1 / 39

Josephson Flux Qubits in Charge-Phase Regime

D-Wave Systems Inc. THE QUANTUM COMPUTING COMPANY TM. Josephson Flux Qubits in Charge-Phase Regime. M. H. S. Amin. D-Wave Systems Inc., Vancouver, Canada. Thanks to:. P. Echternach (JPL) M. Grajcar (IPHT/Comenius) E. Il’ichev (IPHT) M. Kenyon (JPL) A. Kleinsasser (JPL).

ninon
Download Presentation

Josephson Flux Qubits in Charge-Phase Regime

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. D-Wave Systems Inc. THE QUANTUM COMPUTING COMPANYTM Josephson Flux Qubits in Charge-Phase Regime M. H. S. Amin D-Wave Systems Inc., Vancouver, Canada Thanks to: P. Echternach (JPL) M. Grajcar (IPHT/Comenius) E. Il’ichev (IPHT) M. Kenyon (JPL) A. Kleinsasser (JPL) A. Maassen van den Brink (D-Wave) G. Rose (D-Wave) A. Shnirman (Kalsruhe) A. Smirnov (D-Wave) A. Zagoskin (D-Wave)

  2. Van der Wal et al. Nakamura et al. Guillaume et al. Chiorescu et al. Il’ichev et al. Pashkin et al. Vion et al. Duty et al. r 10-1 0 10-2 10 Large sensitivity to flux noise Large sensitivity to charge noise Charge-phase regime; The most Interesting Charge Qubit vs Flux Qubit r = EC /EJ Charge qubits: r >>1 Flux qubits: r<<1

  3. Charge-phase regime Saclay: t ~ 500 ns Phase-charge regime 3JJ flux qubit t ~? Delft: t ~ 100 ns D-Wave/IPHT: t ~ 2.5 ms Decoherence Time t Charge qubit NEC/Chalmers/JPL: t ~ 5 ns

  4. D-Wave/IPHT:t ~ 2.5 ms -Characterization technique, not readout Delft/MIT:t ~ 100 ns -Requires large L; Large coupling to magnetic environment -DC-SQUID is dissipative Problems with Flux Qubits 1. Single shot readout difficult

  5. Problems with Flux Qubits 1. Single shot readout difficult 2. Exponential dependence of D on qubit parameters 3. Controllable coupling difficult 4. Large sensitivity to flux noise

  6. Why Charge-Phase Regime? • The effects of both charge and flux noise can be minimized • Readout can be easily switched on and off • Two degrees of freedom (instead of one) are available for e.g. coupling and readout • Smaller sensitivity to system parameters

  7. |n |n+1 Quantronium Qubit |1 E EJ |0 ng 1/2 |0 = 2-1/2 ( |n + |n+1) + . . . Qubit States: |1 = 2-1/2 ( |n - |n+1) + . . . Uncertainty in Charge  Localization of phase Phase can be used for readout

  8. ( @ Ng = 1/2 ) i1 1 1 1 1 1 1 1 2 4 2 4 2 2 2 current (nA) i0 d/2p - - - Quantronium Qubit ¶ E 2p persistent currents: j = i F0 j ¶d Magic point E01 d/2p ng

  9. |R |L Dual of Quantronium Flux qubit: E D Energy Levels 1/2 Fe/ F0 Uncertainty in phase  Localization of charge What charge?

  10. Example: DC-SQUID F Aharonov-Casher Effect Aharonov-Bohm effect: e F Interference

  11. Aharonov-Casher Effect F Q Interference

  12. Quasicharge Island Voltage: State Dependent Island Charge: Aharonov-Casher Effect J.R. Friedman and D.A. Averin, PRL (2002). t1 t1 Cg F Vg t2 t2  Two paths for flux to tunnel  Interference

  13. Problems:  Large energy derivatives Large coupling to background charges  Large flux  Large coupling to magnetic environment Two Josephson Junction Qubit Cg Q Vg To charge/voltage detector F Coupling can beswitched offduring the operation

  14. Three Josephson Junction Qubit h = t2 /t1 t1 t2 T.P. Orlando et al. PRB 60, 15398 (1999)  Small flux, small coupling to environment  Two islands available for coupling

  15. Hamiltonian: Energy Eigenstates

  16. Energy Eigenstates Effective Hamiltonian:

  17. Energy Eigenstates Effective Hamiltonian: r= EC /EJ Eigenenergies: h = t2 /t1 nA (=VgACg/2e)

  18. Energy Eigenstates Effective Hamiltonian: r= EC /EJ Eigenenergies: h = t2 /t1 nA (=VgACg/2e)

  19. Island Voltages Atf = Fx/F0-1/2= 0: Magic Point:nA = nB = f =0 VA = VB =0 No Coupling

  20. Charge/flux fluctuations affect decoherence only in the 2nd order Island Voltages Atf = Fx/F0-1/2= 0: Magic Point:nA = nB = f =0 VA = VB =0 No Coupling

  21. Island Voltages Atf = Fx/F0-1/2= 0: Magic Point:nA = nB = f =0 VA = VB =0 No Coupling Coupled regime: VA = Max , VB =0 Directional Coupling

