We demonstrate quantum amplitude estimation (QAE) as a route to quadratic speedup for Monte Carlo-type expectation values in nuclear engineering. Using QPE-based QAE, we study two examples: a discrete fission-neutron-yield expectation and a U-238 resonance integral under a $1/E$ slowing-down spectrum. The toy problem is implemented as a gate-level Qiskit circuit, while the resonance-integral example is simulated through an exact eigendecomposition of the Grover operator to avoid state-preparation decomposition bottlenecks. In both cases, the squared error scales as $O(1/T^2)$ with the number of oracle calls $T$, compared with the classical Monte Carlo scaling $O(1/N)$. For the U-238 example, QAE recovers the resonance integral to approximately $0.03%$ relative error with $m=14$ phase-estimation qubits.
Quantum Amplitude Estimation promises to accelerate Monte Carlo integration by replacing the classical $\varepsilon \propto N^{-1/2}$ sampling law with the Heisenberg-limited $\varepsilon \propto N^{-1}$ scaling, but whether any part of that advantage survives on present-day hardware is an empirical question. We report...
Aditi Lal, Alex Khan, Rut Lineswala et al.· 0 citations
Quantum Amplitude Amplification (QAA), the generalization of Grover's algorithm, is well-positioned for combinatorial optimization and is particularly promising for Quadratic Unconstrained Binary Optimization (QUBO) problems. QAA is appealing due to its ability to drive the quantum system to a target state, yielding th...
Numerical integration with Monte Carlo methods is a central computational task in many scientific and industrial applications, including financial derivative pricing and risk management. Classical Monte Carlo algorithms are computationally demanding: achieving an accuracy $\epsilon$ typically requires a number of funct...
Paolo Recchia, Yu Zhan, Kelvin Koor et al.· 0 citations
The Monte Carlo Projective Quantum Eigensolver (MC-PQE) was recently introduced as an alternative to hybrid algorithms like the variational quantum eigensolver (VQE). By using a quantum Monte Carlo-inspired scheme for energy estimation, MC\nobreakdash-PQE was found to decrease the required measurement cost relative to...
Monte Carlo methods are fundamental to finance, system verification, and scientific simulation, but converge slowly: achieving an additive error of є requires O(1/є2) samples. Quantum Amplitude Estimation (QAE) offers a quadratic speedup by encoding the target probabilistic model into a quantum circuit. However, constr...
Seungmin Jeon, Jaeho Choi, J. Jeon et al.· Proceedings of the ACM on Pr...· 0 citations
Fermionic Gaussian states are the workhorse reference states for qubit-based quantum simulation of fermionic systems, yet existing certification protocols either proceed via fidelity estimation, leading to suboptimal sample complexity in the target precision $\epsilon$, only apply to Haar-typical states, or require ada...
Ninnat Dangniam, Laphas Premcharoen, Metrasit Sripech et al.· 0 citations
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