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Quantum Computing with Superconducting Circuits

Quantum Computing with Superconducting Circuits. Rob Schoelkopf Yale Applied Physics. QIS Workshop, Virginia April 23, 2009. Overview. Superconducting qubits in general and where they stand Improving decoherence Coupling/communicating between multiple qubits

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Quantum Computing with Superconducting Circuits

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  1. Quantum Computing with Superconducting Circuits Rob Schoelkopf Yale Applied Physics QIS Workshop, Virginia April 23, 2009

  2. Overview • Superconducting qubits in general and where they stand • Improving decoherence • Coupling/communicating between multiple qubits • Snapshot of current state of the art: • - Arbitrary states/Wigner function of an oscillator (UCSB) • - Implementation of two-bit algorithms (Yale) • Outlook/Future Directions 1) There is lots of excellent new science! 2) “We don’t know it’s not going to work…”

  3. Superconducting Qubits Energy nonlinearity from Josephson junction (dissipationless) electromagnetic oscillator See reviews: Devoret and Martinis, 2004; Wilhelm and Clarke, 2008 Several challenges: 1) Each engineered qubit is an “individual”… 2) Can they be sufficiently coherent? 3) How to communicate between them? (i.e. make two-bit gates) 4) How to measure the result?

  4. Three “Flavors” of SC Qubits charge qubit flux qubit phase qubit Shared traits of all of these: Weaknesses Strengths Design your hamiltonian! Inverse problem? Man-made en masse Calibration? Tune properties in-situ Decoh. from 1/f noise Strong interactions Fast relaxation Couple/control with wires Complex EM design

  5. Superconducting QC Requirement Status This IS the Hamiltonian of my system Can mass produce qubits Electronic control – a big advantage “and we really mean it!” (Lehnert, 2003) Some high fidelity (>90%) readout,not routine and sometimes incompatible with best performance Progress but a LONG way to go! Naturally strong: learning how to tameSeveral two qubit gates demonstrated Coupling with photons on wires (after DiVincenzo)

  6. Progress in Superconducting Charge Qubits Transmon (Yale) “Quantronium”: sweet spot (Saclay) Charge echo (NEC) Nakamura (NEC) Similar plots can be made for phase, flux qubits

  7. Outsmarting Noise: Sweet Spot 1st coherence strategy: optimize design sweet spot Energy transition freq. 1st order insensitive to gate noise Charge (CgVg/2e) Strong sensitivity of frequency to charge noise But T2 still < 500 ns due to second-order noise! Vion et al., Science 296, 886 (2002)

  8. “Eliminating” Charge Noise with Better Design EJ/EC = 1 EJ/EC = 25 - 100 Energy exponentially suppresses 1/f! Cooper-pair Box “Transmon” Houck et al., 2008

  9. Coherence in Transmon Qubit Random benchmarking of 1-qubit ops Chow et al. PRL 2009:Technique from Knill et al. for ions Error per gate = 1.2 % Similar error rates in phase qubits (UCSB): Lucero et al. PRL 100, 247001 (2007)

  10. Materials Can Matter… 2nd coherence strategy: improve materials/fabrication Dielectric loss? Martinis et al., 2005 (UCSB) phase qubits losses consistent with two-level defect physicsin amorphous dielectrics quantum regime quantumregime is special! Progress on origin of 1/f flux noise: Spontaneous emission? Superconductors? Junctions? Readout circuitry? Other relaxationmechanisms: Clarke, McDermott, Ioffe… Still not clear for most qubits!

  11. But High Q May Not Be Impossible! V. Braginsky, IEEE Trans on Magnetics MAG-15, 30 (1979) 109 Q ~ 109 @ 1 K ! 108 107 Quality factor 106 105 Nb films on macroscopic sapphire crystal 104 0 5 10 15 T (K) Note: this is not in microfabricated device, and not at single photon level So fundamental limits might be 4-5 orders of magnitude away…

  12. Coupling SC Qubits: Use a Circuit Element a capacitor entangledstates Con ~ 55% Charge qubits: NEC 2003 Phase qubits: UCSB 2006 an inductor tunable element Flux qubits: Delft 2007 Flux qubits: Berkeley 2006, NEC 2007

