Katedra Grafiki Wizji Komputerowej i Systemw Cyfrowych Quantum

Katedra Grafiki, Wizji Komputerowej i Systemów Cyfrowych Quantum Sampling For Computation KAMIL WERESZCZYŃSKI

Deterministic QC Interference Superposition initialization Entanglement Unitary operator Hermitian operator evolution measurement Oracle Phase est. Ph. kick back uncomputation

Quantum Sampling Interference Superposition + Cosine series quantum Sampling QCo. Samp Entanglement - initialization + - + Meas. basis - + Quantum Sampling + Cosine series - measure evolution forging prob. Oracle constants fixing data. Phase encoding est. ordering coords Ph. kick back uncomputation phase extraction agregate Eigen States Appearance hist. FCo. Samp

Two components + 1 0 - + - phase extraction Sketch of the evolution operator idea + -

Distributed phase encoding 1, 2, 3 Meaning of qubits example + ^ ^ 1. 2. 3. + L. Ruiz-Perez and J. C. Garcia-Escartin, “Quantum arithmetic with the quantum Fourier transform, ” Quantum Information Processing, vol. 16, June 2017. T. G. Draper, “Addition on a Quantum Computer, ” ar. Xiv: quant-ph/0008033, Aug. 2000. ar. Xiv: quant-ph/0008033. S. Beauregard, G. Brassard, and J. M. Fernandez, “Quantum Arithmetic on Galois Fields, ” ar. Xiv: quant-ph/0301163, Jan. 2003. ar. Xiv: quant-ph/0301163.

Isn’t it just fancy way of coding numbers? constants fixing phase extraction Quantum Sampling

State comparison data encoding The value of pdf for one or more qubits will give the answare We want to check the state equality state basis State similarity measure The same uncomputation ordering coords Most unsimilar opposite ½

Superposing again (cluster) entanglement similarity measure ½ You can choose the because of best probability It is ugly and the Measurement basis grows exponentially depends on Probabilities:

Forging probability • It is like a „forging die” • „Amp Amp” is like a hammer „good” state We want to achieve it

The architecture of QCo. Samp uncomputation ? ? Unwanted interference uncomputation First component Second component

To balance or not to balance?