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High-Fidelity Josephson qubit gates – winning a battle against decoherence

High-Fidelity Josephson qubit gates – winning a battle against decoherence. Racah Institute of Physics Colloquium, Nov. 2007. Nadav Katz Work done while at UCSB with Prof. John Martinis and group. “Quantum Integrated Circuit” – scalable New breakthroughs: Improved fidelity

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High-Fidelity Josephson qubit gates – winning a battle against decoherence

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  1. High-Fidelity Josephson qubit gates – winning a battle against decoherence Racah Institute of Physics Colloquium, Nov. 2007 Nadav Katz Work done while at UCSB with Prof. John Martinis and group. • “Quantum Integrated Circuit” – scalable • New breakthroughs: • Improved fidelity • Universal gates, with tomography • 50 qubit – easy to couple Contact: katzn@phys.huji.ac.il Ext: 84133

  2. Experimental Quantum Information Processing (QIP) a perplexing explosion of different systems

  3. Smaller Bigger Easier to isolate Easier to couple & construct Ions Neutral Atoms NMR Semiconductor Spins Quantum Dots Superconducting Circuits Experimental QIP – a guide for the perplexed • Dots: LONG T1 (T2?) • Coherent Oscillations • NMR: 2 to 7 qubits; • scalability? • Ions: up to 8 qubits & scalable • No dissipation • Pretty good coherence times • Coupled qubits • Decoherence?? Goal - reach the fault tolerant threshold – F > 99.95%

  4. The Josephson Junction SC “Josephson Phase” ~1nm barrier SC Electrical notation Josephson junction Idc Al bottom electrode AlOx tunnel barrier Silicon or sapphire substrate Al top electrode

  5. The Qubit (phase) I Idc C R V . Kirchoff’s Laws: Idc + C V + V / R = I equation of motion Controllable “kinetic” energy damping potential energy Quantize ( is an operator)… Transform to Hamiltonian rep.

  6. Superconducting Qubits Phase Flux Charge Yale, Saclay, NEC, Chalmers UCSB, NIST, Maryland, Wisconsin, Jerusalem Delft, IBM, Berkeley 102 1 104 Area (µm2): 10-100 (1) 0.1-1 0.01 Potential & wavefunction Engineering ZJ=1/10C 30  103 105

  7. Our Qubit SQUID microwave drive Junction inductor Flux bias Idc Iµw Qubit SQUID VSQ Flux bias ~ 100 microns

  8. Operation of the Phase Qubit Qubit basis states |0, |1 Flux bias Idc Iµw |1 Qubit |0 10 SQUID VSQ Measure state occupation by selective tunneling Tune qubit state energies E10 with dc current Idc Control qubit states with microwave current Iµwat 10 Minimize fluctuations and dissipation for qubit coherence

  9. potential U Josephson-junction qubit (1) State Preparation Wait t > 1/10for decay to |0> |1> |0> phase (2) Qubit logic with current bias dIp(t) I = Idc + dIp(t) + Imwc(t)cosw10t+ Imws(t)sinw10t (3) State Measurement: U(Idc+dIp) Fast single shot – high fidelity I mwc I mws |0> |1> 3 ns Gaussian pulse 96% Prob. Tunnel • |1> : tunnel • |0> : no tunnel pulse height of dIp

  10. X Y Imw Z Ip Reset Compute Meas.Readout time If Repeat 1000x Probability 0,1 Is 1 0 Vs Is Vs If Sequencer & Timer 300K V source ~10ppm noise ExperimentalApparatus rf filters fiber optics V source Ip ~10ppm noise Z, measure Imw X, Y I-Q switch mwaves 20dB 20dB ~5 ns pulses 4K 20mK mw filters 20dB 10ns 3ns 30dB

  11. mw 14 bits, 2x Gs/s FPGA memory, ~2k$ I Q GHz DAC Electronics Old analog system: mwave amplitude measured waveform time (ns)

  12. Spectroscopy 6 2 Imw saturate Ip meas. 10(I) P1 = grayscale Bias current I (au)

  13. x lifetime time Qubit Characterization Rabi Meas. time 1 T1 ~450ns 0 P1 T~100ns x/2 x/2 Ramsey time 1 T2~350ns y x/2 x/2 Echo time 0 0 100 200 300 400 500 600 time [ns]

  14. Standard State Tomography (Z, Y, X meas.) X Y/2 Y I,X,Y P1 Z I State prep. time (ns)

  15. Measurement in detail  pulse Imw Idc p~1 p=0.5 Full measurement (p=1) projects to either or Question: What is the quantum state after a partialmeasurement (p<1) ?