  13. Qubits Coupled with a Quantum Bus use microwave photons guided on wires! “Circuit QED” Blais et al., Phys. Rev. A (2004) transmissionline “cavity” out Josephson-junctionqubits 7 GHz in Expts: Sillanpaa et al., 2007 (Phase qubits / NIST) Majer et al., 2007 (Charge qubits / Yale)

  14. Recent Highlights: Arbitrary States of Oscillator Hofheinz et al., Nature 2008 (UCSB)

  15. Wigner Functions of Complex Photon States Thy. Expt. Hofheinz et al., Nature in press 2009 (UCSB)

  16. Wow! Requires: • Dozen pulses with sub-ns timing • Per pulse accuracy >> 90% • Many initial calibrations • Many field displacements for W(a) Shows the beauty of strong coupling + electronic control…

  17. A Two-Qubit Processor 1 ns resolution DC - 2 GHz T = 10 mK cavity: “entanglement bus,” driver, & detector transmon qubits L. DiCarlo et al., cond-mat/0903.2030 (Yale)

  18. Spectroscopy of Qubits Interacting with Cavity right qubit Qubit-qubit swap interaction Majer et al., Nature(2007) left qubit Cavity-qubit interaction Vacuum Rabi splitting Wallraff et al., Nature(2004) cavity

  19. Spectroscopy of Qubits Interacting with Cavity 01 Qubits mostly separated and non-interacting due to frequency difference Preparation 1-qubit rotations Measurement 10 cavity

  20. Two-Qubit Gate: Turn On Interactions Use voltage pulse oncontrol lines to push qubits near a resonance: 01 A controlled z-z interaction also ala’ NMR Conditional phase gate 10 cavity Adiabatic pulse (30 ns)-> conditional phase gate

  21. Measuring Two-Qubit States Joint measurement of both qubits and correlations using cavity frequency shift rightqubit leftqubit correlations Density matrix Ground state:

  22. Measuring Two-Qubit States Apply p-pulse to invert state of right qubit 00 01 10 11 One qubit excited:

  23. Measuring Two-Qubit States Now apply a c-Phase gate to entangle the qubits 00 01 10 11 Fidelity: 94% Concurrence: 94% Bell State:

  24. Two-Qubit Grover Algorithm Challenge: Find the location of the -1 !!! “unknown” unitary operation: Classically: 2.25 evaluations QM: 1 evaluation only! ORACLE 10 pulses w/ nanosecond resolution, total 104 ns duration

  25. Grover in action Grover Step-by-Step Begin in ground state:

  26. Grover in action Create a maximal superposition:look everywhere at once!

  27. A Grover step-by-step movie Grover in action Apply the “unknown”function, and mark the solution

  28. Grover in action Some more 1-qubitrotations… Now we arrive in one of the four Bell states

  29. Grover in action Grover search in action Grover in action Another (but known) 2-qubit operation now undoes the entanglement and makes an interferencepattern that holds the answer!

  30. Grover in action Grover search in action Grover in action Final 1-qubit rotations reveal the answer: The binary representation of “location 3”! The correct answer is found >80% of the time.

  31. Future Directions • Analog quantum information: • parametric amplifiers, squeezing, continuous variables QC • Topological/adiabatic QC models?? • Multi-level quantum logic (qudits), or level structures? • “Hybrid” systems (combine SC with spin, ion, molecule,…)? • Quantum interface to optical photons? • A really long-lived solid-state memory Engineering Wish List • A low-electrical loss fab process (with Q > 107?) • Cheap waveform generators (16 bits, 10 Gs/sec, $2k/chan?) • Controlled couplings with high on/off ratio (> 40 dB?) • Quantum-limited amplifiers/detectors in GHz range (readout!) • Stable funding! • Reliable dilution refrigerators…

  32. Summary – Superconducting Qubits • Can make, control, measure, and entangle qubits, • in several different designs • Play moderately complex games with 10’s of pulses, and error per pulse ~ 1% • Coherence times ~ microseconds, operation times ~ few ns (improved x 1,000 in last decade!) • Two complimentary approaches for improving this further • 1) Design around the decoherence • 2) Make better materials, cleaner systems • Immediate future: multi-partite entanglement, rudiments of error correction…

  33. Two-Excitation Manifold of System “Qubits” and cavity both have multiple levels…

  34. Adiabatic Conditional Phase Gate • Avoided crossing (160 MHz) • A frequency shift Use large on-off ratio of z to implement 2-qubit phase gates. Strauch et al. (2003): proposed use of excited states in phase qubits

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