  22. Some Numerics Small sensitivity to system parameters at large r(= EC /EJ)

  23. Readout Scheme Switchable Readout: Sensitive charge (voltage) detector Off: Vg = 0 during the operations On: Vg = e/2Cg at the time of readout

  24. Two Qubit Coupling Switchable Coupling: Qubits are coupled only if V(1)gB 0 and V(2)gA 0.

  25. Multi-Qubit Coupling Coupling via a bus island: Can couple every two qubits

  26. Multi-Qubit Coupling Nearest neighbors coupling:

  27. Suggested Parameters EC /EJ = 0.1, a = 0.8, Cg= 0.1C D  5.6 GHz, h  0.13 Island Voltage: VA 3.7 mV Island Charge: QA 0.2e QA large enough to be measured by rf-SET

  28. L can be small; Small coupling to magnetic environment Needs finite L for readout Comparison with Other Qubits 3JJ flux qubit: Charge-phase qubit:

  29. L can be small; Small coupling to magnetic environment Needs finite L for readout D exponentially depends on parameters Significantly smaller parameter dependence Comparison with Other Qubits 3JJ flux qubit: Charge-phase qubit:

  30. L can be small; Small coupling to magnetic environment Needs finite L for readout D exponentially depends on parameters Significantly smaller parameter dependence EJ/D0~ 10 ~3 orders of magnitude smaller kf; smaller effect of flux fluctuations EJ/D0~ 350 Comparison with Other Qubits 3JJ flux qubit: Charge-phase qubit:

  31. kC ~ 1.8, CS ~ 8 fF kC ~ 1.3, CS ~ 5 fF Comparison with Other Qubits Quantronium qubit: Charge-phase qubit: Same sensitivity to background charge noise

  32. En kC ~ 1.8, CS ~ 8 fF kC ~ 1.3, CS ~ 5 fF E3 E2 E21 E10 E1 E0 Comparison with Other Qubits Quantronium qubit: Charge-phase qubit: Same sensitivity to background charge noise Anharmonicity: A = (E21-E10 )/ E10 Harmonic oscillator:A = 0 Ideal qubit:A =

  33. kC ~ 1.8, CS ~ 8 fF kC ~ 1.3, CS ~ 5 fF Comparison with Other Qubits Quantronium qubit: Charge-phase qubit: Same sensitivity to background charge noise A = 0.2 A = 1.7 ~10 times better anharmonicity

  34. Conclusion -Operation in charge-phase regime is possible and desirable for flux qubits -Single shot readout possible with no effect on other qubits -Controlled coupling to other qubits easily achievable Compared to the 3JJ qubit -Three orders of magnitude less sensitive to flux fluctuations -Smaller L, i.e. smaller coupling to the magnetic environment -One order of magnitude less sensitive to system parameters Compared to the quantronium: - Same sensitivityto the background charge fluctuations - 10 times larger anharmonicity

  35. Conclusion -Operation in charge-phase regime is possible and desirable for flux qubits -Single shot readout possible with no effect on other qubits -Controlled coupling to other qubits easily achievable Compared to the 3JJ qubit -Three orders of magnitude less sensitive to flux fluctuations -Smaller L, i.e. smaller coupling to the magnetic environment -One order of magnitude less sensitive to system parameters Compared to the quantronium: - Same sensitivityto the background charge fluctuations - 10 times larger anharmonicity

  36. Conclusion -Operation in charge-phase regime is possible and desirable for flux qubits -Single shot readout possible with no effect on other qubits -Controlled coupling to other qubits easily achievable Compared to the 3JJ qubit -Three orders of magnitude less sensitive to flux fluctuations -Smaller L, i.e. smaller coupling to the magnetic environment -One order of magnitude less sensitive to system parameters Compared to the quantronium: - Same sensitivityto the background charge fluctuations - 10 times larger anharmonicity

  37. Conclusion -Operation in charge-phase regime is possible and desirable for flux qubits -Single shot readout possible with no effect on other qubits -Controlled coupling to other qubits easily achievable Compared to the 3JJ qubit -Three orders of magnitude less sensitive to the flux fluctuations -Smaller L, i.e. smaller coupling to the magnetic environment -One order of magnitude less sensitive to system parameters Compared to the quantronium: - Same sensitivityto the background charge fluctuations - 10 times larger anharmonicity

  38. Conclusion -Operation in charge-phase regime is possible and desirable for flux qubits -Single shot readout possible with no effect on other qubits -Controlled coupling to other qubits easily achievable Compared to the 3JJ qubit -Three orders of magnitude less sensitive to flux fluctuations -Smaller L, i.e. smaller coupling to the magnetic environment -One order of magnitude less sensitive to system parameters Compared to the quantronium: - Same sensitivityto the background charge fluctuations - 10 times larger anharmonicity

  39. Conclusion -Operation in charge-phase regime is possible and desirable for flux qubits -Single shot readout possible with no effect on other qubits -Controlled coupling to other qubits easily achievable Compared to the 3JJ qubit -Three orders of magnitude less sensitive to flux fluctuations -Smaller L, i.e. smaller coupling to the magnetic environment -One order of magnitude less sensitive to system parameters Compared to the quantronium: - Same sensitivity to the background charge fluctuations - 10 times larger anharmonicity

More Related