Quantum Computing with Superconducting CircuitsRob SchoelkopfYale Applied PhysicsQIS Workshop, Virginia April 23, 2009

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!

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?

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:

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?)

Progress in Superconducting Charge QubitsNakamura (NEC)Charge echo (NEC)Quantronium:sweet spot(Saclay)Transmon(Yale)Similar plots can be made for phase, flux qubits

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

EnergyEJ/EC = 1EJ/EC = 25 - 100Eliminating Charge Noise with Better DesignCooper-pair BoxTransmonexponentially suppresses 1/f!Houck et al., 2008

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)

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

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

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

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!

Recent Highlights: Arbitrary States of OscillatorHofheinz et al., Nature 2008 (UCSB)

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

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

A Two-Qubit Processor1 ns resolutioncavity: entanglement bus, driver, & detectortransmon qubitsDC - 2 GHzT = 10 mKL. DiCarlo et al., cond-mat/0903.2030 (Yale)

Spectroscopy of Qubits Interacting with CavityQubit-qubit swap interactionMajer et al., Nature (2007)cavityleft qubitright qubitCavity-qubit interactionVacuum Rabi splittingWallraff et al., Nature (2004)

Spectroscopy of Qubits Interacting with Cavity01Preparation1-qubit rotationsMeasurementcavity10Qubits mostly separatedand non-interacting due to frequency difference

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

Measuring Two-Qubit StatesJoint measurement of both qubits and correlations using cavity frequency shiftGround state: Density matrixleft qubitright qubitcorrelations

Measuring Two-Qubit StatesApply p-pulse to invert state of right qubitOne qubit excited: 00011011

Measuring Two-Qubit StatesBell State: Now apply a c-Phase gate to entangle the qubits00011011Fidelity: 94%Concurrence: 94%

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!

Grover Step-by-Step Grover in actionBegin in ground state:

Grover in actionCreate a maximalsuperposition: look everywhere at once!

A Grover step-by-step movie Grover in actionApply the unknown function, and mark the solution

Grover in action Some more 1-qubit rotationsNow we arrive in one of the four Bell states

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!

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.

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

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

Two-Excitation Manifold of SystemQubits and cavity both have multiple levels

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