Improved quantum volume estimation with transducers and amortized quantum walks

arXiv:2609.40217 · quant-ph, cs.CG, cs.DS · Submitted 2026-09-30 · Read on arXiv

quant-ph, cs.CG, cs.DS

Submitted: 2026-09-30

Updated: 2026-10-05

Terminology

• Spectral Gap — 22× in this paper · explained in 5 episodes
• Query Complexity — 19× in this paper · explained in 2 episodes
• Hilbert Space — 13× in this paper · explained in 2 episodes
• Quantization — 7× in this paper · explained in 12 episodes
• Amortization — 6× in this paper · explained in 1 episode
• Algorithmic Primitives — 3× in this paper · explained in 1 episode
• Core — 3× in this paper · explained in 2 episodes
• ACM-SIAM Symposium on Discrete Algorithms — 2× in this paper
• Generalization — 2× in this paper · explained in 13 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Gibbs State — 1× in this paper · explained in 2 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes

Sources

• Elfs, transducers and quantum walks
• Variations on Quantum Adversary
• One-Way Ticket to Las Vegas and the Quantum Adversary
• Quantum walks through generalized graph composition
• Quantum Subroutine Composition
• A Slightly Improved Bound for the KLS Constant
• The KLS constant is $O(\log^{1/4} n)$
• A Nearly Quadratic Lower Bound for Linear Optimization over Convex Bodies in the Membership Oracle Model
• Hit-and-Run Mixes as Fast as the Ball Walk

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• Theory of quantum-enhanced interferometry with general Markovian light sources
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