Introduction To Superconducting Qubits And Quantum Experience - Kias
IBM T.J. Watson Research CenterINTRODUCTION TO SUPERCONDUCTING QUBITSAND QUANTUM EXPERIENCE:A 5-QUBIT QUANTUM PROCESSOR IN THE CLOUDHanhee PaikIBM Quantum Computing GroupIBM T. J. Watson Research Center,Yorktown Heights, NY USA 2016 IBM Corporation
IBM T.J. Watson Research CenterOUTLINETODAY Superconducting Josephson junction qubit:an artificial atom Circuit Quantum electrodynamics: Interactionbetween microwave light and artificial atomsTOMORROW Quantum Experience: A 5-qubit in the cloud2016 ICAP Summer SchoolJuly, 2016 2016 IBM Corporation
IBM T.J. Watson Research CenterINTRODUCTION TOSUPERCONDUCTINGJOSEPHSON JUNCTION QUBIT44th IFF Spring SchoolMarch, 2013 2016 IBM Corporation
IBM T.J. Watson Research CenterQUANTUM INFORMATION SYSTEMSmicro PHOTONScouplingwith environment NUCLEAR SPINS IONS ATOMS MOLECULES QUANTUM DOTS SUPERCONDUCTING CIRCUITSMACRO 2016 IBM Corporation
IBM T.J. Watson Research CenterQUANTUM INFORMATION SYSTEMSmicro PHOTONScouplingwith environment NUCLEAR SPINS IONS ATOMS MOLECULES QUANTUM DOTS SUPERCONDUCTING CIRCUITSMACROCircuits are quantized!!- FIRST DEMONSTRATION BY DEVORET, MARTINIS, CLARKE (1985)- engineered hamiltonian with "LEGO" blocks:capacitors, inductors and Josephson junctionsA.J. Leggett, 1982 2016 IBM Corporation
IBM T.J. Watson Research CenterATOM SUPERCONDUCTING CIRCUIT;ELECTRON DEGREES OF FREEDOM MACROSCOPIC CURRENTS AND VOLTAGESSIMPLEST EXAMPLE: SUPERCONDUCTINGSub-mm dimensionsLC OSCILLATORL nH, C pF, wr /2p GHzCIRCUITLumped elementsELECTRONIC FLUID SLOSHES BACK AND FORTHFROM ONE PLATE TO THE OTHER, NO INTERNAL DISSIPATION 2016 IBM Corporation
IBM T.J. Watson Research CenterDEGREE OF FREEDOM IN ATOM vs CIRCUITSuperconductingLC oscillatorRydberg atomLCvelocity of electron voltage (charge) across capacitorforce on electron current (flux) through inductor 2016 IBM Corporation
IBM T.J. Watson Research CenterLC OSCILLATOR AS A QUANTUM CIRCUITEf q-qwrf fˆ, qˆ i wr kBT5-10 GHz10mK 2016 IBM Corporation
IBM T.J. Watson Research CenterSUPERCONDUCTING JOSEPHSON JUNCTION QUBIT Qubit (two level system) requires nonlinearity. No lossSuperconducting Josephson Junction Josephson junction provides a nonlinear element. Conducts electricity without resistance (no loss). Couple two superconductorsvia oxide layer Oxide layer acts as tunnelingbarrierAlSCAlOxAlSC 2016 IBM Corporation
IBM T.J. Watson Research CenterJOSEPHSON JUNCTIONS – FEYNMAN’S MODELAldensity of electrons oneither side of the SCAlOxphase of the SCAlEquations of motion from a toy modelK – tunneling energy2eV – energy across the junctionAC-Josephson effectDC-Josephson effect 2016 IBM Corporation
IBM T.J. Watson Research CenterTHE JOSEPHSON JUNCTION HAMILTONIAN211 Energy storedU K CV 2 C 2in the capacitor22 2e Energy storedin the inductorU P IVdt EJ cos What is the conjugate momentum Pj for ? L p C CV (2en) n 2e2e 2e 2 ̂ , nˆ iJosephson Hamiltonianqext 2ˆH EC (nˆ ) EJ cos ̂2eChargingEnergyJosephsonEnergy 2016 IBM Corporation
IBM T.J. Watson Research CenterTHE CHARGE LIMITCharge fluctuationsFirst experiment in 1999FIRST coherent manipulation of SC qubit by Nakamura et. al. Nature 398, 786 (1999) 2016 IBM Corporation
IBM T.J. Watson Research CenterTHE CHARGE LIMITCharge fluctuationsFirst experiment in 1999Sweet spot operation in 2002FIRST BREAKTHROUGH IN COHERENCE by Vion et. al. Science 296, 886 (2002) 2016 IBM Corporation
IBM T.J. Watson Research CenterTHE TRANSMONCsThe transmon Capacitively-shunted Josephson junction qubitwhereand Engineering an artificial atom with a capacitor and an inductor(JJ critical current). Depending on EJ/Ec, the transmon dynamics varies.Koch et. al. PRA 76, 04319 (2007) 2016 IBM Corporation
