1. Quantum Information Storage in Solid State Systems David P. Pappas National Institute of Standards & Technology Boulder, CO M. Vissers, Jeff Kline

2. Something... “took a Quantum Leap!” Misnomer?  E = mgh = (60 kg) x (9.8 m/s 2 )x(0.1 m) = 60 kg m 2 /s 2  E ~ 60 Joules 0.1 meter Equivalent of man jumping 0.000 000 000 000 000 001 meters high < millionth of an atom Quantum leap 1  E = 10 electron-volts 1 eV =1.602 x 10 -19 Joules Quantum Leap -  E ~ 1 x 10 -18 Joules Hydrogen atom energy levels -13.6 eV -3.4 eV 2 n=1 n=2 3

3. electron acts like a wave not measured electron acts like particle when measured at some position =>Quantum Hydrogen “Quantum Leap” ≡ fundamental change in paradigm Classical Hydrogen electron charged particle accelerating e - loses energy spirals in atom collapses + -

4. Quantum mechanics is Nature’s calculator …very very fast Example – Self assembly of atoms into molecules Difficult for classical computer to simulate the simplest molecule Can we turn situation around? –make artificial atoms –redefine rules=> system solves problem Caffeine Ethanol Aspirin R. Marx, A. F. Fahmy, J. M. Myers, W. Bermel, S. J. Glaser Phys. Rev. A 62, 012310-1-8 (2000) BOC-(13C2-15N-2D -glycine)-fluoride 5 “qubit” molecule NMR

5. Quantum Information Quantum Computing Factor large numbers Simulate physical systems Search databases Quantum Cryptography Send messages securely Alternative to public key  Detect eavesdroppers What is different about Quantum Information? How is it useful? Can we control it? Software Hardware

6. Classical Cryptography Public key Send public key =15 Alice Bob Eve Eavesdropper needs to figure out 15=3x5 to decode : 1094173864157052742180970732204035761200373294544920599091384213147634998428893478471799725789126733249762575289978183379 7076537244027146743531593354333897= 102639592829741105772054196573991675900716567808038066803341933521790711307779 x 106603488380168454820927220360012878679207958575989291522270608237193062808643 7 months to reduce this number into it’s two prime factors  Need faster factoring - Quantum Computing  Need code that can’t be eavesdropped - Quantum Cryptography Send message back Pick 2 private keys, 3 & 5 Send public key 15=3 x 5 Use private keys to decode Receive public key = 15 Encode data with public key Send encrypted message back

7. Progress in Quantum Information Quantum Computing –Software Quantum error correction – Steane, Shor PRL (1996) Fault tolerant algorithms – Knill, Nature (2005) –Hardware NMR quantum computers have reached 5 bits –Grovers algorithm - Vandersypen APL (2000) –Shor’s alorithm - Nature (2001) Ion traps – demonstrated factoring –Semi-classical QFT – Wineland, Science (2005) –Quantum error correction – Nature (2004) –Six atom Schroedinger Cat State – Nature (2005) Linear optics gate with photons – Franson PRA (2001) Solid state qubits demonstrate 2 coupled qubits Quantum cryptography –Demonstrated, tested Practical demos - Zeilinger Optics Expr. (2004) 1.45 km through Vienna sewer system –Scaling up to commercial products Bank City Hall

8. Quantum Computing software – Digital Logic One classical bit 50% Measure Quantum bit (qubit) “0” “1” or if a=b 2 states 6 states

9. Quantum computing more possible states & intrinsically parallel Classical computation: Quantum computation: n bits => 2 n possible states S 1 =00…000 S 2 =00…001 S 3 =00…010 … Classical Gate f(x) Output f(S 1 ) f(S 2 ) 2 n computations Spans all input states Quantum gate f(x) 1 computation operates on all states measure n bits Output state n qubits => possible states

10. Classical algorithm: –N =8 Items (states): –On average, need to search N/2 (=4) items to find –: O(N) Quantum Algorithm: –Compares all coefficients at the same time Quantum Interference Speed up of unsorted data search

11. a b c d e f g h Grover’s Search Algorithm F( ) => change sign if matches “diffusion” operator - reflect around average Weights:

12. Grover’s algorithms conducts search in O(N 1/2 ) vs. O(N)  Quantum systems “recognize” solutions  classical database doesn’t gain for simple search  N operations to load!  Resources - NlogN amplitudes for algorithm  Cryptography key search algorithms can benefit greatly –Shor’s algorithm factors numbers Quantum Fourier Transform: Exponential speedup of FT Used to find factors of numbers –Crack public key encryptions Quantum algorithms take fundamentally different mindset! Quantum problem solving is fast

