Superconducting Quantum Circuits

http:// DPG-Frühjahrstagung Sektion Kondensierte Materie Berlin, 11.03. - 16.03.2018 Superconducting Quantum Circuits Rudolf Gross Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften and Technische Universität München

Press Releases

Intel Delivers 17-Qubit Superconducting Chip Oct. 2017 chip with advanced packaging delivered to QuTech Intel s 17-qubit superconducting test chip for quantum computing has unique features for improved connectivity and better electrical and thermo-mechanical performance. 11.03.2018/RG - 7

Intel Fabricates Quantum Chip Tangle Lake Jan. 2018 Intel's new superconducting quantum chip called Tangle Lake has enough qubits to make things very interesting from a scientific standpoint 11.03.2018/RG - 8

72 qubit processor Google has lifted the lid on its new quantum processor, Bristlecone. The project could play a key role in making quantum computers "functionally useful."

Quantum Annealing @ mk temperature D-Wave 2000 Q: 2 000 superconducting qubits, operating temperature: 30 mk 11.03.2018/RG - 10

Superconducting Quantum Circuits 11.03.2018/RG - 11

2 nd Quantum Revolution

... solid state circuits go quantum today near future far future multi electron, spin, fluxon, photon devices superposition of states quantum entanglement confinement quantized em-fields tunneling single/few electron, spin, fluxon, photon devices quantum electron, spin, fluxon, photon devices classical description quantum 1.0 quantum 2.0 quantifiable, but not quantum quantum description Intel PTB WMI 2007 65 nm process 2005 single electron transistor superconducting qubit 11.03.2018/RG - 13 2 µm

2 nd Quantum Revolution Quantum Information Theory Solid-State Physics Mathematics realization and full control of quantum systems!! 11.03.2018/RG - 14

Nobel Prize in Physics 2002 Serge Haroche David J. Wineland The Nobel Prize in Physics 2012 was awarded jointly to Serge Haroche and David J. Wineland "for groundbreaking experimental methods that enable measuring and manipulation of individual quantum systems" 11.03.2018/RG - 15

Quantum Science & Technology powerful quantum resources quantum 2.0 Δx Δp ħ uncertainty 2 1 01 + i 10 entanglement 2 1 0 + i 1 superposition 2 11.03.2018/RG - 17

Application fields quantum computing quantum communication quantum sensing http://web.physics.ucsb.edu/~martinisgroup/pho tos/bbcrezqu1103.jpg quantum simulation http://research.physics.illinois.edu/qi/pho tonics/research/ quantum metrology. 11.03.2018/RG - 18

Public Funding of QST Research Programs in QST @ Europe United Kingdom: 270 million for a five-year program Netherlands: 146 million for a ten-year program ERANet program QUANTERA Cofund Initiative in quantum science and technologies (launch: January 2018): 30 million. Planned Research Programs in QST QUTE Flagship: Call for Flagship ramp-up phase early in 2018: > 1 000 million BMBF program QUTEGA: about 300 million (Quantum Technology Foundations & Applications) starting in 2018 11.03.2018/RG - 19

World s biggest quantum research facility in China Is China winning race with the US to develop quantum computers? Chinese funding to research the next generation in computing may be dwarfing American efforts, according to US experts PUBLISHED : Monday, 09 April, 2018, 12:37pm China is building the world s largest quantum research facility to develop a quantum computer and other revolutionary forms of technology that can be used by the military for code-breaking or on stealth submarines, according to scientists and authorities involved in the project. 11.03.2018/RG - 20

Interest of Industry Industry starts to get interested in important future technology field of Quantum Science & Technology already existing industry efforts Spin qubits in semiconductors: Intel, HRL Laboratories, NTT, Superconducting quantum circuits: Google, IBM, Intel, Anyon Systems Inc., Quantum Circuits Inc., Raytheon BBN Technologies, Rigetti Computing, Superconducting quantum annealer: D-Wave Topological qubits: Microsoft Trapped ions interfaced with photons: Lockheed Martin.. 11.03.2018/RG - 22

The Belief in New Technologies 11.03.2018/RG - 23

Quantum Simulation N interacting quantum two-level systems.. N = 50: dimension of Hilbert space: 2 50 10 15 > memory of supercomputer N = 1000: dimension of Hilbert space: 2 1000 > number of atoms in universe Richard Feynman (1981):...trying to find a computer simulation of physics, seems to me to be an excellent program to follow out...and I'm not happy with all the analyses that go with just the classical theory, because nature isn t classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem because it doesn't look so easy. 11.03.2018/RG - 24