IBM T.J. Watson Research CenterFROM A CHARGE REGIME TO A “TRANSMON” REGIMEIncreasing Charge dispersionbecomes flat anharmonicitydecreases“Transmon’ regimeNowadays (2016), T2 50000 ns (50 ms) to 200000 ns (200 ms).Koch et. al. PRA 76, 04319 (2007) 2016 IBM Corporation
IBM T.J. Watson Research CenterEIGENFUNCTIONS OF THE TRANSMONEigen functions similar to a harmonic oscillator – suggest agood basis is the harmonic oscillators eigenfunctions 2016 IBM Corporation
IBM T.J. Watson Research CenterLARGE EJ/EC HAMILTONIANExpanding the cosine to 4th order giveswhereDefining dimensionless variableswhereandQubit frequency engineered byEc and Ej (capacitance and inductance)This is just a weakly anharmonic oscillator (w0 Ec) 2016 IBM Corporation
IBM T.J. Watson Research CenterIMPROVEMENTS IN COHERENCE TIMESBest T2– Understand charge noise e.g. [1]Reproducible T2– 3D transmon [5](1)3D2D– IR Shielding [6,7],– Cold cavities & cold qubits [8]T2 (sec)– High Q cavities [9]T1Decay 1 0as 𝑒 𝑡/𝑇1– Materials e.g. [2,10]– Design and geometries [4,10]– Microwave environment [3][1] Koch et. al. PRA 76, 04319 (2007)[2] J. Martinis et al., PRL 95 210503 (2005)[3] Houck et. al. PRL 101, 080502 (2008)[4] K. Geerlings et al., APL 100, 192601 (2012)[5] H. Paik et al., PRL 107, 240501 (2011)[6] R. Barends et al., APL 99, 113507 (2011)[7] A. Corcoles et al., APL 99, 181906 (2011)[8] C. Rigetti et al., PRB 86, 100506 (2012)[9] M. Reagor et al., APL 102, 192604 (2013)[10] J. Chang et al. APL 103, 012602 (2013)Quality factor ofthe transmonqubit 2MroutinelyachievableYear(1) Noise threshold for 2D fault tolerant computation assuming 30-100ns gate time 2016 IBM Corporation
IBM T.J. Watson Research CenterSUPERCONDUCTING QUBITS IN 3D CAVITIES:MITIGATING SURFACE LOSSESdtSubstrate (Si/Al2O3)E-fieldNative oxide( Esurf / Etot )2 1/d Big features predicted to have higher Q (less surface contribution)– But radiation also increasingly worse– flux trapping quickly can be an issue Placing a large qubit in a 3D microwave cavity mitigates both surface andradiation losses with decreased surface participation.Paik et al. PRL, 107, 240501 (2011) 2016 IBM Corporation
IBM T.J. Watson Research CenterINTERACTING WITH SUPERCONDUCTING QUBITCIRCUIT QUANTUMELECTRODYNAMICS (cQED) 2016 IBM Corporation
IBM T.J. Watson Research CenterCAVITY QUANTUM ELECTRODYNAMICS(CQED)2g vacuum Rabi freq.k cavity decay rateg “transverse” decay rateJaynes-Cummings HamiltonianH wc a a wq2 ˆ z g (a ˆ a ˆ ) 2016 IBM Corporation
IBM T.J. Watson Research CenterCIRCUIT QUANTUM ELECTRODYNAMICS(cQED)Theory: Blais et al., Phys. Rev. A 69, 062320 (2004)outSuperconductingtransmissionline “cavity”Superconducting artificial10 mmMicrowave“atom”in Strong coupling achieved! 2016 IBM Corporation
IBM T.J. Watson Research CenterTHE JAYNES CUMMINGS HAMILTONIANThe resonator can be represented by a simple harmonic osc.withThe voltage is given byThe interaction with the resonator is described bywhereIt is possible to reach the strong coupling regime 2016 IBM Corporation
IBM T.J. Watson Research CenterTHE STRONG COUPLING REGIMEWallraff et al. Nature, 431, 162 (2004) 2016 IBM Corporation
IBM T.J. Watson Research CenterTHE (Ultra-Strong) DISPERSIVE LIMITSolving to second order after a dispersive approximation is AC Stark shift: a state-dependent qubit or cavity frequency shiftg e; n 2g e; n 1g e; n 02 n 0n 0.5Lambn 1 shiftn 2n 2n 1n 0 k, gn 1Stark shiftper photonnown 0 1,000linewidthsQubit Frequency (GHz) 2016 IBM Corporation
IBM T.J. Watson Research CenterMICROWAVE CONTROLS OF TRANSMON:SINGLE QUBIT GATESA microwave drive V is applied to thequbit through a resonatorDriving HamiltonianqubitHˆ d VQˆ VQZPF (bˆ bˆ ) (t )(bˆ bˆ )drive resonatorAfter making the rotating wave approximation (driving frame D wd w)Rotationoperator alongPauli matrix A RA ( ) exp iAˆ Iˆ cos iAˆ sin 2 2 2 Complete control in the qubit subspace by using 2016 IBM Corporation
