Parameterized Quantum Circuits

Min-Hsiu Hsieh

(UTS)

Joint Work with

Yuxuan Du

Tongliang Liu

Dacheng Tao

(USyd)

Grover Search

P_\omega= |\omega\rangle\langle \omega|

P_\omega= |\omega\rangle\langle \omega|

P_s= |+\rangle\langle +|^{\otimes n}

P_s= |+\rangle\langle +|^{\otimes n}

U_s= 2|+\rangle\langle +|^{\otimes n} - I

U_s= 2|+\rangle\langle +|^{\otimes n} - I

U_\omega= 2|\omega\rangle\langle \omega| - I

U_\omega= 2|\omega\rangle\langle \omega| - I

\min_{\phi} \langle \phi |P_{\omega^\perp} | \phi\rangle

\min_{\phi} \langle \phi |P_{\omega^\perp} | \phi\rangle

Morales, Tlyachev, and Biamonte. Variationally Learning Grover’s Quantum Search Algorithm. arXiv:1805.09337

U(\alpha) = e^{i\alpha P_\omega}

U(\alpha) = e^{i\alpha P_\omega}

V(\beta) = e^{i\beta P_s}

V(\beta) = e^{i\beta P_s}

$\mathcal{D}=\{\bm{x}_i,y_i\}_{i=1}^{10000}$

$\mathcal{D}_i=\{\bm{x}_k,y_k\}_{k=1}^{8}$

$\mathcal{D}=\{\bm{x}_i,y_i\}_{i=1}^{10000}$

$\mathcal{D}_i=\{\bm{x}_k,y_k\}_{k=1}^{8}$