1. High fidelity Josephson phase qubits winning the war (battle…) on decoherence “Quantum Integrated Circuit” – scalable Fidelity b reakthrough: single-shot tomography Tunable qubit – easy to use Two qubit gates – new results Collaboration with NIST – Boulder UC Santa Barbara John Martinis Andrew Cleland Robert McDermott Matthias Steffen (Ken Cooper) Eva Weig Nadav Katz PD GS Markus Ansmann Matthew Neeley Radek Bialczak Erik Lucero

2. The Josephson Junction SC ~1nm barrier Silicon or sapphire substrate SiN x insulator Al top electrode Al bottom electrode AlOx tunnel barrier Josephson junction  2 = i2i2 e  1 = i1i1 e I J = I 0 sin  V = (  0 / 2  ) . “Josephson Phase”  =  1 -  2

3. Qubit: Nonlinear LC resonator  23  2/3 0 00 /1 24 II I U      C  4/1 0 2/1 0 0 1 22 II I p              I R CLJLJ    Lifetime of state |1> 05 0.7 0.8 0.9 1  10  21  32   p n n E E   / 1    RC UU pp   U(  ) = 0 pulse (state measurement) I0I0 =  0 /2  I 0 cos  nonlinear inductor I  cos I 0j  V ) (1/L J  0  sinI I  LJLJ 2 V 0     1: Tunable well (with I) 2: Transitions non-degenerate 3: Tunneling from top wells 4: Lifetime from R E0E0 E1E1 E2E2 00 11 22 nn  n+1 1000~

4. Superconducting Qubits PhaseFluxCharge Ce I E E C J 2/ 2/ 2 00   10 4 10 2 1 Area (  m 2 ): 10-100 0.1-10.01 Potential & wavefunction Engineering Z J =1/w 10 C 10  10 3  10 5  Yale, Saclay, NEC, Chalmers Delft, Berkeley UCSB, NIST, Maryland

5. Josephson-Junction Qubit |0> |1> State Preparation Wait t > 1/   for decay to |0> Qubit logic with bias control State Measurement:  U( I+I pulse ) Single shot – high fidelity Apply ~3ns Gaussian I pulse I pulse (lower barrier) I = I dc +  I dc (t) + I  wc (t)cos  10 t + I  ws (t)sin  10 t phase potential ) 2 / ( )2( z  ws y  wc x I IH          I dc (t) dc IE  / 10 |0> |1> |2> I pulse Prob. Tunnel 96% |0> : no tunnel |1> : tunnel

6. The UCSB/NIST Qubit  11  01 I dc Qubit Flux bias 1 01 0 IwIw V SQ SQUID microwave drive Qubit Flux bias SQUID

7. Experimental Apparatus V source 20dB 4K 20mK 300K I-Q switch Sequencer & Timer  waves IsIs II VsVs fiber optics rf filters  w filters ~10ppm noise V source ~10ppm noise 20dB Z, measure X, Y IpIp IwIw IsIs II time Reset Compute Meas. Readout IpIp IwIw VsVs 0 1 XY Z Repeat 1000x prob. 0,1 10ns 3ns 20dB

8. Spectroscopy Bias current I (au) saturate IpIp IwIw meas. Microwave frequency (GHz)  10 ( I ) 26 few TLS resonances P 1 = grayscale

9. Qubit Fidelity Tests  Rabi:  Ramsey:  Echo:  T1:T1: Probability 1 state Large Visibility! T 1 = 110 ns, T  ~ 85 ns ~90% visibility

10. State Tomography |0  |1  |0  + |1  |0  + i|1  y x X,Y P1P1 state tomography Good agreement with QM Peak position gives state  ), amplitude gives coherence DAC-Q (X) DAC-I (Y) |0  |1  X Y |0  +|1  |0  +i|1 

11. Standard State Tomography (I,X,Y) time (ns) P1P1 I,X,Y I X Y |0  +|1 

12. State Evolution from Partial Measurement tomography & final measure state preparation 15 ns10 ns |0  +|1  Needed to correct errors. First solid-state experiment. partial measure p Prob. = p/2 “State tunneled” Prob. = 1-p/2 |0  IwIw IpIp p t Theory: A. Korotkov, UCR

