Noise and trainability in quantum machine learning ; Bruit et capacité d'apprentissage en apprentissage automatique quantique
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| Title: | Noise and trainability in quantum machine learning ; Bruit et capacité d'apprentissage en apprentissage automatique quantique |
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| Authors: | Heyraud, Valentin |
| Contributors: | Laboratoire Matériaux et Phénomènes Quantiques (MPQ (UMR_7162)), Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Université Paris Cité, Cristiano Ciuti |
| Source: | https://theses.hal.science/tel-04702049 ; Mathematical Physics [math-ph]. Université Paris Cité, 2023. English. ⟨NNT : 2023UNIP7237⟩. |
| Publisher Information: | CCSD |
| Publication Year: | 2023 |
| Subject Terms: | Kernel methods, Clifford circuits, Variational quantum algorithms, Quantum computing, Decoherence, Reservoir computing, Machine learning, Quantum information, Open quantum systems, Circuits Clifford, Algorithmes quantiques variationnels, Calcul quantique, Décohérence, Informatique de réservoir, Méthodes à noyau, Apprentissage automatique, Intelligence artificielle, Information quantique, Systèmes quantiques ouverts, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] |
| Description: | This thesis is devoted to the exploration of the interface between quantum computing and machine learning, with an emphasis on the effects of noise and decoherence. In the first part, we investigate the use of open quantum systems to tackle classical pattern recognition tasks. In particular, we study the impact of noise on quantum kernel machines in a reservoir computing setup. The models we consider are based on the use of a large and uncontrolled quantum system, the reservoir, that is excited with an input signal to be processed. Measurements are then performed on the system, and a linear combination of the outcomes is optimized to achieve the desired processing task. Within the theoretical framework associated with kernel methods, we analyze the effect of dissipation on the expressive power of these models. We show that the noise affecting the reservoir can act as an implicit regularization that helps to prevent over-fitting. These findings are supported by a numerical study of a set of noisy kernel machines based on driven-dissipative chains of spins exhibiting decoherence and whose Markovian evolution is described by a Lindblad master equation. The second part of the thesis focuses on variational quantum algorithms. There, we present an efficient classical simulation scheme to estimate the trainability of a parameterized quantum circuit. We first study the quantum channels associated with the averages of random Z-rotations of one and two qubits. Upon some assumptions, we show that these average rotation channels can be decomposed into convex sums of Clifford channels. This result, which can be interpreted as an artificial decoherence induced by the random choice of the rotation angles, allows us to derive our efficient estimation scheme based on the celebrated Gottesman-Knill theorem. Among other figures of merits, this method enables to efficiently estimate the average amplitude of the cost-function gradient through classical simulations. This method is scalable and can be used to certify trainability for ... |
| Document Type: | doctoral or postdoctoral thesis |
| Language: | English |
| Relation: | NNT: 2023UNIP7237 |
| Availability: | https://theses.hal.science/tel-04702049 https://theses.hal.science/tel-04702049v1/document https://theses.hal.science/tel-04702049v1/file/va_Heyraud_Valentin.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| Accession Number: | edsbas.EAF23682 |
| Database: | BASE |
Nájsť tento článok vo Web of Science | Abstract: | This thesis is devoted to the exploration of the interface between quantum computing and machine learning, with an emphasis on the effects of noise and decoherence. In the first part, we investigate the use of open quantum systems to tackle classical pattern recognition tasks. In particular, we study the impact of noise on quantum kernel machines in a reservoir computing setup. The models we consider are based on the use of a large and uncontrolled quantum system, the reservoir, that is excited with an input signal to be processed. Measurements are then performed on the system, and a linear combination of the outcomes is optimized to achieve the desired processing task. Within the theoretical framework associated with kernel methods, we analyze the effect of dissipation on the expressive power of these models. We show that the noise affecting the reservoir can act as an implicit regularization that helps to prevent over-fitting. These findings are supported by a numerical study of a set of noisy kernel machines based on driven-dissipative chains of spins exhibiting decoherence and whose Markovian evolution is described by a Lindblad master equation. The second part of the thesis focuses on variational quantum algorithms. There, we present an efficient classical simulation scheme to estimate the trainability of a parameterized quantum circuit. We first study the quantum channels associated with the averages of random Z-rotations of one and two qubits. Upon some assumptions, we show that these average rotation channels can be decomposed into convex sums of Clifford channels. This result, which can be interpreted as an artificial decoherence induced by the random choice of the rotation angles, allows us to derive our efficient estimation scheme based on the celebrated Gottesman-Knill theorem. Among other figures of merits, this method enables to efficiently estimate the average amplitude of the cost-function gradient through classical simulations. This method is scalable and can be used to certify trainability for ... |
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