Quantum evaluation of HHL rotation angles
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How efficiently can a reversible quantum circuit compute the rotation angle used in the HHL linear-systems routine? Input range, fixed-point precision and approximation error define the numerical task.
Why it matters and what counts as progress
Why it matters: The angle computation has a gate-and-memory cost separate from the surrounding linear-systems algorithm.
What counts as progress: Lower Toffoli and peak-qubit counts for the same promised angle-evaluation specification, including coherent control and temporary-register cleanup.
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 an HHL rotation-angle circuit with 1,348 Toffolis and 115 qubits, compared with a tuned Häner–Roetteler–Svore baseline of 16,000 Toffolis and 300 qubits (32× 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.
Sources
Website timeline
Publication dates and editorial changes.
LLM-discovered quantum circuits reduce Toffoli and qubit costs