13. Partial Measurement |0  +|1  |0  p mm -30  -10  -20  0  /4  /2 3  /4 p=0.25 p=0.75

14. Decoherence and Materials Im{  }/Re{  } =  = 1/Q 1/2 [V] future a- Dielectric loss in x-overs Where’s the problem? TLS in tunnel barrier Two Level States (TLS) New design Theory: Martin et al Yu & UCSB group xtal Al 2 O 3 a-Al 2 O 3

15. New Qubits 60  m SiN x capacitor I: CircuitII: Epitaxial Materials (loss of SiN x limits T 1 ) Al 2 O 3 (substrate) Al 2 O 3 Re Al LEED: Bias current I  wave freq. (GHz) Spectroscopy: epi-Re/Al 2 O 3 qubit ~30x fewer TLS defects! (NIST)

16. Long T 1 in Phase Qubits t Rabi (ns) UCSB/NIST T 1 = 500 ns P 1 (probability) t Rabi (ns) These results: Conventional design (May 2005): High visibility more useful than long T 1 T 1 will be longer with better C dielectric

17. Future Prospects Coherence T 1 > 500 ns in progress, need to lengthen T  STOP USING BAD MATERIALS! Single Qubit operations work well Coupled qubit experiment in DR Simultaneous state measurement demonstrated Bell states generated Violate Bell’s inequality soon Tunable qubit : 4+ types of CNOT gates possible Scale-up infrastructure (for phase qubits) Very optimistic about 10+ qubit quantum computer

18. Dielectric Loss in CVD SiO 2 f [GHz] P out [mW] Im{  }/Re{  } =  = 1/Q P in lowering HUGE Dissipation C L 1/2 [V] P in P out T = 25 mK

19. Theory of Dielectric Loss Im{  }/Re{  } =  = 1/Q 1/2 [V] Two-level (TLS) bath: saturates at high power, decreasing loss high power Amorphous SiO 2 von Schickfus and Hunklinger, 1977 E Bulk SiO 2 : SiO 2 (no OH) SiO 2 (100ppm OH)

20. Theory of Dielectric Loss Im{  }/Re{  } =  = 1/Q 1/2 [V] Spin (TLS) bath: saturates at high power, decreasing loss high power Amorphous SiO 2 von Schickfus and Hunklinger, 1977 E Bulk SiO 2 : SiN x, 20x better dielectric Why?

21. Junction Resonances = Dielectric Loss at the Nanoscale qubit bias (a.u.)splitting size S' (GHz) N/GHz (0.01 GHz < S < S')  wave frequency (GHz) 13  m 2 70  m 2 13  m 2 S/h 70  m 2 avg. 5 samples: New theory (suggested by I. Martin et al): e d 1.5 nm Al AlO x theory d=0.13 nm (bond size of OH defect!) Explains sharp cutoff S max in good agreement with TLS dipole moment: Charge (not I 0 ) fluctuators likely explanation of resonances 2-level states (TLS).

22. Junction Resonances: Coupling Number N c 0 1 qubit junction resonances … N c >> 1, Fermi golden rule for decay of 1 state: Number resonances coupled to qubit: S g e Statistically avoid with N c << 1 (small area) Same formula for  i as bulk dielectric loss Implies  i = 1.6x10 -3, AlO x similar to SiO x (~1% OH defects) E 10

23. State Decay vs. Junction Area Monte-Carlo QM simulation: (  -pulse, delay, then measure) time (ns) probability P 1 A=2500 um 2 (Nc=5.3) A=260 um 2 (Nc=1.7)

24. State Decay vs. Junction Area Monte-Carlo QM simulation: (  -pulse, delay, then measure) time (ns) probability P 1 A=2500  m 2 (N c =5.3) A=260  m 2 (N c =1.7) A=18  m 2 (N c =0.45) N c 2 /2 Need N c < 0.3 (A < 10  m 2 ) to statistically avoid resonances ~~

25. State Measurement and Junction Resonances 0 1 qubit junction resonances … N c ’ >> 1, Landau-Zener tunneling: Number resonances swept through: tptp Couple to more resonances With t p ~ 10 ns, explains fidelity loss in measurement! (10 ns) -1