IBM T.J. Watson Research CenterTOMORROW TWO-QUBIT GATE FOR SC QUBITS:CROSS RESONANCE EXPERIMENTAL SET UP QUANTUM EXPERIENCE DEMO 2016 IBM Corporation
IBM T.J. Watson Research CenterIBM RESEARCHQUANTUM EXPERIENCESIGN UP FOR FREE AThttps://quantumexperience.ng.bluemix.net 2016 IBM Corporation
IBM T.J. Watson Research CenterBUILDING A QUANTUM COMMUNITY:IBM QUANTUM EXPERIENCEIBM Quantum Experience (launched May 2016) Free to use Sign up at www.ibm.com/quantumcomputing Access to real 5Q device. Compare noise &deficiencies of real device to ideal simulation. 25,000 registered users Detailed user guide about quantum computing Learn about quantum algorithms, try your own! Universities adopting our tool for teachingNew papers enabled by IBM Become part of a growing community of users.Quantum Experience within firstmonth of operation Just the beginning arXiv:1605.04220 External users to contribute content arXiv:1605.05709 Expanded hardware capabilities Others in preparation! IBM Research Frontiers Institute to foster closercollaborations with university, industry partners 2016 IBM Corporation
INTRODUCTION TO SUPERCONDUCTING QUBITS AND QUANTUM EXPERIENCE: A 5-QUBIT QUANTUM PROCESSOR IN THE CLOUD Hanhee Paik IBM Quantum Computing Group IBM T. J. Watson Research Center, . Detailed user guide about quantum computing Learn about quantum algorithms, try your own!
Nitrogen vacancy centers HeH 2 qubits Wang, et al., ACS Nano 9 7769 2015 Superconducting qubits Hydrogen molecule 3 qubits O'Malley, et al, Phys Rev X 6 031007 2016 BeH 2 6 qubits Kandala, et al. Nature 548 242 2017 Ion traps HeH 3 qubits Shen, et al, arXiV:1506.00443 2015 LiH 3 qubits Hempel, et al. To be submitted 2016 45 46
Superconducting Qubits and the Physics of Josephson Junctions 3 f L f R V I J Figure 1. Schematic diagram of a Josephson junction connected to a bias voltage V. The Josephson current is given by IJ I0 sin–, where – L ¡ R is the di
The computational building block of quantum computers are so-called qubits (quantum bits) Any qubit is a quantum system defined by ground ȁ ۧand excited states A quantum computer would have many qubits coupled together, along with input control lines and output measurement lines
We also demonstrated long spin lifetimes at elevated Annual report 2018 temperatures (Phys. Rev. Lett. 2018), providing scope for quantum integrated circuits hosting both the qubits and the classical control electronics. Superconducting qubits// In 2018, we made decisive (). (((, 2018).
Introduction to Quantum Mechanics of Superconducting Electrical Circuits What is superconductivity? What is a Josephson junction? What is a Cooper Pair Box Qubit? Quantum Modes of Superconducting Transmission Lines See R.-S. Huang PhD thesis on Boulder 2004 web page.
Nexans was able to design, produce and deliver two resistive superconducting limiter devices. Both devices are designed for the medium voltage grid and were tested at the high-voltage and high-power lab IPH in Berlin. The superconducting components of both limiters, coils of bulk MCP BSCCO-2212, have been designed and produced by Nexans. 1.
the binding energy of the Cooper pair is large as compared to the thermal energy scattering. As a result, Cooper pairs propagate through the material and current ows without any resistance. The typical transition from normal to superconducting behavior is shown in Figure 1. e Temperature TC v v Non-superconducting metal Superconductor
(half serious, half playful) Yes – except for last summer, when you never came near me –Sheila (Act 1) Suggesting that she doesn [t fully trust him, despite the fact that theyre going to be married soon, but again shows how she is childish, and relatively light-hearted, as she is still half playful [ even in something which could be seen as quite serious. men with important work to do .
