Machine Learning Meets Quantum Computation

f: X\to Y

f: X\to Y

Unknown Function

\{(x_i,y_i)\}_{i=1}^N

\{(x_i,y_i)\}_{i=1}^N

Training Data

\mathcal{H}

\mathcal{H}

Hypothesis Set

Learning

Algorithm

\hat{f}

\hat{f}

Comp. Complexity

Sample Complexity

Quantum Challenge #1

\frac{a}{b} \mapsto A B^{-1}?

\frac{a}{b} \mapsto A B^{-1}?

e^{a+b} \mapsto e^A e^B?

e^{a+b} \mapsto e^A e^B?

CQ

CC

QC

QQ

CQ

QQ

QC

CC

CQ

QQ

CC

Hao-Chung Cheng, MH, Ping-Cheng Yeh. The learnability of unknown quantum measurements. QIC 16(7&8):615–656 (2016).