13. Quantum Computing Hardware Coupling Initialize Store Interact Measure Systems: Superconductors Phase, charge, flux ~~~~~~~~~~ Semiconductor spin Quantum dot ~~~~~~~~~ NMR Neutral atoms Ions Photons Lifetimes

14. NIST - Quantum computing with real atoms 9 Be + ions - MEMs RF traps Addressed with focused lasers Shuttle ions around –Store – interact Long lifetimes Challenge is scaling & interaction –initialization –operation –measurement

15. Making artificial atoms 1) Use Superconductors 1.Zero DC resistance - PDG-conductor at AC 2.Complete diamagnetism 3.Macroscopic quantum effects 2) Make LC circuit 3) Add non-linearity to define energy levels I L C Intensity frequency Quality factor: Lifetime: Thin, non-linear junction & capacitor

16. What temperature & frequency? Freeze out quasiparticles (unpaired e - ) in the superconductor Excitation energy >> Thermal f = 2 – 10 GHz range Need high Q for long lifetimes ~ 10 6 gives  s time constants Need enabling technology for low T operation –0.05 to 0.1 K!

17. 10/1/201517 Adiabatic demagnetization refrigerattor (ADR) High Precision Devices – Louisville, CO Automated mag cycl & T PID Demonstrated T 400 hr < 1 day turnaround Hold time > 12 hr @ 0.1 K w /2 coax Closed cycle dilution refrigerators (DR) Multiple vendors – Oxford, BlueFors, Cryomagnetics, HPD, Quantum Design … 20 mK base Continuous > 400 μW power - ~ 100 coax ~ 10 kW power for He compressor & electronics Closed cycle plug & play refrigerators T< 0.1 K

18. NIST – Quantum computing with superconductors Al/AlO X junctions on Si wafers –optical lithography ~ 1  m features –standard processing Al wiring w/SiO 2 dielectric Addressed with RF pulses, DC bias currents Couple qubits with capacitors Challenge –Improve lifetimes –Reduce decoherence Operate at 20 mK – Expected to reduce thermal – decoherence sources

19. Solid State Quantum Iinformation –Challenges Need many qubits – 10 ~ 100 (logical) Need long quantum coherence times ~ ms Need high measurement fidelity ~ 99% –Superconducting Josephson junction “phase” qubits Operation Spectroscopy –Materials Al ring w/weak link “Josephson Junction” SiO x substrate, insulator Al0 x tunnel barrier Identification of decoherence Improvements

20. How do you talk to a phase qubit? RF in ~ 5-10 GHz current bias in SQUID Meas. Artificial atom - use radiation Apply bias to adjust frequency “Listen” with SQUID magnetometer qubit junction

21. Fabrication – trilayer process (Al) Si a-SiO x Al/a-AlO x /Al Mesa Tunnel Barrier Al Al – superconductor, T C ~ 1 K a-SiO2: amorphous SiO2 - substrate & insulation Chemical vapor deposition a – AlO x : amorphous Al 2 O 3 + OH - - tunnel barrier Self passivated oxide ~ 1.5 nm thick

22. Superconducting Josephson junction phase qubit principle Tunnel Junction ~1.5 nm Top superconductor Bottom superconductor I  top =  0  bot =  0 e i  Cooper pair wavefunction Josephson relations I depends on  Voltage only when phase is changing

23. Electrical circuit model of Josephson junction I = CJCJ L J ~1/cos  Qubit oscillates like an L-C circuit Adjust potential to get two state system – “0” & “1” Want very low damping of oscillator High Q gives long lifetimes

24. Quantum behavior - potential that phase qubit lives in Increase bias => cubic potential lifts degeneracy Use the |0> and |1> states for information

25. T 1 ’s in phase qubits – historically been short 13  m 2 junctions: T 1 ~ 25 ns 70  m 2 junctions: T 1 ~ 40 to 100 ns 0.5 0.25 0 0 100 200 T 1 = 23 ns Prob. |1> state Meas. delay (ns) Loss mostly external to junction

26. Coherence of first phase quantum bit Single operation time can be ~ 1 ns Information in system decayed rapidly ~ 100 ns Need to preserve information > 104 x operation time to be useful => Increase coherence times & measurement fidelity!

27. Materials development – can we improve coherence? Absorption in dielectric & junction (a-SiO 2 ) & (a-AlO 2 ) Gets worse at low temperature (two – level fluctuators) Si a-SiO x Al Focus on: Insulators: along traces & around junction in substrate crossovers Tunnel barrier - between superconductors

28. ~T R SiO2 =2.1k  Test actual L-C resonators using thin SiO2 Q decreases at low temperature!

