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Experimental implementation of Grover's algorithm with transmon qubit architecture

Experimental implementation of Grover's algorithm with transmon qubit architecture. Andrea Agazzi Zuzana Gavorova Quantum systems for information technology, ETHZ. What is Grover's algorithm?. Quantum search algorithm

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Experimental implementation of Grover's algorithm with transmon qubit architecture

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  1. Experimental implementation of Grover's algorithm with transmonqubit architecture Andrea Agazzi ZuzanaGavorova Quantum systems for information technology, ETHZ

  2. What is Grover's algorithm? • Quantum search algorithm • Task: In a search space of dimension N, find those 0<M<N elements displaying some given characteristics (being in some given states). a .

  3. The oracle • The oracle MARKS the correct solution Dilution operator (interpreter) • Solution is more recognizable x

  4. Grover's algorithm Procedure • Preparation of the state • Oracle application • Dilution of the solution • Readout O Filipp S., Wallraff A., Lecture notes “quantum system for information technology”, ETHZ, 2012

  5. Geometric visualization • Preparation of the state O Michael A. Nielsen and Isaac L. Chuang, Quantum computation and quantum information, 2011

  6. Grover's algorithm Performance • Every application of the algorithm is a rotation of θ • The Ideal number of rotations is: Michael A. Nielsen and Isaac L. Chuang, Quantum computation and quantum information, 2011

  7. Grover's algorithm2 qubits N=4 Oracle marks one state M=1 After a single run and a projection measurement will get target state with probability 1!

  8. Grover's algorithmCircuit Preparation X X for t=2 Dewes, A; Lauro, R; Ong, FR; et al. arXiv:1109.6735 (2011)

  9. Grover's algorithmOracle Will get 2 cases: for t=2 Dewes, A; Lauro, R; Ong, FR; et al. arXiv:1109.6735 (2011)

  10. Grover's algorithmDecoding X X for t=2 Dewes, A; Lauro, R; Ong, FR; et al. arXiv:1109.6735 (2011)

  11. Experimental setup ωq= qubit frequency ωr= resonator frequency Ω = drive pulse amplitude Dewes, A; Lauro, R; Ong, FR; et al. arXiv:1109.6735 (2011)

  12. Single qubit manipulation • Qubit frequency controlvia flux bias • Rotations around z axis:detuning Δ • Rotations around x and y axes:resonant pulses with amplitude Ω Δ a Filipp S., Wallraff A., Lecture notes “quantum system for information technology”, ETHZ, 2012

  13. Experimental setup ωq,I = 1st qubit frequency ωq,II= 2nd qubit frequency g = coupling strength Dewes, A; Lauro, R; Ong, FR; et al. arXiv:1109.6735 (2011)

  14. Qubit capacitive coupling In the rotating frame where ω = ωq,II the coupling Hamiltonian is: a Bialczak, RC; Ansmann, M; Hofheinz, M; et al.,Nature Physics 6, 409 (2007)

  15. iSWAP gate |eg⟩ • Controlled interaction between ⟨10∣ and ⟨01∣ • By letting the two states interact for t = π/gwe obtain an iSWAP gate! |ge⟩ Filipp S., Wallraff A., Lecture notes “quantum system for information technology”, ETHZ, 2012

  16. Pulse sequence X X X Dewes, A; Lauro, R; Ong, FR; et al. arXiv:1109.6735 (2011)

  17. Linear transmission line and single-shot measurement Quality factor of empty linear transmission line With resonant frequency Presence of a transmon in state shifts the resonant frequency of the transmission line If microwave at full transmission for state, partial for state Current corresponding to transmitted EM Filipp S., Wallraff A., Lecture notes “quantum system for information technology”, ETHZ, 2012

  18. Linear transmission line and single-shot measurement Single shot • If there was no noise, would get either blue or red curve • Real curve so noisy that cannot tell whether or Cannot do single-shot readout We need an amplifier which increases the area between and curves, but does not amplify the noise Filipp S., Wallraff A., Lecture notes “quantum system for information technology”, ETHZ, 2012

  19. Josephson Bifurcation Amplifier (JBA) Nonlinear transmission line due to • Josephson junction Resonant frequency At Pin = PC max. slope diverges Bifurcation: at the correct (Pin ,ωd) two stable solutions, can map the collapsed state of the qubit to them Dewes, A; Lauro, R; Ong, FR; et al. arXiv:1109.6735 (2011) E. Boaknin, V. Manucharyan, S. Fissette et al: arXiv:cond-mat/0702445v1

  20. Josephson Bifurcation Amplifier (JBA) Switching probability p: probability that the JBA changes to the second solution • Excite • Choose power corresponding to the biggest difference of switching probabilities Errors • Nonzero probability of incorrect mapping • Crosstalk Dewes, A; Lauro, R; Ong, FR; et al. arXiv:1109.6735 (2011)

  21. Errors • Nonzero probability of incorrect mapping • Crosstalk Dewes, A; Lauro, R; Ong, FR; et al. arXiv:1109.6735 (2011)

  22. Conclusions • Gate operations of Grover algorithm successfully implemented with capacitively coupled transmon qubits • Arrive at the target state with probability 0.62 – 0.77 (tomography) • Single-shot readout with JBA (no quantum speed-up without it) • Measure the target state in single shot with prob 0.52 – 0.67 (higher than 0.25 classically)

  23. Sources • Dewes, A; Lauro, R; Ong, FR; et al.,“Demonstrating quantum speed-up in a superconducting two-qubit processor”,arXiv:1109.6735 (2011) • Bialczak, RC; Ansmann, M; Hofheinz, M; et al.,“Quantum process tomography of a universal entangling gate implemented with Josephson phase qubits”,Nature Physics 6, 409 (2007)

  24. Thank you for your attention Special acknowledgements: S. Filipp A. Fedorov

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