Quantum chemistry alias–Select circuit costs
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Can the Fe₂S₂ alias–Select circuit for electronic-structure simulation be implemented with fewer Toffoli gates and peak qubits? Select applies a labeled Pauli term; alias sampling helps prepare its label.
Why it matters and what counts as progress
Why it matters: This primitive contributes repeatedly to the resource cost of the specified chemistry simulation.
What counts as progress: Lower gate and peak-qubit costs for the same Hamiltonian encoding and accuracy, including the reversible preparation and cleanup required by the benchmark.
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 the Fe₂S₂ alias–Select circuit at 15,000 Toffolis and 126 qubits, versus a 55,000-Toffoli, 139-qubit baseline (4.1× 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
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Publication dates and editorial changes.
LLM-discovered quantum circuits reduce Toffoli and qubit costs