Resource-Tunable Quantum Circuit Implementation of Nonlinear Element-Wise Transformations

arXiv:2609.39295 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Comments: 28 pages, 13 figures

Code: https://github.com/ChunlinYANG0/QuantumHadamardProcedure

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Block Encoding — 31× in this paper · explained in 4 episodes
• Post-Selection — 14× in this paper · explained in 2 episodes
• Query Complexity — 12× in this paper · explained in 2 episodes
• Accuracy — 11× in this paper · explained in 1 episode
• Activation Function — 7× in this paper · explained in 1 episode
• Quantum Circuits — 6× in this paper · explained in 2 episodes
• Ancilla Qubits — 3× in this paper · explained in 1 episode
• Chebyshev Polynomials — 2× in this paper · explained in 2 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Alternation — 1× in this paper · explained in 1 episode
• Benchmarking — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Quantum Singular Value Transformation (QSVT) — 1× in this paper · explained in 4 episodes
• Transformer — 1× in this paper · explained in 2 episodes

Sources

• Quantum Transformer: Accelerating model inference via quantum linear algebra
• Non-Linear Transformations of Quantum Amplitudes: Exponential Improvement, Generalization, and Applications
• Quantum element-wise transforms

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