Quantum Information Storage in Solid State Systems

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

2. Hydrogen atom energy levels n=2 n=1 -3.4 eV 2 Quantum leap 0.1 meter -13.6 eV 1 DE = 10 electron-volts 1 eV =1.602 x 10-19 Joules Quantum Leap - DE ~ 1 x 10-18 Joules DE = mgh = (60 kg) x (9.8 m/s2)x(0.1 m) = 60 kg m2/s2 DE ~ 60 Joules Something... “took a Quantum Leap!” Misnomer? 3 Equivalent of man jumping 0.000 000 000 000 000 001 meters high < millionth of an atom

3. => Quantum Hydrogen • electron acts like a wave • not measured • electron acts like particle • when measured • at some position “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 Caffeine Aspirin Ethanol • 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 5 “qubit” molecule NMR R. Marx, A. F. Fahmy, J. M. Myers, W. Bermel, S. J. GlaserPhys. Rev. A 62, 012310-1-8 (2000) BOC-(13C2-15N-2D -glycine)-fluoride

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 Bob Alice 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 Send public key =15 • Public key Send message back Eve Eavesdropper needs to figure out 15=3x5 to decode : 10941738641570527421809707322040357612003732945449205990913842131476349984288934784717997257891267332497625752899781833797076537244027146743531593354333897= 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

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 City Hall Bank

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

9. Quantum computing more possible states & intrinsically parallel Output f(S1) f(S2) S1 =00…000 S2 =00…001 S3 =00…010 … Classical computation: n bits Classical Gate f(x) n bits => 2n possible states 2n computations Spans all input states Quantum computation: n qubits => possible states Quantum gate f(x) Output state measure 1 computation operates on all states

10. Quantum Interference Speed up of unsorted data search • 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

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

12. Quantum problem solving is fast • Grover’s algorithms conducts search in O(N1/2) 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!

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

14. NIST - Quantum computing with real atoms • 9Be+ 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 I 1) Use Superconductors • Zero DC resistance - PDG-conductor at AC • Complete diamagnetism • Macroscopic quantum effects 2) Make LC circuit 3) Add non-linearity to define energy levels Thin, non-linear junction & capacitor Intensity Quality factor: L C Lifetime: frequency

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 ~ 106 gives ms time constants • Need enabling technology for low T operation • 0.05 to 0.1 K!

17. Closed cycle plug & play refrigerators T< 0.1 K • Adiabatic demagnetization refrigerattor (ADR) • High Precision Devices – Louisville, CO • Automated magcycl & T PID • Demonstrated T < 100 mK > 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

18. NIST – Quantum computing with superconductors • Al/AlOX junctions on Si wafers • optical lithography • ~ 1 mm features • standard processing • Al wiring w/SiO2 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” • SiOx substrate, insulator • Al0x tunnel barrier • Identification of decoherence • Improvements

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

21. Al Mesa Tunnel Barrier Al/a-AlOx/Al a-SiOx Fabrication – trilayer process (Al) Al – superconductor, TC ~ 1 K a-SiO2: amorphous SiO2 - substrate & insulation Chemical vapor deposition a – AlOx: amorphous Al2O3 + OH- - tunnel barrier Self passivated oxide ~ 1.5 nm thick Si

22. Superconducting Josephson junction phase qubit principle Top superconductor Cooper pair wavefunction Ytop= Y0 Tunnel Junction ~1.5 nm I Ybot= Y0eid Bottom superconductor • I depends on d • Voltage only when phase is changing Josephson relations

23. LJ ~1/cosd CJ I = Electrical circuit model of Josephson junction • 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. T1’s in phase qubits – historically been short 0.5 13 m2 junctions: T1~ 25 ns T1 = 23 ns Prob. |1> state 70 m2 junctions: T1~ 40 to 100 ns 0.25 0 200 100 0 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? Al a-SiOx • Absorption in dielectric & junction (a-SiO2) & (a-AlO2) • Gets worse at low temperature (two – level fluctuators) Si • Focus on: • Insulators: along traces & around junction • in substrate • crossovers • Tunnel barrier - between superconductors

28. Test actual L-C resonators using thin SiO2 Q decreases at low temperature! ~T RSiO2=2.1kW

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

30. dissipation increases, by 10 – 1000! Problem - amorphous SiO2Why short T1’s in phase Josephson qubits? • Dissipation: Idea - Nature: • At low temperatures (& low powers) • environment “freezes out”: • dissipation lowers Change the qubit design: • find better substrates • find better dielectric & minimize insulators in design

31. Common insulator/substrate materials • SiO2 • Bridge bond, unstable • Amorphous films have uncompensated O- , H, OH- • Si3N4 • 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 • Al2O3 • Amorphous – high loss, similar to a-SiO2, has H, OH- in film • Single crystal (sapphire) - Very low loss system

32. Minimize, optimize dielectric & substrate Phys. Rev. Lett. 95, 210503 (2005) Maximum Dielectric SiO2 Rabi oscillations > 600 ns !! Minimum Dielectric SiO2 Minimum Dielectric SiNx Sapphire substrate + SiN insulator: Minimum Dielectric SiNx (UCSB, high T) Time (ns)

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

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

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

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

37. Number & splitting of Resonators 70 um2 junction 13 um2 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. Design of tunnel junctions Existing technology: What we need: Amorphous Aluminum oxide barrier Spurious resonators in junctions Fluctuations in barrier No spurious resonators Stable barrier Top electrode Poly - Al Crystalline barrier a-Al2O3 Amorphous tunnel barrier a –AlOx – OH- SC bottom electrode Poly- Al amorphous SiO2 Low loss substrate Silicon

40. Q: Can we prepare crystalline Al2O3 on Al? 68 Metallic aluminum 10 Å AlOx on Al (300 K + anneal) 10 Å AlOx on Al (exposed at elevated temp.) AES Energy of Reacted Al (eV) Aluminum Melts Al in sapphire Al203 Annealing Temp (K) • Anneal the natural oxides • Oxidize at elevated temp. Binding energy of Al AES peak in oxide A: No

41. Chose bottom superconducting electrode to stabilize crystalline Al2O3 tunnel barrier Elements with high melting temperature

42. Elements with TC > 1K

43. Elements that lattice match sapphire (Al203)

44. Elements that form weaker bond with oxygen than Al

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

46. Load Lock UHV surface science &growth system Al2O3 growth: Al thermal deposition under O2 exposure on top of base epitaxial Re. LEED, RHEED, Auger Re Sputtering STM/AFM O2 Al Oxygen

47. 100 nm Re Base layer @ 850 C on sapphire 0.5 x 0.5 mm • 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

48. Al2O3 Re(0001) AFM/RHEED of single crystal Al2O3 on Re(0001) Epi Re Grow Al2O3 @ RT + Anneal @ 800 ◦C 4x10-6 Torr O2 3m

49. Source of residual two-level fluctuators: Al-Al2O3 interface? Oxygen Profile across the tunnel barrier Oxygen is white Long tail Sharp Al2O3 Al Re Oxygen content Distance (μm) • Electron Energy Loss Spectroscopy (EELS) from TEM shows • Sharp interface between Al2O3 and Re • Noticeable oxygen diffusion into Al from Al2O3 ???

50. Al Re Fabricate test junctions with epi-Al2O3 barrier Al Al2O3 • Low sub-gap conductance • First high quality junctions made with epitaxial barrier Re(0001) I-V curve at 20 mK 1/R vs. Area at 300 K V(mV)