journal article

Journal Article

Text

Physical Review Research. 2024, 6(1), p. 013200

Quantum algorithm for the Vlasov simulation of the large-scale structure formation with massive neutrinos

American Physical Society

English

Text

2024-02-26

https://doi.org/10.1103/PhysRevResearch.6.013200

Miyamoto K., Yamazaki S., Uchida F., et al. Quantum algorithm for the Vlasov simulation of the large-scale structure formation with massive neutrinos. Physical Review Research 6, 013200 (2024); https://doi.org/10.1103/PhysRevResearch.6.013200.

Investigating the cosmological implication of the fact that neutrino has finite mass is of importance for fundamental physics. In particular, massive neutrino affects the formation of the large-scale structure (LSS) of the universe, and, conversely, observations of the LSS can give constraints on the neutrino mass. Numerical simulations of the LSS formation including massive neutrino along with conventional cold dark matter is thus an important task. For this, calculating the neutrino distribution in the phase space by solving the Vlasov equation is a suitable approach, but it requires solving the PDE in the (6+1)-dimensional space and is thus computationally demanding: Configuring ngr grid points in each coordinate and nt time grid points leads to O(ngr6) memory space and O(ntngr6) queries to the coefficients in the discretized PDE. We propose a quantum algorithm for this task. Linearizing the Vlasov equation by neglecting the relatively weak self-gravity of the neutrino, we perform the Hamiltonian simulation to produce quantum states that encode the phase-space distribution of neutrino. We also propose a way to extract the power spectrum of the neutrino density perturbations as classical data from the quantum state by quantum amplitude estimation with accuracy ϵ and query complexity of order Õ[(ngr+nt)/ϵ]. Our method also reduces the space complexity to O[polylog(ngr/ϵ)] in terms of the qubit number, while using quantum random access memories with O(ngr3) entries. As far as we know, this is the first quantum algorithm for the LSS simulation that outputs the quantity of practical interest with guaranteed accuracy.

This article is licensed under a Creative Commons Attribution 4.0 International License.

94885

Quantum algorithm for the Vlasov simulation of the large-scale structure formation with massive neutrinos

American Physical Society

English

2024-02-26

Physical Review Research

6

1

013200

https://doi.org/10.1103/PhysRevResearch.6.013200

https://hdl.handle.net/11094/94885