Spin Qubits in Silicon

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au Australian National Fabrication Facility Spin-based

1 Spin Qubits in Silicon Andrew Dzurak University of New South Wales Australian National Fabrication Facility Spin-based Quantum Information Processing Spin Qubits 2 Konstanz, Germany, 18 August 2014

2 Please Note: Some slides have been deleted from the presentation given at the conference because the data is pre-publication

4 Co-Workers & Sponsors UNSW A/Prof Andrea Morello Henry Yang Jason Hwang Jason Cheng Juan-Pablo Dehollain Fahd Mohiyaddin Rachpon Kalra Dr Juha Muhonen Dr Arne Laucht Dr Menno Veldhorst Dr Fay Hudson Dr Alessandro Rossi University of Melbourne David Jamieson, Jeff McCallum, Lloyd Hollenberg Jarryd Pla, John Morton UCL, UK Malcolm Carroll Sandia National Lab Gerhard Klimeck, Rajib Rahman Purdue Charles Tahan, Rusko Ruskov LPS, USA Kohei Itoh Keio University, Japan Mikko Möttönen, Kuan Yen Tan Aalto, Finland Floris Zwanenburg Twente, Netherlands

5 Spin Qubits in Semiconductors

6 Spin Qubits in Silicon Long Coherence Times in Silicon at 1K: Nuclear mins Electron ms-s Scalable Industry Compatible B=2T Intel 300 mm Si Wafer 22nm Gate Length

7 DiVincenzo Criteria for Quantum Computing 1. A scalable physical system with well characterized qubits 2. The ability to initialize the state of the qubits to a simple fiducial state, such as Long relevant decoherence times, much longer than the gate operation time 4. A universal set of quantum gates (qnot, CNOT, etc) 5. A qubit-specific measurement capability Plus two additional criteria 6. The ability to interconvert stationary and flying qubits 7. The ability faithfully to transmit flying qubits between specified locations D.P. DiVincenzo, The physical implementation of quantum computation, Fortschr. Phys. 48, (2000); arxiv:quant-ph/

8 Scalable + Fault-tolerant Architecture Spin transport rails Classical CMOS circuitry 1-qubit & 2-qubit Gates L. Hollenberg et al., PRB 74, (2006) Spin Readout & Initialization (spin charge conversion)

9 Single Atom Nanotechnologies: Top-Down & Bottom-Up Jamieson, Yang, Hopf, Hearne, Pakes, Prawer, Mitic, Gauja, Andresen, Hudson, ASD and Clark, Appl. Phys. Lett. 86, (2005). O'Brien, Schofield, Simmons, Clark, ASD, Curson, Kane, McAlpine, Hawley and Brown, Phys.Rev. B 64, R (2001) 1 nm

10 Progress in Atomically Precise STM Devices I SET (pa) Nature Nanotechnology 9, 430 (2014) Nano Letters 14, 1830 (2014) Nature Materials 13, 605 (2014) Simmons Group UNSW Time (ms) Nature Communications 4, 2017 (2013) 0 Nature Nanotechnology 7, 242 (2012) Science (2012) Nature Nanotechnology 5, 502 (2010) Nano Letters 11, 4376 (2011)

11 Ion Implanted Qubits in Silicon Jamieson, Yang, Hopf, Hearne, Pakes, Prawer, Mitic, Gauja, Andresen, Hudson, ASD and Clark, Appl. Phys. Lett. 86, (2005).

12 Ion-Implanted Counted Atom Devices 2 DP3 Chip Map mm Fabrication Pathway 2 2 mm Detector fabrication Atom implantation Complete measurement

13 Single Atom Nanoelectronics : Top Down UNSW U Melbourne

14 S.J. Angus et al., Nano Letters 7, 2051 (2007) Readout Device: Si-MOS SET

15 Device Fabrication TEM n ++ n ++ Al top gate source Al Al x O y 100 nm 20 nm SiO 2 Silicon plunger 10 mm n ++ drain n ++

16 Charge Sensing: 100% Contrast donor I SET N-1 N N+1 Electron on P-donor I SET = 0 (Coulomb blockade) P-donor Empty I SET > 0 V top gate I SET V top gate V plunger A. Morello et al., Phys. Rev. B 80, (R) (2009)

B 80, 081307R (2009) Hans Huebl et al., Phys.

