Quantum computation of stopping power for inertial fusion target design II: Quantum algorithm and resource estimation

Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it -- one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions. First-principles stopping calculations are classically challenging because they involve the dynamics of large electronic systems far from equilibrium, with accuracies that are particularly difficult to constrain and assess in the warm-dense conditions preceding ignition. In these two talks, we will describe a protocol for using a fault-tolerant quantum computer to calculate stopping power from a first-quantized representation of the electrons and projectile. The second talk will introduce the quantum protocol for estimating a material's stopping power with a cost-benefit analysis on a variety of subroutines for mean-estimation and time-evolution. Finally, after compiling the algorithms to determine constant factors we provide resource estimates for stopping power calculations relevant to current inertial fusion experiments. We estimate that these scientifically interesting and classically intractable stopping power calculations can be quantum simulated with roughly the same number of logical qubits and about one hundred times more Toffoli gates than is required for state-of-the-art quantum simulations of industrially relevant molecules such as FeMoco or P450.