Hardware Platforms Superconducting quantum circuits Trapped ion systems Optical lattices Quantum dot computer, spin-based Quantum dot computer, spatial-based Nuclear magnetic resonance on molecules in solution (liquid-state NMR) Solid-state NMR, Kane quantum computers Electrons-on-helium quantum computers Cavity quantum electrodynamics (c-qed) Molecular magnets Fullerene-based ESR quantum computer Linear optical quantum computer Diamond-based quantum computer (NV centers).. 11.03.2018/RG - 25

Superconducting Quantum Electronics

... from conventional to quantum electronics conventional electronic circuits quantum electronic circuits 1 2 1 2 classical physics no quantization of fields no superposition of states no entanglement quantum mechanics quantization of fields coherent superposition of states entanglement H = Φ2 2L + Q2 2C LC oscillator H = Φ 2 2L + Q 2 2C = ħω a a + 1 2 Y. Nakamura et al., Nature 398, 786 (1999) Φ, Q = iħ 11.03.2018/RG - 27

Superconducting Quantum Electronics capacitors inductors tunable, lossless nonlinear inductor Josephson Junction nonlinearity: I S 1 S 2 I s = I cj sin φ φ t = 2eV ħ I s t = I cj cos φ φ t = I cj cos φ 2eV ħ L J = V I s / t = ħ 2eI cj cos φ tunability: I s1 = I cj sin φ 1 S 1 S 2 Φ S 1 S 2 I s2 = I cj sin φ 2 I s = I c cos π Φ Φ 0 sin φ 1 + φ 2 2 I c (Φ) φ I c = 2I cj L J (Φ) = V I s / t = ħ 2eI c (Φ) cos φ 11.03.2018/RG - 29

Josephson Junction quasi-classical treatment (quantum 1.0 ) t E pot = න V I s dt 0 V = ħ 2e E pot = Φ 0I c (Φ) 2π φ t = Φ 0 φ 2π t ; I s = I c cos π Φ Φ 0 sin φ 1 cos φ Iφ external force quantum treatment (quantum 2.0 ): E pot / E J0 2 0-2 -4-6 I = I c I = 0 I = 0.5 I c -8 0.0 0.5 1.0 1.5 2.0 φ/2π / 2 H = E J 1 cos φ + E C N 2 φ = φ 2π Φ 0 φ, Q = iħ Φ 0 I c Φ 2π (2e) 2 2C nonlinear quantum harmonic oscillator Q = N 2e position momentum 11.03.2018/RG - 30

Linear and nonlinear quantum electronic circuits harmonic LC oscillator tunable Josephson junction Φ I tunable, anharmonic LC oscillator E H = ħω a a + 1 2 5> 4> 3> 2> 1> 0> artificial solid-state photon tunable, lossless Josephson inductance quantum optics on a chip E L J Φ = e> g> Φ 0 2πI c cos π Φ Φ 0 artificial solid-state atom quantum 2-level system = qubit 11.03.2018/RG - 31

Tunable artificial atoms & photon boxes photon box: microwave resonator artificial atom: solid state quantum circuit 75 µm coplanar waveguide (CPW) resonator small mode volume (V mod /l 3 10-5 10-6 ) high quality factor (Q 10 4 10 6 ) Circuit QED persistent current flux qubit many more: quantronium, fluxonium, transmon, x-mon, anharmonic level structure (quantum two-level system: qubit) quantum coherence (coherence time: < 100 µs) A. Wallraff et al., Nature 431, 162 (2004). S. Girvin, R. Schoelkopf, Nature 451, 664-669 (2008). 11.03.2018/RG - 32

Cavity & Circuit QED cavity QED natural atom in optical cavity Rempe group circuit QED solid state circuit in µ-wave cavity Gross group MPQ e.g. Kimble and Mabuchi groups at Caltech Rempe group at MPQ Garching,. WMI e.g. Wallraff (ETH), Martinis (UCSB), Schoelkopf (Yale), Nakamura (Tokyo),. resonator QED 11.03.2018/RG - 33

Quantum Bit geometrical representation on Bloch sphere 1 or e Ψ = cos Θ 2 1 + eiφ sin Θ 2 0 0 or g 11.03.2018/RG - 34

Quantum Processor Qubit Bloch sphere two1 qubit gate (C-NOT) 1 0 1 0 1 0 0 1 readout U 1 single qubit gate U 1 0 U 1 Ψ = cos Θ 2 1 + eiφ sin Θ 2 0 M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000) 11.03.2018/RG - 35

Advantages of SC Quantum Circuits

continuum of excitations Why Superconducting Systems? E E E E F normal metal D superconductor ħω ge g> e > >> k B T 2D / h 10 GHz 1 THz ω ge /2π 1 10 GHz e.g. Al: 2Δ h = 50 GHz long coherence time established fabrication technology design flexibility, tunability, scalability strong & ultrastrong coupling @ 5 GHz: ħω ge 3 10 24 J ħω ge k B 0. 2 K 11.03.2018/RG - 38

