Chern-number estimation: nearly optimal quantum algorithm and provable quantum speedup

arXiv:2609.35978 · quant-ph · Submitted 2026-09-28 · Read on arXiv

quant-ph

Submitted: 2026-09-28

Updated: 2026-09-28

Terminology

• Chern Number — 59× in this paper · explained in 4 episodes
• BQP — 22× in this paper · explained in 2 episodes
• Trace — 7× in this paper · explained in 2 episodes
• BQP-complete — 6× in this paper · explained in 2 episodes
• Spectral Gap — 6× in this paper · explained in 5 episodes
• Ancilla Qubits — 4× in this paper · explained in 1 episode
• Berry Curvature — 4× in this paper · explained in 3 episodes
• Quantization — 4× in this paper · explained in 12 episodes
• Algorithmic Primitives — 3× in this paper · explained in 1 episode
• Calibration — 3× in this paper · explained in 7 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Trace Distance — 3× in this paper · explained in 3 episodes
• Effective Hamiltonian — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• BQP-Completeness — 1× in this paper · explained in 2 episodes
• Block Encoding — 1× in this paper · explained in 4 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Holonomy — 1× in this paper · explained in 2 episodes
• Topological Order — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Fractional Chern Insulators and Competing States in a Twisted MoTe$_2$ Lattice Model
• Adiabatic Error Cancellation in Berry Phase Estimation
• Computational complexity of Berry phase estimation in topological phases of matter
• Adversary lower bounds in the Hamiltonian oracle model
• Hardness of recognizing phases of matter

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