---
res:
  bibo_abstract:
  - |-
    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.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Ulysse
      foaf_name: Chabaud, Ulysse
      foaf_surname: Chabaud
  - foaf_Person:
      foaf_givenName: Sevag
      foaf_name: Gharibian, Sevag
      foaf_surname: Gharibian
  - foaf_Person:
      foaf_givenName: Saeed
      foaf_name: Mehraban, Saeed
      foaf_surname: Mehraban
  - foaf_Person:
      foaf_givenName: Arsalan
      foaf_name: Motamedi, Arsalan
      foaf_surname: Motamedi
  - foaf_Person:
      foaf_givenName: Hamid Reza
      foaf_name: Naeij, Hamid Reza
      foaf_surname: Naeij
  - foaf_Person:
      foaf_givenName: Dorian
      foaf_name: Rudolph, Dorian
      foaf_surname: Rudolph
  - foaf_Person:
      foaf_givenName: Dhruva
      foaf_name: Sambrani, Dhruva
      foaf_surname: Sambrani
  dct_date: 2025^xs_gYear
  dct_title: Energy, Bosons and Computational Complexity@
...