Advantages of SC Quantum Circuits exploit macroscopic quantum nature of sc ground state and gap in excitation spectrum long coherence time Yale group (2016) Moore s Law for Qubit Lifetime M. H. Devoret and R. J. Schoelkopf, Science 339, 1169 (2013) 11.03.2018/RG - 39

Coherence Time of SC-Qubits coherence time (s) 10-3 10-4 10-5 10-6 10-7 10-8 10-9 best T 2 times reproducible T 2 times fluxonium quantronium 3D transmon CPB transmon cqed 2000 2004 2008 2012 2016 year 11.03.2018/RG - 40

Coherence Time Extending the lifetime of a quantum bit with error correction in superconducting circuits Yale group: 3D circuit QED architecture N. Ofek et al., Nature 536, 441 445 (2016) 11.03.2018/RG - 41

Qubit Lifetime energy relaxation and dephasing Ψ t = cos θ(t) 2 e + e iφ(t) sin θ(t) 2 g φ t = E e E g ħ t = ω q t θ t amplitude energy, population φ(t) phase coherence population energy relaxation time T 1 or T r decay from e to g nonadiabatic (irreversible) processes induced by high-frequency fluctuations (ω ω ge ) phase pure dephasing time T φ adiabatic (reversible) processes induced by low-frequency fluctuations (ω 0) often encountered: 1/f-noise real measurements always contain T 1 -effects T 2 1 = 2T 1 1 + T φ 1 nomenclature not very consistent in literature! δφ = δω q T φ 2π 11.03.2018/RG - 42

Qubit T 1 and T 2 Times Ramsey decay 2 MHz spin-echo decay 2 MHz relaxation 4 MHz T 2 2T 1 transmon qubit is T 1 -limited J. Goetz et al., Quantum Sci. Technol. 2, 025002 (2017) 11.03.2018/RG - 43

Advantages of sc quantum circuits make use of established fabrication technology design flexibility, tunability and scalability fabricate tailor-made quantum circuits 3D coplanar waveguide resonator (Al) T 2 10 ms M. Reagor et al., APL 102, 192604 (2013) coplanar waveguide resonator (Nb) flux qubit (Al) 2 µm transmon qubit (Al) T 2 100μs Megrant et al., APL 100, 113510 (2012) T 2 500μs N. Ofek et al., Nature 536, 441 (2016) 11.03.2018/RG - 44

Qubit Design Qubit Hamiltonian H = E J 1 cos φ + E C N 2 + E ex Josephson Junction C L J Φ 0 I c Φ 2π (2e) 2 2C external circuit φ = φ 2π Φ 0 Q = N 2e φ, Q = iħ position momentum bias circuit Josephson Junction (JJ) tunable, lossless nonlinear inductor + parallel capacitor Qubit design engineering of the qubit Hamiltonian 11.03.2018/RG - 45

Flexibility in Qubit Design (@2003) phase qubit (E J >> E C ) current biased JJ flux qubit (E J > E C ) fluxon boxes charge qubit (E J < E C ) Cooper pair boxes I I V nowadays superconducting qubit zoo is larger I transmon, camel-back, capacitively shunted 3JJ-FQB, quantronium, fluxonium traditional classification via E J /E C is increasingly difficult J. Martinis (NIST) H. Mooij (Delft) V. Bouchiat (Quantronics) 11.03.2018/RG - 46

Qubit Design by Potential Engineering phase qubit (E J >> E C ) current biased JJ flux qubit (E J > E C ) fluxon boxes charge qubit (E J < E C ) Cooper pair boxes I I V engineered qubit potential 11.03.2018/RG - 47

Qubit Design by Potential Engineering H = E J 1 cos φ + E C N 2 + E ex unsuitable for TLS! flux/phase engineering add junctions (3JJ flux qubit) add inductance (rf SQUID &phase qubit) add bias current (phase qubit) L J L J C J C L J LαL J I charge engineering add gate capacitor (charge qubit) add shunt capacitor (transmon qubit) E J naturally induces anticrossings change curvature of charge parabola C s C J C J N V g E J C g 11.03.2018/RG - 48

Qubit Fabrication by Shadow Evaporation 11.03.2018/RG - 49

Superconducting Quantum Circuits 11.03.2018/RG - 51

Superconducting Quantum Circuits 11.03.2018/RG - 52

Superconducting Quantum Circuits nano-electromechanical circuit interferometer 11.03.2018/RG - 54

Superconducting Quantum Switch M. Mariantoni et al. Phys. Rev. B 78, 104508 (2008) A. Baust et al., Phys. Rev. B 91, 014515 (2015); Phys. Rev. B 93, 214501 (2016) 11.03.2018/RG - 55

