantum computing are gate-based computation and analog computation, which are polynomially equivalent in terms of complexity, and they are often seen as alternatives to each other. In this work, we present a method for fitting one-dimensional probability distributions as a practical example of how analog and gate-based computation can be used together to perform different tasks within a single algorithm. In particular, we propose a strategy for encoding data within an adiabatic evolution model, which accomodates the fitting of strictly monotonic functions, as it is the cumulative distribution function of a dataset. Subsequently, we use a Trotter-bounded procedure to translate the adiabatic evolution into a quantum circuit in which the evolution time t is identified with the parameters of the circuit. This facilitates computing the probability density as derivative of the cumulative function using parameter shift rules. |
| title | Determining probability density functions with adiabatic quantum computing |
| topic | Quantum Physics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2303.11346 |