Amplitude Estimation for Neutronics Monte Carlo
Quantum amplitude estimation offers a quadratic speedup for Monte Carlo integrals like neutron transport, useful only far past today's hardware.
The neutronics integral
Neutronics for both machines, tritium breeding in the blanket, 14 MeV neutron transport, activation and shielding, is computed by classical Monte Carlo: sample enormous numbers of particle histories and average. The statistical error of Monte Carlo falls as 1/sqrt(M) in the number of samples M. Quantum amplitude estimation (QAE) changes that exponent.
# Classical Monte Carlo estimate of mean mu = E[f(X)]:
error ~ sigma / sqrt(M) # M samples
# Quantum amplitude estimation:
error ~ sigma / M # quadratic speedup in sample count
# to reach error eps: classical ~ 1/eps^2 , quantum ~ 1/eps queriesHow QAE gets the square
QAE encodes the quantity of interest as the amplitude of a marked state and uses phase estimation on a Grover-like operator to read that amplitude with error falling as 1/M rather than 1/sqrt(M). The tritium breeding ratio the breeder treats as a lever (1.1, 1.5, 1.8) is exactly the kind of integrated response QAE would estimate.
# Grover/amplitude operator Q, applied M times, phase ~ arcsin(sqrt(a))
# a = probability of the 'success' (e.g. neutron absorbed in breeder)
# estimating a to error eps costs O(1/eps) applications of Q
# vs classical O(1/eps^2) samplesWhy it is long-term only
- Quadratic, not exponential: the win is real but modest, and easily eaten by hardware overhead.
- Each 'sample' becomes a coherent circuit encoding the transport process, which is deep and needs error correction.
- Loading cross-section data and geometry into the circuit is itself a hard state-preparation problem.
Because the speedup is only quadratic, it must clear a high hardware bar before beating a mature, massively parallel classical Monte Carlo pipeline. Kronos keeps QAE as a documented long-horizon possibility for neutronics, not a plan. Near term, all breeding-ratio and activation results come from classical Monte Carlo validated against nuclear data, with quantum used only to benchmark the primitive on toy geometries. See amplitude estimation for the algorithmic detail.