Superconducting Quantum Circuit UCSB & chip with 9 X-mon qubits State preservation by repetitive error detection in a superconducting quantum circuit, J. Kelly et al., Nature 519, 66-69 (2015) 11.03.2018/RG - 56

Advantages of sc quantum circuits large dipole moments strong & ultrastrong coupling fast manipulation T. Niemczyk et al., Nature Phys. 6, 772 (2010) interaction energy = dipole moment respective field ħg = p el E rms ħg = μ mag B rms E vac rms = B vac rms = ħω ε 0 V mod μ 0ħω V mod make electric (p el ) or magnetic dipole moment (μ mag ) as big as possible make mode volume of cavity as small as possible big atoms strong coupling: g κ, γ (loss rates) small cavities ultrastrong coupling: g ω q, ω r (system frequencies) 11.03.2018/RG - 57

ω q /2π (GHz) Qubit Lifetime Qubits strongly couple to electromagnetic fields decoherence due to environmental fluctuations place qubit in cavity: Purcell filtering large detuning δ = ω r ω q g strongly reduced photon DOS @ ω q ω q ω r ω operate qubit @ sweet spot: 1st order coupling to noise vanishes δω q δω q δω q = ω q λ δλ + 1 2 ω q 2 λ 2 δλ2 + 1st order coupling 2nd order coupling λ = δφ/φ 0 11.03.2018/RG - 58

Qubit Readout dispersive readout strategy Blais et al. PRA 2004, Walraff et al., Nature 2004 rf signal in ω ω 01 qubit circuit 0 or 1 rf signal out qubit state is encoded into phase of outgoing rf-signal no energy is dissipated on chip repeat with enough photons to beat noise, use low-noise amplifiers already demonstrated multiplexed readout of several qubits, 80 ns readout pulse, fidelity >97% 11.03.2018/RG - 59

Experimental Techniques

Drawbacks of sc quantum circuits resonator atom ω r ω ge energy scales experimental challenges ω r ω ge 2π 2π 1 GHz 50 mk ħω r 10-24 J few GHz ultra-low temperatures ultra-sensitive µ-wave experiments nano-fabrication 11.03.2018/RG - 61

Experimental Techniques key physical ingredients and technological challenges ultra-low T techniques microwave technology nanotechnology 11.03.2018/RG - 62

mk technology for sc quantum circuits Optical table @ mk temperature 1 GHz 50 mk ħω r 10-24 J 11.03.2018/RG - 63

mk technology for circuit QED 11.03.2018/RG - 64

Optical table @ mk temperature 1 GHz 50 mk ħω r 10-24 J 11.03.2018/RG - 65

mk technology for sc quantum circuits Optical table @ mk temperature 1 GHz ~ 50 mk ħω r ~ 10-24 J 11.03.2018/RG - 66

µ-wave Technology + mk temperature IBM cryostat wired for a 50 qubit system 11.03.2018/RG - 67

Additional Topics

Hybrid Quantum Systems......many degrees of freedom (e.g. charge, spin, flux, photonic, phononic, plasmonic) flux qubit ferromagnetic spin ensemble T. Niemczyk et al., Nature Phys. 6, 772 (2010) H. Huebl et al., PRL 111, 127003 (2013) paramagnetic spins superconducting resonator nanomechanical beam Ch. Zollitsch et al., Appl. Phys. Lett. 107, 142105 (2015) X. Zhou, et al., Nature Physics 9, 179 (2013) 11.03.2018/RG - 177

Propagating Quantum Microwaves vacuum & coherent states squeezed thermal states squeezed vacuum squeezed coherent states L. Zhong et al., New. J. Phys. 15, 125013 (2013). E. P. Menzel et al., Phys. Rev. Lett. 105, 250502 (2010). 11.03.2018/RG - 178

Prospects realize analog superconducting quantum simulator example: bottom-up construction of many-body Hamiltonians tunable coupling J tunable nonlinearities U Bose-Hubbard or JC chain driven dissipative dynamics, scaling behavior M. Leib et al., NJP (2010) M. Leib, et al., NJP 14, 075024 (2012) 11.03.2018/RG - 181

Prospects superconducting qubits in open transmission lines ω ω q flux qubit H SB = ħω q Φ x 2 σ z + ħω k a k a k + ħ sin θ σ x g k a k +a k k k tunable spin bosonic bath interaction (Ohmic) spin-boson Hamiltonian in circuit QED J.-T. Shen and S. Fan, Phys. Rev. Lett. 95, 213001 (2005). O. Astafiev et al., Science 327, 840 (2010). I.-C.Hoi et al., arxiv:1410.8840 11.03.2018/RG - 182

Prospects The future looks bright! 11.03.2018/RG - 185

The WMI team Thank you! 11.03.2018/RG - 186