17 P-donor Electron Spin: Single-Shot Readout A. Morello et al., Nature 467, 687 (2010) Andrea Morello et al. Phys. Rev. B 80, R (2009) Hans Huebl et al., Phys. Rev B 81, (2010) Andrea Morello et al., Nature 467, 687 (2010) T 1e = 6s (at 1.5T) Fidelity > 90%

18 Summary

, Nanotechnology 24, 015202 (2013) 31 P:Si P-Donor

19 Qubit Gate Operations: P-Donor ESR & NMR On-chip microwave transmission line: J.P. Dehollain et al., Nanotechnology 24, (2013) 31 P:Si P-Donor Electron/Nuclear Spin Levels B 0 Bac H = gm B B 0 S z n B 0 I z + A I S = Electron Spin, S = Nuclear Spin, I

21 Coherent Control: Electron Spin Qubit Rabi Oscillations T ~ 150 ns; -pulse Fidelity = 57% Measurement Fidelity = 77% J.J. Pla et al., Nature 489, 541 (2012)

22 Electron Spin Qubit: Hahn Echo, XYXY Dynamical Dec. Single P Donor: T 2e = 206 µs Cf. Bulk: T 2e = 240 µs XYXY DD: T 2e = 410 µs J.J. Pla et al., Nature 489, 541 (2012) Gordon and Bowers, PRL 1, 368 (1958)

23 J.J. Pla et al., Nature 496, 334 (2013) 18 April 2013

24 31 P Nuclear Spin Qubit: Single-Shot Readout J.J. Pla et al., Nature 496, 334 (2013)

25 electron spin-up counts 31 P Nuclear Spin Qubit: Single-Shot Readout Pulse Sequence: 256 repetitions 260 ms per measurement Readout Fidelity > 99.8% > 7 hours Cross-Relaxation Process mw1 mw Time (min) J.J. Pla et al., Nature 496, 334 (2013) T 1n ~ mins (cf. hrs in bulk)

26 31 P Nuclear Spin Qubit: Rabi Coherent Control Neutral Donor J.J. Pla et al., Nature 496, 334 (2013) Ionized Donor Rabi (Ionised Donor) Gate Fidelity > 98% & T ~ 30 µs

27 Spectral Diffusion in nat Si 28 Si, 30 Si Lattice o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 31 P 29 Si (~5%) o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o T 2e > 1 s in 28 Si [A.M. Tyryshkin et al., Nature Materials 11, 143 (2011)]

Ultra-Long Coherence: Avogadro Project 28 Si

density of 28 Si 5 kg crystal Enrichment: 99.

Thewalt, Simon Fraser University 31 P Nuclear

995% 28 Si wafer - optical readout via electron

28 Ultra-Long Coherence: Avogadro Project 28 Si Redefine kilogram based on lattice constant and density of 28 Si 5 kg crystal Enrichment: % Dislocation free Image courtesy of Mike Thewalt, Simon Fraser University 31 P Nuclear Spin - in % 28 Si wafer - optical readout via electron spin (bound exciton) 13 C Nuclear Spin - in 99.99% 12 C diamond - optical readout via NV centre

29 Single 31 P Qubit in 28 Si Isotopically Purified 28 Si Epilayer < 0.1% residual 29 Si - via Kohei Itoh (Keio U.) J. Muhonen et al., arxiv: ; to appear in Nature Nanotechnology

9% - Via Kohei Itoh, Keio University, Japan 1 Electron Spin Rabi Oscillations - 28 Si-enriched Qubit 0.9 0.8 0.7 0.6 0.5 0.4 0.

30 Spin-up Proportion Implanted 31 P Electron Spin Qubit in 28 Si P-atom Implanted Electron Spin Qubit Natural Silicon, 5% 29 Si Pla et al, Nature (2012) Rabi oscillations T 2 * = 55 ns P-atom Implanted Electron Spin Qubit 28 Si Epilayer Enriched to 99.9% - Via Kohei Itoh, Keio University, Japan 1 Electron Spin Rabi Oscillations - 28 Si-enriched Qubit Microwave Pulse Length (µs) J. Muhonen et al., arxiv: ; to appear in Nature Nanotechnology

31 Spin-up Fraction 31 P: 28 Si Electron Spin Qubit High-Fidelity Rabi Oscillations -pulse Fidelity: F c > -10 dbm e Read Error, α Load Error, β μ DOT Read Fidelity: F M = 97% Donor μ DOT Dot Rabi Pulse Length (ms)

8 khz Linewidth T 2e * = 270 ms FWHM < 2 khz Crucial for multi-qubit coupling

32 Single 31 P Qubit in 28 Si: Electron Coherence Benchmarks Ramsey Hahn echo e ESR Linewidth 1.8 khz Linewidth T 2e * = 270 ms FWHM < 2 khz Crucial for multi-qubit coupling T 2e = 0.95 ms Indicates extra source of decoherence (not 29 Si nuclei) J. Muhonen et al., arxiv: ; to appear in Nature Nanotechnology

Single 31 P Qubit in 28 Si: Electron Noise Spectroscopy Coloured low-frequency noise 1/f 2.5 Unrelated to any electrical or charge noise at the Si/SiO 2 interface - measured 1/f 0.

