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Results for “sublinear algorithms”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Unified architecture for quantum lookup tables

Quantum access to arbitrary classical data encoded in unitary black-box oracles underlies interesting data-intensive quantum algorithms, such as machine learning or electronic structure simulation. The feasibility of these applications depends crucially on gate-efficient implementations of these oracles, which are commonly some reversible versions of the Boolean circuit for a classical lookup table. Here, we present a general parametrized architecture for quantum circuits implementing a lookup table that encompasses all prior work in realizing a continuum of optimal trade-offs between qubits, non-Clifford gates, and error resilience, up to logarithmic factors. Our architecture assumes only local 2D connectivity, yet recovers results, with the appropriate parameters, polylogarithmic error scaling. We also identify regimes, such as simultaneous sublinear scaling, in all parameters. These results enable tailoring implementations of the commonly used lookup table primitive to any given quantum device with constrained resources.

quantum circuits↗
DOE OSTI2021

Efficient Trainability of Linear Optical Modules in Quantum Optical Neural Networks

The existence of “barren plateau landscapes” for generic discrete-variable quantum neural networks, which obstructs efficient gradient-based optimization of cost functions defined by global measurements, would be surprising in the case of generic linear optical modules in quantum optical neural networks due to the tunability of the intensity of continuous variable states and the relevant unitary group having exponentially smaller dimension. We demonstrate that coherent light in m modes can be generically compiled efficiently if the total intensity scales sublinearly with m, and extend this result to cost functions based on homodyne, heterodyne, or photon detection measurement statistics, and to noisy cost functions in the presence of attenuation. Here, we further demonstrate efficient trainability of m mode linear optical quantum circuits for variational mean field energy estimation of positive quadratic Hamiltonians for input states that do not have energy exponentially vanishing with m.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Ensemble Simulation Techniques and Fast Randomized Algorithms

The major goals of the project were to develop and analyze new ensemble simulation techniques, including trajectory stratification and preconditioned MCMC techniques, as well as develop fast numerical linear algebra techniques closely related to ensemble simulation ideas. The trajectory stratification techniques involve simulating in parallel short trajectory fragments of a Markov process confined to a specific region of space‐time and then patching together the statistics gathered to assemble estimates of very general dynamical properties. We have also developed this approach for rare event simulation and extended the techniques to applications requiring a more general framework (such as electronic structure calculations). The preconditioned MCMC techniques involve simulating multiple Markov chains in parallel and then using information from the ensemble to speed the mixing of each individual chain. The fast randomized linear algebra methods are motivated by the diffusion Monte Carlo technique, but are applicable to finding the dominant eigenvalue of (almost) general matrices. For most non‐negative matrices, the schemes result in an error (compared to the power method) that is constant in the dimension of the problem. For more general matrices, we see a very clear sublinear cost trend in computational tests.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