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