33 Single 31 P Qubit in 28 Si: Electron Noise Spectroscopy Coloured low-frequency noise 1/f 2.5 Unrelated to any electrical or charge noise at the Si/SiO 2 interface - measured 1/f 0.5 Suspected origin: Superconducting magnet White noise background caused by the magnetic field of room-t thermal radiation from a 50 load Reduced by adding cold attenuation J. Muhonen et al., arxiv: ; to appear in Nature Nanotechnology

Single 31 P Qubit in 28 Si: Fidelities > 99%;

5 s Nuclear: T 2n > 30 s - with CPMG DD Electron

34 Single 31 P Qubit in 28 Si: Fidelities > 99%; Very Long T 2 Fidelities Electron Neutral Nucleus Ionized Nucleus All F C > 99% Coherence Times Electron: T 2e > 0.5 s Nuclear: T 2n > 30 s - with CPMG DD Electron Ionized Nucleus J. Muhonen et al., arxiv: ; to appear in Nature Nanotechnology

35 Scalable + Fault-tolerant Architecture Spin transport rails Classical CMOS circuitry 1- and 2-qubit gates L. Hollenberg et al., PRB 74, (2006) Spin readout (spin charge conversion)

36 Future Vision for Spin-based QIP

37 C. Yin et al., Nature 497, 91 (2013) 2 May 2013

38 Electron Transport via Quantum Dots N e SET 1 e Dot 1 e Dot N e SET Rossi et al., Nano Letters 14, 3405 (2014) I. LOAD (SPIN DOWN) II. ROTATE (ESR PULSE) III. SHUTTLE IV. READ SPIN Uncertainty < 30 ppm at f = 0.5 GHz

39 Electron Spin Qubits based on Quantum Dots Coherence times in GaAs limited by nuclear spin bath: Bluhm et al., PRL (2010) & Nature Phys. (2011) T 2 * = ~ 100 ns; T 2 = 30 ms (Hahn); T 2 = 200 ms (CPMG)

40 Silicon Quantum Dots: Many Different Flavours SOI Nanowire Dots H. W. Liu et al., Phys. Rev. B 77, (2008). H. W. Liu et al., Appl. Phys. Lett. 92, (2008). Polysilicon-gated Si-MOS E. P. Nordberg et al., Phys. Rev. B 80, (2009). E. P. Nordberg et al., Appl. Phys. Lett. 95, (2009). Si/SiGe Heterostructures C. B. Simmons, Appl. Phys. Lett. 91, (2007). N. Shaji et al., Nat. Phys. 4, 540 (2008).

41 Si Q-Dot Qubits in Si/SiGe Heterostructures T 2 * = 360 ns arxiv: ; Nature - July 2014 T 2 * = 2-10 ns; T ~ 50 ps; F C = 85-94% arxiv: ; Nature Nanotechnology Aug 2014 T 2 * = 1 ms; T 2 = 37 ms

42 S.J. Angus et al., Nano Letters 7, 2051 (2007) Readout Device for P-donor qubits: Si-MOS SET

43 Commercial Si-MOS Devices & Charge Noise Pentium MOSFET (2005) 65nm Node Zimmerman et al., arxiv: to appear in Nanotechnology

44 UNSW 3 x EBL Systems (Raith, FEI...) Highest Concentration in Australia Sub-10nm Features Silicon MOS Process Line TiAuPd

45 Si-MOS Quantum Dots: Pauli Spin Blockade N.S. Lai et al., Scientific Reports. 1, 110 (2011)

46 Si p-mos Dots: for Hole-based Spin Qubits R. Li et al., Appl. Phys. Lett. 103, (2013) See also: P. Spruijtenberg et al., Appl. Phys. Lett. (2013)

47 Si-MOS Quantum Dot: Spin and Valley Level Spectra 100 nm

48 Si-MOS Quantum Dot: Spin and Valley Level Spectra 100 nm

49 Si-MOS Quantum Dot: Tuneable Valley Splitting, E v 100 nm

Si-MOS Dot: 1e Spin Lifetimes & Spin-Valley Mixing C.H. Yang et al., Nature Comms. 4, 2069 (2013) Single-shot readout of spin-up spin-down lifetime T 1 Longest lifetime: T 1 = 2.6 s @ B = 1.

