Year: 2022
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, Alexander von Humboldt-Stiftung, Villum Fonden, Istituto Nazionale di Alta Matematica "Francesco Severi", Innovationsfonden, Deutsche Forschungsgemeinschaft, Agence Nationale de la Recherche, QuantERA, Munich Center for Quantum Science and Technology, Defense Advanced Research Projects Agency, Horizon 2020 Framework Programme, Intelligence Advanced Research Projects Activity, Gruppo Nazionale per la Fisica Matematica, Army Research Office
OpenAlex ID: W4281385034