29. TLS bath saturates at high E (power), decreasing loss Schickfus and Hunklinger, 1975 Two-level systems in a-SiO2 E d SiO 2 - Bridge bond Amorphous material has all barrier heights present High E Low E

30. Problem - amorphous SiO 2 Why short T 1 ’s in phase Josephson qubits? Dissipation: Idea - Nature: At low temperatures (& low powers) environment “freezes out”: dissipation lowers dissipation increases, by 10 – 1000! Change the qubit design:  find better substrates  find better dielectric & minimize insulators in design

31. Common insulator/substrate materials SiO 2 –Bridge bond, unstable Amorphous films have uncompensated O -, H, OH - Si 3 N 4 –N has three bonds – more stable Amorphous films, still have uncompensated charges, H 20% H for low T films, ~ 2% H in high T films Al 2 O 3 –Amorphous – high loss, similar to a-SiO2, has H, OH - in film –Single crystal (sapphire) - Very low loss system

32. Minimize, optimize dielectric & substrate Rabi oscillations > 600 ns !! Sapphire substrate + SiN insulator: Time (ns) Maximum Dielectric SiO 2 Minimum Dielectric SiO 2 Minimum Dielectric SiN x Minimum Dielectric SiN x (UCSB, high T ) Phys. Rev. Lett. 95, 210503 (2005)

33. Can couple 2 qubits => Do logical operations in ~ 100 ns – density matrix J. Martinis

34. Superconductor - Aluminum I Tunnel junction a- AlO x -OH - Found improvements due to optimized materials in insulators => Can we improve the tunnel barrier?

35. Qubit spectroscopy Increase the bias voltage (tilt) Frequency of |0> => |1> transition goes down Resonances Increase bias

36. Effects of resonances Quench Rabi Oscilations – strong coupling to qubit Rabi oscillations Spectroscopy

37. Number & splitting of Resonators 13 um 2 junction 70 um 2 junction Smaller area – Fewer resonators, larger splitting (strong coupling) Larger area - More resonators, smaller splitting (weaker coupling)  Resonances are randomly distributed

38. Two level systems in junction Amorphous AlO tunnel barrier Continuum of metastable vacancies Changes on thermal cycling Resonators must be 2 level, coherent with qubit! I

39. What we need: Crystalline barrier  -Al 2 O 3 Poly - Al Existing technology: Amorphous tunnel barrier a –AlO x – OH - No spurious resonators Stable barrier Amorphous Aluminum oxide barrier Spurious resonators in junctions Fluctuations in barrier Silicon amorphous SiO 2 Low loss substrate Design of tunnel junctions SC bottom electrode Top electrode

40. Q: Can we prepare crystalline Al 2 O 3 on Al? Binding energy of Al AES peak in oxide Annealing Temp (K) AES Energy of Reacted Al (eV) Al in sapphire Al 2 0 3 Metallic aluminum Aluminum Melts 68 10 Å AlO x on Al (300 K + anneal) 10 Å AlO x on Al (exposed at elevated temp.)  Anneal the natural oxides  Oxidize at elevated temp. A: No

41. Chose bottom superconducting electrode to stabilize crystalline Al 2 O 3 tunnel barrier Elements with high melting temperature

42. Elements with T C > 1K

43. Elements that lattice match sapphire (Al 2 0 3 )

44. Elements that form weaker bond with oxygen than Al

45. Elements that are not radioactive  Use Re for Al2O3 barrier

46. LEED, RHEED, Auger Re Sputtering Load Lock STM/AFM UHV surface science &growth system Al Oxygen O2O2 Al 2 O 3 growth: Al thermal deposition under O 2 exposure on top of base epitaxial Re.

47. 1.5 nm RMS roughness 1-2 atomic layer steps Screw dislocations on mesas Stranski-Krastanov growth –Initial wetting of substrate Formation of 3-d islands –Islands fill in gradually 0.5 x 0.5  m 100 nm Re Base layer @ 850 C on sapphire

48. Epi Re Grow Al 2 O 3 @ RT + Anneal @ 800 ◦ C 4x10 -6 Torr O 2 3m3m AFM/RHEED of single crystal Al 2 O 3 on Re(0001) Re(0001) Al 2 O 3

49. Source of residual two-level fluctuators: Al-Al 2 O 3 interface? Electron Energy Loss Spectroscopy (EELS) from TEM shows 1.Sharp interface between Al 2 O 3 and Re 2.Noticeable oxygen diffusion into Al from Al 2 O 3 ??? Distance (μm) Oxygen content Al 2 O 3 Oxygen is white Long tailSharp Oxygen Profile across the tunnel barrier AlRe