50 Si-MOS Dot: 1e Spin Lifetimes & Spin-Valley Mixing C.H. Yang et al., Nature Comms. 4, 2069 (2013) Single-shot readout of spin-up spin-down lifetime T 1 Longest lifetime: T 1 = 2.6 B = 1.25 T By tuning valley splitting we study two regimes: E z < E vs & E z > E vs E vs = 0.33 mev E vs = 0.75 mev When E z = E vs we see a relaxation hot spot First exptl. observation Interface disorder permits mixing between spin & valley states via SOC

51 Si-MOS Dot ESR Spectroscopy of Spin-Valley States Nature Communications (2014); arxiv:

52 Si-MOS Quantum Dot Qubit in 28 Si Isotopically Purified 28 Si Epilayer 800 ppm residual 29 Si M. Veldhorst et al., arxiv: , to appear in Nature Nanotechnology (2014)

53 Silicon MOS Dots: Electron Spin Qubit in 28 Si M. Veldhorst et al., arxiv: , to appear in Nature Nanotechnology (2014)

54 28 Si-MOS Dot: e Spin Qubit Coherent Control f = Ω 2 / Ω R2 sin 2 (Ω R τ/2) M. Veldhorst et al., arxiv: , to appear in Nature Nanotechnology (2014)

55 28 Si-MOS Dot: e Spin Qubit Long Coherence Times Ramsey: T 2 * 120 ms Hahn: T ms CPMG 500 : T 2 28 ms M. Veldhorst et al., arxiv: , to appear in Nature Nanotechnology (2014)

56 28 Si-MOS Dot e Spin Qubit: Gate-Addressable f ESR Tunabilty = 8 MHz Cf. 2.4 khz Linewidth M. Veldhorst et al., arxiv: , to appear in Nature Nanotechnology (2014)

Microwave 39,045+ 39,045+ (Mhz) (Mhz) Microwave 39,045+ 39,045+ (Mhz) (Mhz) Microwave 39,045+ (Mhz) Microwave 39,045+ (Mhz)

Microwave 39,170+ (Mhz) (Mhz) 28 Si-MOS Dot Qubit: 3e Occupancy Qubit -1-1 N e = 2 state forms singlet in valley V - 3 rd

f=300khz, f=300khz, Visibilty=0.7, Visibilty=0.

7, T2=200us -1-1 Simulation, f=300khz, Visibilty=0.7, T2=200us -1-1 -1 3-electron state -0.5-0.5-0.5-0.5-0.5-0.5-0.5-0.5 0 0 0 0 0 0 0 0.

Width (us) (us) Pulse Pulse Width Width (us) (us) 0.5 0.

Width (us) Pulse Pulse Width Width (us) (us) [ν -, 1e] Qubit -1-1 -1-1 Experimental Experimental Experimental Experimental

73, T2=50us T2=50us Simulation, Simulation, f=174khz, f=174khz, Visibilty=0.73, Visibilty=0.73, T2=50us T2=50us -0.5-0.

57 Microwave 39, ,045+ (Mhz) (Mhz) Microwave 39, ,045+ (Mhz) (Mhz) Microwave 39,045+ (Mhz) Microwave 39,045+ (Mhz) Microwave Microwave 39, ,170+ (Mhz) (Mhz) Microwave Microwave 39, ,170+ (Mhz) (Mhz) Microwave 39,170+ (Mhz) Microwave 39,170+ (Mhz) (Mhz) 28 Si-MOS Dot Qubit: 3e Occupancy Qubit -1-1 N e = 2 state forms singlet in valley V - 3 rd electron has unpaired spin with s = ½ Rabi Control Experiment Model Experimental Experimental Simulation, Simulation, f=300khz, f=300khz, Visibilty=0.7, Visibilty=0.7, T2=200us T2=200us -1 Experimental Experimental Simulation, f=300khz, Visibilty=0.7, T2=200us -1-1 Simulation, f=300khz, Visibilty=0.7, T2=200us electron state Pulse Pulse Width Width (us) (us) Pulse Pulse Width Width (us) (us) Pulse Width Pulse (us) Width (us) Pulse Pulse Width Width (us) (us) [ν -, 1e] Qubit Experimental Experimental Experimental Experimental Simulation, Simulation, f=174khz, f=174khz, Visibilty=0.73, Visibilty=0.73, T2=50us T2=50us Simulation, Simulation, f=174khz, f=174khz, Visibilty=0.73, Visibilty=0.73, T2=50us T2=50us Pulse Width (us) Pulse Pulse Pulse Width Width Width (us) (us) (us) Pulse Width (us) Pulse Pulse Width Pulse Width (us) Width (us) (us) [ν +, 3e] Qubit

