Quantum circuit costs for Hermitian-code decoding
Follow the latest progress by email.
Can Hermitian-code syndrome decoding be compiled coherently into a quantum circuit with lower gate and storage costs? The decoding routine forms part of the studied quantum optimization task.
Why it matters and what counts as progress
Why it matters: An efficient classical decoder can become costly when overwritten data must be retained or uncomputed.
What counts as progress: A reversible decoder with stated failure allowance and resource counts; improvements must distinguish the paper’s naive reversible baseline from an established prior compilation.
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 Hermitian-code decoder using 930,000 Toffolis and 2,395 qubits. The paper compares it with a naïve reversible implementation at 100 million Toffolis and 190,000 qubits; it notes no prior reversible compilation in the literature.
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