50. Fabricate test junctions with epi-Al 2 O 3 barrier Low sub-gap conductance First high quality junctions made with epitaxial barrier Re(0001) Al 2 O 3 Al 1/R vs. Area at 300 K V(mV) I-V curve at 20 mK ReRe AlAl

51. Epitaxial trilayer fabrication Change just one thing at a time –Still have a-SiO2 insulator (max-insulator design) –Polycrystalline Al on top of trilayer Sapphire epi-Re/Al 2 O 3 /Al Al

52. Resonance data from epi-Re/Al2O3/Al junction Significantly reduced number & coupling of resonances All 3 of 3 qubits on chip showed same effect Rabi oscillations match with those expected for max-SiO 2 design

53. 5x Reduction of splitting density Residual splittings are interfacial effect ~1 in 5 oxygens at Al interface Agrees with reduced splitting density to 1/5 2 nm epi-Re interface non-epi Al interface Oxygen 0.43 nm

54. Outlook Integrating epi-Re into min-SiN devices Materials optimization is critical to solid state QC devices Investigating possibility of single crystal V-MgO barriers –Opens the possibility of crystalline insulators –Both V & MgO can deposit and crystallize at lower temp. Other avenues –Vacuum crossovers –Minimize junction area using e-beam lithography & shadow evaporation

55. Shameless optimism slide How many years in the future is too many? Bardeen Brattain Shockley Kilbey

56. 50% Quantum Information Logic – based on digital 0&1! Can only measure one direction at a time – U/D or L/R Quantum systems only remember 1 direction at a time Example – 4 way switch Set in middle Quantum bit - “qubit” up ≡1, down≡0 - left & right intermediate 50% Up/Down Left/Right 50% Up Down Left Right Measure Vertical Measure Horizontal Up Down Vertical

57. Prepare state & measure qubit with  pulse Readout SQUID w/o  pulse |0> |1> |0> Check SQUID t

58. Electrical circuit model of Josephson junction I = CJCJ L J ~1/cos  Potential: , V across junction will slosh around in minimum cos  is x 2 potential => simple harmonic oscillator Need to change potential to get two state system

59. Increase current bias to modify potential Too much tilt I ~ 1 - 20  A Just right tilt 

60. Experimental setup Qubit is operated at 20 mK Expected to reduce thermal decoherence sources

61. Insert qubit pic here Qubit L Stripline (C-SiO 2 ) Josephson Junction (L&C) => Measure “Q” of simple LC resonators at lot T Qubit has SiO 2 Cap in || with J.J. & around lines SiO 2 AlO x

62. Power dependence to parallel plate capacitor resonators  wave resonator L f [GHz] P out [mW] P in lowering Q of the resonator with SiO 2 goes down as power decreases! Parallel plate capacitor resonators w/SiO dielectric C L => Compare to capacitors with vacuum dielectric

63. => With & without SiO2 over the capacitor C/2 L Dissipation is in SiO2 dielectric of the capacitor! ~P out Interdigitated capacitor resonators

64. Power dependence of Q LC for parallel plate capacitors HUGE Dissipation Q decreases with at very low power (where we run qubits) N photons Q LC Explains small T 1 ! L C

65. Strong coupling interaction of qubit with coherent resonator qubit - |0> or |1> res. - |g> or |e> |0e> |0g> 0 |1e> |1g> On resonance  E=0 Form either symmetric (+) or anti-symmetric (-) state |1e> |1g> EE Off resonance

66. Qubit-resonator coupled interaction On resonance, put qubit in |1> Wait some time,  int /2 Qubit goes into |0> =>Wait  int  Qubit goes back to |1> with enhanced amplitude!  States oscillate |1g> |0e> Resonator has longer coherence time than qubit! off on

67. J. Martinis

68. Early history of Quantum Information 1982 “It seems that the laws of physics present no barrier to reducing the size of computers until bits are the size of atoms and quantum behavior holds sway.” Richard Feynman Peter Shor Factoring Algorithm 1994 QC - Lov Grover Quantum Search 1996 1970’s Quantum Crypotography Stephen Weisner "Conjugate Coding“ David Deutsch ”Quantum Computer” 1985 1991 Entangled photons Artur Ekert 1984 Polarized photons Bennett, Brassard Deutsch, Josza algorithm “balanced function” 1992

69. Resources - Quantum error correction Classical – repetition code, need 3 bits: 0≡000, 1 ≡ 111 –Single bit flip: 001, 010, 100 => 0 110, 101, 011 => 1 Quantum – Need to check two variables: –Need 3 2 = 9 bits bit sign 1 “logical” qubit = 9 physical qubits Need hardware with high stability!

70. System of two qubits 2 Qubits => 4 amplitudes n Qubits => 2 n 2 128 = 3.4 x 10 38