58 28 Si-MOS Dot Qubit: Fidelities via Randomized Benchmarking We apply randomized benchmarking (RBM) protocol to assess single-qubit gate fidelities - see, e.g.: NMR Qubit: C.A. Ryan, M. Laforest & R. Laflamme, New J. Phys. 11, (2009); Superconducting Qubit: R. Barends et al., arxiv/ ALL 1-electron 1-qubit gate operations are > 99% surface code threshold for F-T QC 1-Electron Qubit 1-Electron Qubit 3-Electron Qubit

59 28 Si-MOS Dots: Multi-Qubit Devices

60 28 Si-MOS Dots: Multi-Qubit Device Reservoir G1 G2 ESR Drive Q C Q B Q A Confinement G3 G4 x SET Sensor AlO x Aluminium 28 Si x 1 Gate 1 Qubit

61 28 Si-MOS Dots: Multi-Qubit Device Reservoir G1 G2 ESR Drive Q C Q B Q A Confinement G3 G4 x SET Sensor Qubit Q A (Dot-A; 3e ): Rabi Control Qubit Q C (Dot-C; 3e ): Rabi Control

62 28 Si-MOS Double Dots: Charge State Hysteresis Yang et al., arxiv:

63 28 Si-MOS Dots: Devices for 2-qubit Tomography

64 28 Si-MOS Dot Qubits: S-T Qubit & Dispersive Readout Jason Cheng, Henry Yang, Alex Hamilton

65 28 Si-MOS Dot Qubits: Scaling Up Error Threshold for Fault-Tolerant QC as high as 1%

66 Experimental Postdoctoral Positions Available

Silicon-based Spin Qubits: Summary Phosphorus Donors: Kane Concept 2012 1-Qubit: Donor Electron in nat Si (ESR) T 1 ~ secs; T 2 ~ 0.

3 ms; Fidelity > 99% 2014 1-Qubit: 31 P Nuclear Spin in 28 Si T 1 ~ hrs; T 2 ~ 30 s; T * 2 ~ 0.3 s; Fidelity > 99.

67 Silicon-based Spin Qubits: Summary Phosphorus Donors: Kane Concept Qubit: Donor Electron in nat Si (ESR) T 1 ~ secs; T 2 ~ 0.2 ms; Fidelity ~ 50% Qubit: 31 P Nuclear Spin in nat Si (NMR) T 1 ~ mins; T 2 ~ 60 ms; Fidelity > 98% Qubit: Donor Electron in 28 Si T 1 ~ s; T 2 ~ 0.5 s; T * 2 ~ 0.3 ms; Fidelity > 99% Qubit: 31 P Nuclear Spin in 28 Si T 1 ~ hrs; T 2 ~ 30 s; T * 2 ~ 0.3 s; Fidelity > 99.9% Si/SiGe Quantum Dots: Singlet-Triplet; Loss-DiVincenzo; Hybrid Qubit: 2-electron Singlet-Triplet T 1 ~ s; T * 2 ~ 400 ns Qubit: 1-electron Spin-Charge Hybrid T * 2 ~ 10 ns; Fidelity = 85% 95% Qubit: 1-electron ESR Control T 2 ~ 30 ms; T * 2 ~ 1 ms; Si-MOS Quantum Dots: Loss-DiVincenzo (so far ) Qubit: 1-electron ESR Control in 28 Si T 1 ~ s; T 2 ~ 30 ms; Fidelity > 99% Qubit: Electron-Electron Exchange Coupling CNOT Gate Demonstrated

Silicon-based Quantum Computing:

Silicon-based Quantum Computing: The path from the laboratory to industrial manufacture Australian National Fabrication Facility Andrew Dzurak UNSW - Sydney a.dzurak@unsw.edu.au Leti Innovation Days, Grenoble,