  16. Partial measurement evolution Answer: Theory: A. Korotkov, UCR Following Dalibard et al. PRL 68, 580 (1992). Prob. = 1-p/2 tunnel out Prob. = p/2 Apply state tomography to test theory

  17. Partial measurement - results High fidelity z rotations But can the effect of such a partial measurement be undone?

  18. partial measure p partial measure p state preparation x tomography & final measure Iw p p Iz t 10 ns 10 ns 7 ns 7 ns Quantum erasure Partial measure Probablistic recovery of quantum state even with strong measurement Erasure Nontrivial sequence – Very good control Erasure (0.9) Process tomography of the erasure (~85% fidelity)

  19. Coupled Qubits Straightforward to implement: simple coupling tunable fast readout simultaneous measurement Cc C Cc On Resonance: 11 01 10 00 eg. UMaryland

  20. Simultaneous Measure of Coupled Qubits: i-SWAP gate p PAB tosc P10 A /2 z-gate B P01 Eigenstate, Bell singlet P11 S 11 01 10 z-gate p 00 i-SWAP gate

  21. Tomography: Direct Proof of Entanglement state tomography p I,X,Y p/2 A I,X,Y B fidelity = 0.86 expect = 0.87

  22. Process Tomography state tomography p I,X,Y i-swap A (i-swap)1/2 is a universal gate I,X,Y B Samples Bloch sphere enough to describe gate for ANY initial state 4 initial states / qubit

  23. Process Tomography 16 Density Matrices: Data (3 min.)

  24. Preliminary Data Re [] Im [] Fidelity: Tr(thy exp) = 0.427 DATA T1 = 450ns CM = 8% CuW= 5% vis = 85% g/π = 20MHz SIM

  25. Qubit Coherence: Where’s the Problem? Capacitors Inductors & Junctions Circuits Energy eV 2D~4Tc resonator D. of States (X-tal) (amorphous) Superconductors: Gap protects from dissipation X-tal or amorphous metal Protected from magnetic defects Good circuit design (uwave eng.) Many low-E states Only see at low T

  26. 1st gen. Qubit Improvements(dielectric loss) 40% T1 = 40 ns 2nd gen. No Si wafer SiO2 -> SiNx P1 (probability) T1 = 500 ns 60% 3rd gen. Small junction + shunting C SiNx capacitor 60 m T1 = 110 ns 90% (loss of SiNx limits T1) tRabi (ns)

  27. New Qubit Data 90% 4th gen. P1 (probability) T1 = 470 ns T  ~ 300 ns Interdigitated C – (topologically protected) sapphire dielectric (radiation from large size?) tRabi (ns) a-Si:H dielectric (Q ~ 40000) 5th gen. T1 = 450 ns • Optimistic for further dramatic improvements • We know crystals are “superinsulators” • How to fabricate?

  28. TLS Resonance – not a bug, a feature… • Strong interaction with TLS (S = 40MHz) • Long-lived TLS is quantum memory “on” excite qubit off-resonance Frequency • On-Off coupling with change in bias z-pulse into resonance “off” Tswap ~ 12ns Bias X interact with TLS measure P1 8% time [ns] off TLS on 16 ns time time [s] T1,TLS ~ 1.2s X swap hold swap P1 off TLS on 16 ns 12 ns time 12 ns time [s]

  29. init store mem load TLS 16 ns 16ns 12 ns 12 ns 1 2 3 Quantum Memory with Process Tomography Process tomography: identity operation dominates process Fidelity: Tr(thmeas) = 79% 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.

  30. New Frontier: 50atoms • “Atom” with 50 W impedance • |Zqubit| =1/w10C atoms phase qubit Zqubit () F Q 1M 1K 1 377 50 Z mismatch makes coherence easier Z match makes coupling easier • 50  enables long distance coupling • Much better error threshold ! Architecture Error threshold Unlimited range 10-3 – 10-4 2D lattice nearest-neighbor 10-5 1D lattice nearest-neighbor 10-8

  31. Future Prospects • Demonstrated basic qubit operations • Initialize, gate operations, controlled measurement • 10 to 100 logic operations Tomography conclusively demonstrates entanglement • Decoherence mechanism understood • Optimize dielectrics, expect future improvements • Problem is NOT (only) T1 !! • Future: tunable coupling, CNOT gate with process tomography • New designs and regimes (cavity QED and microbridges) • Scale-up infrastructure designed (“brute force” to ~40 qubits) Very optimistic about 4 -10 qubit quantum computer

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