1. Scaling up a Josephson Junction Quantum Computer Basic elements of quantum computer have been demonstrated 4-5 qubit algorithms within reach 8-10 likely With improvement in coherence, further scaling up John Martinis, UCSB

2. Quantized Voltages and Currents of Microfabricated Circuit 100  m Qubit (old NIST design) control port control port readout port Josephson Junction forms non-linear LC resonator

3. (1) State Preparation Wait t > 1/   for decay to |0> Josephson-Junction Qubit I = I dc +  I dc (t) + I  wc (t)cos  10 t + I  ws (t)sin  10 t |0> : no tunnel |1> : tunnel 3 ns pulse  wc I  ws I  I dc (t) (2) Qubit logic with current bias (3) State Measurement:  U( I dc +  I p ) Fast single shot – high fidelity U(  ) E0E0 E1E1 E2E2 |0> |1>

4. Experimental Apparatus V source 20dB 4K 20mK 300K 30dB 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 Probability 0,1 10ns 3ns ~5 ns pulses

5. Qubit Characterization  ~350ns Meas. time T 1 ~400ns 0100200300400500600 time [ns] T  ~100ns Rabi time x  /2 time x  /2 yy Ramsey Echo time xx lifetime P1P1 0 1 0 1

6. Single Qubit Gate Errors: Measurement Errors 3 ns IwIw IzIz 8 ns nothing or  -pulse measure measurement TLS leakage Spectroscopy |1> (misidentified as |0>) 4.5% splitting at 7GHz 3-5% other splittings 1% T 1 during measurement 7.22 GHz 6.75 GHz I meas / I c thy: 96.6% exp: 85.0% thy: 96.6% exp: 89.5% |0> (misidentified as |1>) 3.4% stray tunneling Error Budget |0> |1> Tunneling Prob.

7. Single-Qubit Gate Errors: Limited by T 1 measure IwIw IzIz 8 ns XX XX P 1 [%] separation 3.4% stray tunneling pulse separation [ns] 4% error at separation 11 ns T 1 decay pulse non-linearity double -  error: 4% single-qubit gate fidelity: 98% Vary the time between pi pulses to separate gate fidelity from decoherence due to T1 decay. (limited by T 1 ) Direct measure of probability Checks on measurement &  -gates

8. Coupled Qubits CcCc C 0 00 0 1 01 0 0 10 1 1 11 1 On Resonance: Straightforward to implement: simple coupling tunable fast readout simultaneous measurement CcCc

9. Entangling 2-Qubit Gate (Universal) 050025050100150200300350400450 0 20 40 60 80 100 t [ns] Probability of |01>, |10>, or |11> [%] |00> Entanglement of Formation 0.2635 ebit realimag t  0 00 0  1 01 0 0 10 1 1 11 1 S

10. DATA T 1 = 450ns C M = 8% C uW = 5% vis = 85% π g/π = 20MHz Re [  ]Im [  ] Process Tomography of 2-Qubit Gate SIM Fidelity: Tr(  thy  exp ) = 0.427

11. time 16 ns XX 12 ns swap hold time 16 ns TLS XX interact with TLS time [  s] T 1,TLS ~ 1.2  s time [ns] T swap ~ 12ns Strong interaction with TLS (S = 40MHz) Long-lived TLS is quantum memory P1P1 P1P1 excite qubit off-resonance z-pulse into resonance “on” “off” measure off on TLS off on Bias Frequency On-Off Coupling to TLS Memory On-Off coupling with change in bias 8%

12. Quantum Memory with Process Tomography 16ns TLS init 12 ns storeloadmem 123 1 – Initialize Create states over the entire Bloch sphere. 2 – Store Swap state into TLS. Qubit now in ground state. 3 – Load After holding for 16ns, swap again to retrieve state from TLS. Process tomography: identity operation dominates process Fidelity: Tr(  thy  meas ) = 79%

13. Summary and Future Prospects Demonstrated basic qubit operations with fidelity Initialize, gate operations, simultaneous measurement 10 to 50 logic operations Tomography conclusively demonstrates entanglement Decoherence mechanism understood Optimize dielectrics, expect future improvements Working on Bell violation, advanced CNOT gates (+ tunable) Simulating 4-5 qubit algorithms Scale-up infrastructure designed (“brute force” to ~100 qubits) Very optimistic about 4 -10 qubit quantum computer

14. Single-Qubit Gate Errors: Tomography Check detuning  [MHz] measure IwIw IzIz 8 ns XX  detuning  (both pulses) phase  [/  ] theory experiment Goal: Measure fidelity of pi-pulse (longest single-qubit gate) separately from measurement errors. Idea: Two pi-pulses bring state back to |0>, where the only measurement error is stray tunneling. Remaining error is due to pi-pulses only. Tomography Check: On resonance, phase of second pulse has no effect, as expected for pi-pulses.  P1P1 P1P1

15. |2> Errors from Fast Pulses Zoom in on 2-state errors for many pulse lengths Two State Errors Measure  (FWHM) XX Gaussian pulses: Minimum width in time and frequency frequency pulse power  10  21 4ns 8ns  10  21

16.  -  Pulses Give Low Background & Error Filtering Measure |2> State 5 ns |2> Error Two Photon Qubit 200MHz  delay Ramsey Fringe Filtering of |2> state 4P 2-error XX XX Delay time  delay [ns] High Power Spectroscopy

17. Error vs. Gaussian Pulse Width 10 -4 S-curve -- FT theory Spectrum analyzer Quantum simulation