Limitations of variational quantum algorithms: a quantum optimal transport approach
| Autor: | Giacomo De Palma, Milad Marvian, Cambyse Rouzé, Daniel Stilck França |
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| Přispěvatelé: | De Palma, Giacomo, Marvian, Milad, Rouzé, Cambyse, França, Daniel Stilck, University of Bologna/Università di Bologna, Department of Electrical and Computer Engineering [Albuquerque] (ECE Department), The University of New Mexico [Albuquerque], Zentrum Mathematik [Munchen] (TUM), Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne] (TUM), Traitement optimal de l'information avec des dispositifs quantiques (QINFO), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Université Grenoble Alpes (UGA)-Inria Lyon, Institut National de Recherche en Informatique et en Automatique (Inria) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Quantum Physics
[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] Quantum information General Computer Science Applied Mathematics Quantum algorithm FOS: Physical sciences General Physics and Astronomy Electrical and Electronic Engineering Quantum Physics (quant-ph) Mathematical Physics Electronic Optical and Magnetic Materials |
| Zdroj: | De Palma, G, Marvian, M, Rouzé, C & França, D S 2023, ' Limitations of Variational Quantum Algorithms : A Quantum Optimal Transport Approach ', PRX Quantum, vol. 4, no. 1, 010309 . https://doi.org/10.1103/PRXQuantum.4.010309 |
| Popis: | The impressive progress in quantum hardware in the last years has raised the interest of the quantum computing community in harvesting the computational power of such devices. However, in the absence of error correction, these devices can only reliably implement very shallow circuits or comparatively deeper circuits at the expense of a nontrivial density of errors. In this work, we obtain extremely tight limitation bounds for standard NISQ proposals in both the noisy and noiseless regimes, with or without error-mitigation tools. The bounds limit the performance of both circuit model algorithms, such as QAOA, and also continuous-time algorithms, such as quantum annealing. In the noisy regime with local depolarizing noise $p$, we prove that at depths $L=\mathcal{O}(p^{-1})$ it is exponentially unlikely that the outcome of a noisy quantum circuit outperforms efficient classical algorithms for combinatorial optimization problems like Max-Cut. Although previous results already showed that classical algorithms outperform noisy quantum circuits at constant depth, these results only held for the expectation value of the output. Our results are based on newly developed quantum entropic and concentration inequalities, which constitute a homogeneous toolkit of theoretical methods from the quantum theory of optimal mass transport whose potential usefulness goes beyond the study of variational quantum algorithms. Close to the published version |
| Databáze: | OpenAIRE |
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