Quantum Machine Learning

Using quantum computers to enhance machine learning, from quantum speedups to variational classifiers.

Quantum Machine Learning (QML) explores the intersection of quantum computing and machine learning. It encompasses both quantum algorithms for ML tasks and ML techniques for quantum systems.

The Landscape

                    QML
                     │
    ┌────────────────┼────────────────┐
    │                │                │
Quantum for ML    Hybrid        ML for Quantum
    │                │                │
HHL, sampling    VQC, QSVM      Error mitigation,
speedups         on NISQ        circuit optimization

Quantum Speedups for ML

Theoretical Speedups

Algorithm	Classical	Quantum	Caveat
HHL (linear systems)	$O (N)$	$O (lo g N)$	Input/output issues
Recommendation	$O (mn)$	$O (poly (lo g mn))$	Dequantized
PCA	$O (d^{2})$	$O (d)$	Data loading

The Catch

Many quantum ML speedups have been “dequantized” (classical algorithms found that match them). Data loading often kills the advantage.

Near-Term QML (NISQ)

Variational Quantum Classifiers

Parameterized circuits as ML models:

Classical data → Encode → [VQC(θ)] → Measure → Prediction

Quantum Kernels

Use quantum circuits to compute kernel functions: $K (x, x^{'}) = ∣ ⟨ ϕ (x) ∣ ϕ (x^{'})⟩ ∣^{2}$

Then use classical SVM.

Quantum Neural Networks

Hybrid models combining quantum circuits with classical networks.

Challenges

Challenge	Issue
Barren plateaus	Gradients vanish
Data encoding	Classical → quantum bottleneck
Readout	Limited information extraction
Advantage unclear	Classical ML is very good
Noise	Errors corrupt learning