Quantum machine learning overview 9 HHL algorithm Solving

Quantum machine learning - overview 9

HHL algorithm • Solving systems of linear equations • Does it for O(poly(log. N)), according to paper • Practically, has a number of major caveats • Anyway, useful as a template for another quantum algorithms 10

HHL in details 11

HHL drawbacks 1. Full vector state x – O(N) entries – only some features are available 2. Input vector b – either on QC or with q. RAM 3. Restrictions for matrix A (“well-invertible”) 4. Anyway, useful as a template for another quantum algorithms Not yet Machine Learning – but used extensively in other approaches 12

Quantum principal component analysis principal components q. RAM: 13

Quantum support vector machines and kernel methods • Support vector is calculated as a quantum state 14

q. BLAS-based optimization 7

Deep (quantum) learning • Boltzmann machine • Linear optical schemes • Ising model 16