In 2013, Clader, Jacobs, and Sprouse developed a quantum computing algorithm that solves electromagnetic scattering problems exponentially faster than the best known classical algorithm for that problem. The authors of this report examine this quantum algorithm's potential practical feasibility for modeling a target's radar cross section. Doing so could be important for modeling and predicting radar behavior against emerging targets.

Assessing the Practical Feasibility of the Clader-Jacobs-Sprouse Quantum Algorithm for Calculating Radar Cross Sections

Edward Parker, Nicholas A. O'Donoughue, Alvin Moon, Nicolas M. Robles

ResearchPublished Feb 24, 2026

Shor's algorithm, which could allow quantum computers to solve cryptographic problems that are intractable for classical computers, has led to decades of intense research into realizing quantum computers physically and finding other quantum algorithms that provide exponential speedups relative to their classical counterparts.

In 2008, Harrow, Hassidim, and Lloyd discovered an algorithm with the potential for such speedup when solving certain linear systems of equations, and in 2013, Clader, Jacobs, and Sprouse developed an extension of that algorithm, the Clader-Jacobs-Sprouse (CJS) algorithm, that solves electromagnetic scattering problems and demonstrates an end-to-end exponential speedup over classical algorithms for the same problem. If quantum computers of sufficient size are realized, then this CJS algorithm could theoretically solve many radio frequency problems, such as the modeling of a target's radar cross section (RCS), much more rapidly than is possible as of 2026. This would be important for modeling and predicting radar behavior against emerging targets.

In this report, the authors compare the end-to-end computational complexity and resource costs of the CJS algorithm (including the read-in and read-out steps that are not always analyzed in the quantum algorithms research literature) with the closest classical approach to the same problem (the frequency-domain finite-element method with a conjugate gradient solver). The authors assess the likelihood that the CJS algorithm will deliver a practically useful quantum advantage over classical computers.

Key Findings

  • Because of the CJS algorithm's exponential speedup over comparable classical algorithms, it is a somewhat promising candidate application for eventual large-scale quantum computers — perhaps one of the most promising candidate applications after the simulation of the physics of quantum systems.
  • However, the authors identify five important technical caveats that reduce the algorithm's promise. They discuss the parameter regimes in which these caveats are most and least important.
  • An asymptotic analysis of the CJS algorithm yields an exponential speedup over classical algorithms, but concrete resource estimates from the literature suggest that the constant prefactor concealed by the asymptotic scaling is enormous. Combined with some plausible hardware assumptions for future quantum computers, these estimates imply that calculating an RCS for even toy problems would require completely infeasible runtimes.
  • The CJS algorithm looks far less promising than quantum simulation as a useful application for near-term quantum computers. Quantum computing research funders should not expect a quick breakthrough in this area.
  • However, it is too soon to write off the CJS algorithm completely; the authors identify several research pathways (such as the Childs-Kothari-Somma algorithm) that could plausibly bring the CJS algorithm's computational requirements down to the realm of practical feasibility.
  • The computational bottleneck for the CJS algorithm is a subroutine known as Hamiltonian simulation, which is usually studied in the context of simulating the physics of quantum systems, such as biomolecules. Thus, a breakthrough in the modeling of RCS could plausibly emerge from a research effort with a completely different goal, such as medical drug discovery.

Recommendations

  • Investigate whether recent improvements to the Harrow-Hassidim-Lloyd algorithm (such as the Childs-Kothari-Somma algorithm or even more-recent improvements in Hamiltonian simulation) might greatly speed up the CJS algorithm from its original version.
  • More carefully calculate how the asymptotic runtime of the CJS algorithm depends on parameters other than the mesh size (such as the matrix's sparseness, its condition number, and the required numerical precision of its solution).
  • Explore ways to more efficiently implement the CJS oracles, especially the matrix oracle.
  • Monitor scientific progress in the field of Hamiltonian simulation, including by biomedical researchers, and consider how this progress might also accelerate the timelines for utility of the CJS algorithm for calculating RCSs.

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Parker, Edward, Nicholas A. O'Donoughue, Alvin Moon, and Nicolas M. Robles, Assessing the Practical Feasibility of the Clader-Jacobs-Sprouse Quantum Algorithm for Calculating Radar Cross Sections. Santa Monica, CA: RAND Corporation, 2026. https://www.rand.org/pubs/research_reports/RRA4086-1.html.
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Funding for this independent research was was made possible by RAND National Defense Research Institute (NDRI) exploratory research funding. The research was conducted within the Acquisition and Technology Policy Program of the RAND National Security Research Division (NSRD).

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