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

Abstract

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 $n_{\mathrm{gr}}$ grid points in each coordinate and $n_t$ time grid points leads to $O(n_{\mathrm{gr}}^6)$ memory space and $O(n_t{n}_{\mathrm{gr}}^6)$ 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 $\epsilon$ and query complexity of order $\tilde{O}((n_{\mathrm{gr}}+n_t)/\epsilon )$. Our method also reduces the space complexity to $O(\mathrm{polylog}(n_{\mathrm{gr}}/\epsilon ))$ in terms of the qubit number, while using quantum random access memories with $O(n_{\mathrm{gr}}^3)$ 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.

References in corpus (15)

• Quantum random access memory
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Search for the Majorana Nature of Neutrinos in the Inverted Mass Ordering Region with KamLAND-Zen
• Quantum algorithm and circuit design solving the Poisson equation
• Circuit-Based Quantum Random Access Memory for Classical Data
• On the most constraining cosmological neutrino mass bounds
• Halo bias in mixed dark matter cosmologies
• Improved quantum algorithms for linear and nonlinear differential equations
• Time-marching based quantum solvers for time-dependent linear differential equations
• Precision reconstruction of the dark matter-neutrino relative velocity from N-body simulations
• Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations
• Quantum algorithms for approximate function loading
• Towards Cosmological Simulations of Dark Matter on Quantum Computers
• A quantum algorithm for the linear Vlasov equation with collisions
• Neutrino winds on the sky

Cited by in corpus (4)

• Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits
• Quantum algorithm for partial differential equations of non-conservative systems with spatially varying parameters
• Quantum Calculation for Two-Stream Instability and Advection Test of Vlasov-Maxwell Equations: Numerical Evaluation of Hamiltonian Simulation
• Solving the Nonlinear Vlasov Equation on a Quantum Computer