Quantum Computing with Superconducting Circuits
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Transcript of Quantum Computing with Superconducting Circuits
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Quantum Computing with Superconducting CircuitsRob SchoelkopfYale Applied PhysicsQIS Workshop, Virginia April 23, 2009
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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
2) We dont know its not going to work1) There is lots of excellent new science!
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Superconducting Qubitsnonlinearity from Josephson junction(dissipationless)electromagnetic oscillatorSee reviews: Devoret and Martinis, 2004; Wilhelm and Clarke, 2008Energy1) Each engineered qubit is an individual2) Can they be sufficiently coherent?3) How to communicate between them? (i.e. make two-bit gates)Several challenges:4) How to measure the result?
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Three Flavors of SC QubitschargequbitfluxqubitphasequbitDesign your hamiltonian!Inverse problem?Man-made en masseCalibration?Tune properties in-situDecoh. from 1/f noiseStrong interactions Fast relaxationCouple/control with wiresComplex EM designStrengthsWeaknessesShared traits of all of these:
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Superconducting QC RequirementStatus(after DiVincenzo)This IS the Hamiltonian of my systemand we really mean it! (Lehnert, 2003)Some high fidelity (>90%) readout, not routine and sometimes incompatiblewith best performanceProgress but a LONG way to go!Naturally strong: learning how to tame Several two qubit gates demonstratedCoupling with photons on wiresCan mass produce qubits Electronic control a big advantage
1. Make and control lots of qubits.2. Measure the result3. Avoid decoherence
4. Make qubits interact with each other (gates) 5. Communicate quantum information (w/ photons?)
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Progress in Superconducting Charge QubitsNakamura (NEC)Charge echo (NEC)Quantronium:sweet spot(Saclay)Transmon(Yale)Similar plots can be made for phase, flux qubits
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Outsmarting Noise: Sweet Spotsweet spotEnergyVion et al., Science 296, 886 (2002)transition freq.1st order insensitiveto gate noiseBut T2 still < 500 ns due to second-order noise!1st coherence strategy: optimize designCharge (CgVg/2e)Strong sensitivity of frequency to charge noise
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EnergyEJ/EC = 1EJ/EC = 25 - 100Eliminating Charge Noise with Better DesignCooper-pair BoxTransmonexponentially suppresses 1/f!Houck et al., 2008
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Coherence in Transmon QubitError per gate = 1.2 %Random benchmarking of 1-qubit opsChow et al. PRL 2009: Technique from Knill et al. for ionsSimilar error rates in phase qubits (UCSB):Lucero et al. PRL 100, 247001 (2007)
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Materials Can Matterlosses consistent with two-level defect physics in amorphous dielectricsMartinis et al., 2005 (UCSB)Other relaxation mechanisms:Spontaneous emission?Superconductors?Junctions?Readout circuitry?Still not clear for most qubits!Dielectric loss?phase qubits2nd coherence strategy: improve materials/fabricationProgress on origin of 1/f flux noise: Clarke,McDermott,Ioffequantum regimeis special!quantum regime
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But High Q May Not Be Impossible!V. Braginsky, IEEE Trans on Magnetics MAG-15, 30 (1979)Nb films on macroscopic sapphire crystalQ ~ 109 @ 1 K !So fundamental limits might be 4-5 orders of magnitude awayNote: this is not in microfabricated device, and not at single photon levelQuality factor104109T (K)051015105106107108
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Coupling SC Qubits: Use a Circuit Elementa capacitorCharge qubits: NEC 2003 Phase qubits: UCSB 2006 entangled statesCon ~ 55%an inductorFlux qubits: Delft 2007 tunable elementFlux qubits: Berkeley 2006, NEC 2007
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Qubits Coupled with a Quantum BusJosephson-junction qubits7 GHz inouttransmission line cavityBlais et al., Phys. Rev. A (2004)Circuit QEDExpts: Sillanpaa et al., 2007 (Phase qubits / NIST) Majer et al., 2007 (Charge qubits / Yale)use microwave photons guided on wires!
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Recent Highlights: Arbitrary States of OscillatorHofheinz et al., Nature 2008 (UCSB)
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Wigner Functions of Complex Photon StatesThy.Expt.Hofheinz et al., Nature in press 2009 (UCSB)
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Wow! Dozen pulses with sub-ns timing Per pulse accuracy >> 90% Many initial calibrations Many field displacements for W(a)Requires:Shows the beauty of strong coupling + electronic control
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A Two-Qubit Processor1 ns resolutioncavity: entanglement bus, driver, & detectortransmon qubitsDC - 2 GHzT = 10 mKL. DiCarlo et al., cond-mat/0903.2030 (Yale)
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Spectroscopy of Qubits Interacting with CavityQubit-qubit swap interactionMajer et al., Nature (2007)cavityleft qubitright qubitCavity-qubit interactionVacuum Rabi splittingWallraff et al., Nature (2004)
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Spectroscopy of Qubits Interacting with Cavity01Preparation1-qubit rotationsMeasurementcavity10Qubits mostly separatedand non-interacting due to frequency difference
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Two-Qubit Gate: Turn On Interactions01cavity10Conditionalphase gateUse voltage pulse on control lines to push qubits near a resonance:A controlled z-z interactionalso ala NMRAdiabatic pulse (30 ns) -> conditional phase gate
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Measuring Two-Qubit StatesJoint measurement of both qubits and correlations using cavity frequency shiftGround state: Density matrixleft qubitright qubitcorrelations
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Measuring Two-Qubit StatesApply p-pulse to invert state of right qubitOne qubit excited: 00011011
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Measuring Two-Qubit StatesBell State: Now apply a c-Phase gate to entangle the qubits00011011Fidelity: 94%Concurrence: 94%
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Two-Qubit Grover Algorithmunknownunitaryoperation:Challenge: Find the location of the -1 !!!10 pulses w/ nanosecond resolution, total 104 ns durationORACLEClassically: 2.25 evaluationsQM: 1 evaluation only!
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Grover Step-by-Step Grover in actionBegin in ground state:
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Grover in actionCreate a maximalsuperposition: look everywhere at once!
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A Grover step-by-step movie Grover in actionApply the unknown function, and mark the solution
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Grover in action Some more 1-qubit rotationsNow we arrive in one of the four Bell states
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Grover in actionGrover search in action Grover in actionAnother (but known)2-qubit operation now undoes the entanglement and makes an interference pattern that holds the answer!
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Grover in actionGrover search in action Grover in actionFinal 1-qubit rotations reveal theanswer:The binary representation of location 3!The correct answer is found >80% of the time.
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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 memoryEngineering 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
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Summary Superconducting Qubits Can make, control, measure, and entangle qubits,in several different designs
Play moderately complex games with 10s 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 further1) Design around the decoherence2) Make better materials, cleaner systems
Immediate future: multi-partite entanglement, rudiments of error correction
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Two-Excitation Manifold of SystemQubits and cavity both have multiple levels
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Adiabatic Conditional Phase Gate A frequency shift Avoided crossing (160 MHz)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
These plots can be found in folderY:\_Talks\ARO Program Review 2008\Benchmarking\IgorExpmts
TimeDomainExpmts.pxp for plots on leftTimeDomainDetuned.pxp for plots on right (option of using 2 us T2 figure is in another experiment, HigherT2Detuned.pxp)To do the decaying exponential cosine fits, the procedure file named RabiEnv1.ipf is needed, and it makes a fit routine under Curve Fitting named RabiEnv
7.356 GHz6.9 Ghz cavity5.98 GHz