Pulse techniques for decoupling qubits

Size: px

Start display at page:

Download "Pulse techniques for decoupling qubits"

Evan Cameron
5 years ago
Views:

1 Pulse techniques for decoupling qubits from noise: experimental tests Steve Lyon, Princeton EE Alexei Tyryshkin, Shyam Shankar, Forrest Bradbury, Jianhua He, John Morton Bang-bang decoupling 31 P nuclear spins Low-decoherence electron-spin qubits and global 1/f noise Dynamical decoupling of the qubits Periodic pulse sequences Concatenated pulse sequences Summary

2 2-pulse Hahn echo Pulses Signal ( ) Decoupling Experiments π/2 π τ FID T 2 T π/2 π π τ Echo ( ) Pulses Signal ( ) T Echo ( )

3 Dynamical Decoupling Replace single π-pulse with sequence of pulses Refocus spins rapidly (< noise correlation time) Bang-bang bang fast strong pulses (or 2 different spins) CP (Carr-Purcell) periodic π-pulses π x /2-τ-X-2τ-X-2τ- -X-τ-echo CPMG (Carr-Purcell-Meiboom-Gill) periodic π-pulses π x /2-τ-Y-2τ-Y-2τ- -Y-τ-echo Aperiodic pulse sequences concatenated sequences Khodjasteh, Lidar, PRL 95, (2005); PRA 75, (2007). π x /2-(p n-1 -X-p n-1 -Z-p n-1 -X-p n-1 -Z)-τ-X-τ-echo with Z=XY Yao, Liu, Sham, PRL 98, (2007). concatenated CPMG π x /2-(p n-1 -Y-p n-1 -p n-1 -Y-p n-1 )-τ-y-τ-echo Experimental pulses ~ 1μs (for π-pulse) Power ~ 1/(pulse length) 2 Energy/pulse ~ power 1/2

4 The Qubits: 31 P donors in Si 31 P donor: Electron spin (S) = ½ and Nuclear spin (I) = ½ X-band: magnetic field = 0.35 T ν μw1 ~ 9.7 GHz ν μw2 ~ 9.8 GHz ν rf1 ~ 52 MHz ν rf2 ~ 65 MHz e, n e, n ν μw1 e, n e, n 3 ν rf1 2 ν μw2 1 ν rf2 0 Blue (microwave) transitions are usual ESR All transitions ii can be selectively l addressed d

5 Bang-Bang control Fast nuclear refocusing 31 P donor: S = ½ and I = ½ e, n 3 (A) Free nuclear spin nutation e, n μw 2π rotation 1 1 e, n rf 1 e, n 0 Ψ i = a 0 + b 1 2π Ψ f = a 0 -b 1 Nu uclear Polar ization (B) One burst of 2π mw pulses (C) Two bursts of 2π mw pulses Nuclear refocusing gpulse would be ~10 μs but electron pulse ~30 ns

6 Doping ~10 15 /cm 3 Electron spin qubits Isotopically purified 28 Si:P 7K electron T 1 ~ 100 s milliseconds 7K electron T 2 ~ 60 milliseconds (extrapolating to ~single donor) 1, T 2 (sec) T 103 (Feher et al, 1958) 102 T 28 1 Si:P GHz 101 T 28 2 Si:P GHz 0 T T 2 Si:P GHz real T 2 x (Gordon, 28 Si, 1958) 10-4 T Temperature (K)

7 Noise in electron spin echo signals Spin echo de ecay Decoherence Single-pulse T 2 = 2 msec averaged T( (msec) Spin ech ho signals In-phase Out-of-phase T (msec) Signal transferred: in-phase out-of-phase Must use single pulses to measure decoherence About 100x sensitivity penalty

8 B-field noise 0.01 Noise (Ga auss/hz 1/2 ) 1E-3 1E-4 1E-5 1E-6 1E-7 Measure noise voltage induced in coil 1E Frequency (Hz) Origin of noise unclear Background field in lab? Domains in the iron? Essentially 1/f

9 Microwave Field Inhomogeneity Sapphire cylinder Vertical B-field Metal Wall Carr-Purcell (CP) sequence CP π x /2-τ-X-2τ-X-2τ- -X-τ-echo-X-τ-echo Sapphire

10 Periodic (standard) CPMG π x /2-τ-Y-2τ-Y-2τ- -Y-τ-echoτ 2τ Y 2τ Y τ Self correcting sequence π/2 pulse π pulse π pulse Microwav ve signal

11 Coherence after N pulses Standard CPMG 1.0 Intensity Echo T 2 = 8.5ms

12 Concatenated CPMG π/2 pulse π pulse π pulse Microwav ve signa al

13 Coherence vs. concatenation level Echo In ntensity 1.0 Concatenated CPMG l = 2 (2 pulses) l = 4 (10 pulses) l = 6 (42 pulses) 0.5 T 2 = 5.8ms

14 Concatenated and periodic CPMG Echo Intensi ity Concatenated CPMG 42 pulses Periodic CPMG 32 pulses

15 Fault-Tolerant Dynamical Decoupling π x /2-(p n-1 -X-p n-1 -X-Y-p n-1 -X-p n-1 -X-Y)-τ-X-τ-echo Not obvious that it self-corrects Concatenated XZXZ (p2) CPMG

16 Coherence vs. concatenation level Echo Int tensity Concatenated XZXZ pulse sequence p 1 (4 pulses) p 2 (14 pulses) p 3 (60 pulses) p 4 (242 pulses) p5 (972 pulses) T 2 = 15ms

17 Sanity check: collapse adjacent pulses Effect of combining pairs of adjacent pulses Ex. Z-Z I n th level concatenation without combining 24 n 2 = 510 for n=4 n th level concatenation with combined pulses = 306 for n=4 Echo De ecay Con ncatenate ed XZXZ 15 p4, p, with all pulses preserved p4, consecutive pulses are combined 10 T 2 = 11 ms

18 Sanity check: white noise 1 Si:P at 10 K Relaxati ion Deca ay 0.1 T 2 = 330 μsμ 2 T 1 =420μs XZXZ(p3) = 410 μs 0 1 2

19 Summary Dynamical decoupling can work for electron spins Through the hyperfine interaction with the electron can generate very fast bang-bang control of nucleus CPMG preserves initial π x /2 with fewest pulses But does not deal with pulse errors for π y /2 CPMG cannot protect arbitrary state Concatenated CPMG does no better Can utilize concatenated XZXZ sequence out to at least 1000 pulses Situation with π y /2 initial states is more complex Not clear fidelity improves monotonically with level But much better than CP May need to combine XZXZ with composite pulses

Electron spin coherence exceeding seconds in high-purity silicon

Electron spin coherence exceeding seconds in high-purity silicon Alexei M. Tyryshkin, Shinichi Tojo 2, John J. L. Morton 3, H. Riemann 4, N.V. Abrosimov 4, P. Becker 5, H.-J. Pohl 6, Thomas Schenkel 7,