Quantum evaluation of Coulomb potentials
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How cheaply can a reversible quantum circuit evaluate the Coulomb potential on its promised numerical input domain? The circuit must compute coherently and clear temporary registers.
Why it matters and what counts as progress
Why it matters: Potential evaluation contributes arithmetic and memory costs to real-space quantum simulation.
What counts as progress: Lower Toffoli and peak-qubit counts at the same input range, precision and error guarantee as the tuned comparison circuit.
How the problem developed
- 15 Oct 2026 · Circuit optimization [1]
Andi Gu, Alek H. Kemeny, Susanne F. Yelin and Mikhail D. Lukin, using LLM-guided search Reported a Coulomb-potential circuit with 1,140 Toffolis and 142 qubits, compared with a tuned Häner–Roetteler–Svore baseline of 6,355 Toffolis and 252 qubits (9.9× lower Toffoli–qubit product).
AI contribution
Discovering state-of-the-art quantum circuits with large language models
Gu, Kemeny, Yelin and Lukin report lower Toffoli and peak-qubit counts in seven specified circuit benchmarks, plus a new prime-field modular-inversion architecture. For fixed-point Gaussian evaluation, their stated benchmark falls from about 24,000 Toffolis and 362 qubits to 1,583 Toffolis and 139 qubits; the reported worst-case error is 9.99×10⁻⁸.
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Publication dates and editorial changes.
LLM-discovered quantum circuits reduce Toffoli and qubit costs