canonical-quantum-neurons

name

canonical-quantum-neurons

description

Methodology for canonical quantization of classical computational primitives (neurons, activation functions, energy-based models) into quantum ML models. Use when designing quantum neural architectures, constructing quantum Hamiltonians from classical energy functions, or developing hybrid quantum-classical training algorithms. Trigger words: canonical quantization, quantum neurons, quantum activation, quantum Hamiltonian, quantum machine learning primitives.

Canonical Quantization of Computational Primitives

Methodology from arXiv:2607.05000 (July 2026) — applying canonical quantization to construct quantum models from classical computational primitives.

Core Methodology

1. Classical → Quantum Mapping: View a classical primitive as composition of energy function E(x) and activation function σ. Replace E(x) with quantum Hamiltonian H, apply σ via matrix functional calculus: O = σ(H).

2. Activation Observable: The resulting operator O is measurable on an input quantum state |ψ⟩. Measurement yields quantum-enhanced computation.

3. Hybrid Training Algorithms:

   • Gradient estimation via: classical random sampling, Hadamard test, Hamiltonian simulation
   • Squared loss error estimation with quantum measurement protocols
   • Hybrid quantum-classical optimization loop

4. Key Quantum Primitives Required:

   • Hadamard test for observable measurement
   • Hamiltonian simulation for time evolution e^{-iHt}
   • Power of one qumode protocol
   • Schroedingerization technique

Application Patterns

Function Approximation

• Objective: learn unknown observable from labeled quantum data
• Training: hybrid gradient descent with quantum measurement
• Advantage: enhanced expressivity over classical counterparts

Architecture Design

• Start from any classical energy-based model
• Quantize the energy function → quantum Hamiltonian
• Apply classical activation via functional calculus
• Result: quantum activation observable

Implementation Notes

• Works with any classical activation function (ReLU, sigmoid, etc.)
• Matrix functional calculus requires spectral decomposition of H
• Numerical experiments show enhanced expressive capabilities
• Foundation for developing full quantum neural architectures

Activation

canonical quantization, quantum neurons, quantum activation function, quantum Hamiltonian, quantum machine learning primitives, function approximation, quantum data, hybrid quantum-classical algorithms