{"citation":{"mla":"Chabaud, Ulysse, et al. “Energy, Bosons and Computational Complexity.” <i>ArXiv:2510.08545</i>, 2025.","short":"U. Chabaud, S. Gharibian, S. Mehraban, A. Motamedi, H.R. Naeij, D. Rudolph, D. Sambrani, ArXiv:2510.08545 (2025).","bibtex":"@article{Chabaud_Gharibian_Mehraban_Motamedi_Naeij_Rudolph_Sambrani_2025, title={Energy, Bosons and Computational Complexity}, journal={arXiv:2510.08545}, author={Chabaud, Ulysse and Gharibian, Sevag and Mehraban, Saeed and Motamedi, Arsalan and Naeij, Hamid Reza and Rudolph, Dorian and Sambrani, Dhruva}, year={2025} }","apa":"Chabaud, U., Gharibian, S., Mehraban, S., Motamedi, A., Naeij, H. R., Rudolph, D., &#38; Sambrani, D. (2025). Energy, Bosons and Computational Complexity. In <i>arXiv:2510.08545</i>.","ama":"Chabaud U, Gharibian S, Mehraban S, et al. Energy, Bosons and Computational Complexity. <i>arXiv:251008545</i>. Published online 2025.","ieee":"U. Chabaud <i>et al.</i>, “Energy, Bosons and Computational Complexity,” <i>arXiv:2510.08545</i>. 2025.","chicago":"Chabaud, Ulysse, Sevag Gharibian, Saeed Mehraban, Arsalan Motamedi, Hamid Reza Naeij, Dorian Rudolph, and Dhruva Sambrani. “Energy, Bosons and Computational Complexity.” <i>ArXiv:2510.08545</i>, 2025."},"year":"2025","title":"Energy, Bosons and Computational Complexity","author":[{"last_name":"Chabaud","full_name":"Chabaud, Ulysse","first_name":"Ulysse"},{"full_name":"Gharibian, Sevag","last_name":"Gharibian","first_name":"Sevag"},{"first_name":"Saeed","last_name":"Mehraban","full_name":"Mehraban, Saeed"},{"first_name":"Arsalan","full_name":"Motamedi, Arsalan","last_name":"Motamedi"},{"last_name":"Naeij","full_name":"Naeij, Hamid Reza","first_name":"Hamid Reza"},{"full_name":"Rudolph, Dorian","last_name":"Rudolph","first_name":"Dorian"},{"last_name":"Sambrani","full_name":"Sambrani, Dhruva","first_name":"Dhruva"}],"date_created":"2025-10-10T13:44:52Z","date_updated":"2026-04-20T13:53:54Z","status":"public","abstract":[{"lang":"eng","text":"We investigate the role of energy, i.e. average photon number, as a resource\nin the computational complexity of bosonic systems. We show three sets of\nresults: (1. Energy growth rates) There exist bosonic gate sets which increase\nenergy incredibly rapidly, obtaining e.g. infinite energy in finite/constant\ntime. We prove these high energies can make computing properties of bosonic\ncomputations, such as deciding whether a given computation will attain infinite\nenergy, extremely difficult, formally undecidable. (2. Lower bounds on\ncomputational power) More energy ``='' more computational power. For example,\ncertain gate sets allow poly-time bosonic computations to simulate PTOWER, the\nset of deterministic computations whose runtime scales as a tower of\nexponentials with polynomial height. Even just exponential energy and $O(1)$\nmodes suffice to simulate NP, which, importantly, is a setup similar to that of\nthe recent bosonic factoring algorithm of [Brenner, Caha, Coiteux-Roy and\nKoenig (2024)]. For simpler gate sets, we show an energy hierarchy theorem. (3.\nUpper bounds on computational power) Bosonic computations with polynomial\nenergy can be simulated in BQP, ``physical'' bosonic computations with\narbitrary finite energy are decidable, and the gate set consisting of Gaussian\ngates and the cubic phase gate can be simulated in PP, with exponential bound\non energy, improving upon the previous PSPACE upper bound. Finally, combining\nupper and lower bounds yields no-go theorems for a continuous-variable\nSolovay--Kitaev theorem for gate sets such as the Gaussian and cubic phase\ngates."}],"publication":"arXiv:2510.08545","type":"preprint","user_id":"71541","_id":"61776","external_id":{"arxiv":["2510.08545"]}}