Spin-based Quantum Computing in Silicon Andrew Dzurak UNSW - Australia [email protected]
Australian National US-Australia Enabling Technologies Exchange Meeting Fabrication Facility Arlington, VA, 13 May 2015 Quantum Information Science
Data Security Decryption National Security Financial Services National Security e-Commerce Intelligence
Integrated Circuits Killer Apps ? Extending Moore’s Law High Performance Computing Database Searching Bioinformatics Modeling & Design
Future Vision for Spin-based QIP Co-Workers & Sponsors
UNSW - Australia David Jamieson, Jeff McCallum, Michael Fogarty Lloyd Hollenberg U. Melbourne Wister Huang Steve Flammia, Stephen Bartlett Jason Hwang University of Sydney Yuxin Sun Jarryd Pla, John Morton UCL, UK Ruichen Zhao Jason Cheng, Charles Smith Dr Fay Hudson Cambridge, UK Dr Alessandro Rossi Malcolm Carroll Sandia National Lab Dr Menno Veldhorst Dr Henry Yang Gerhard Klimeck, Rajib Rahman Purdue Dr Juan-Pablo Dehollain Charles Tahan, Rusko Ruskov LPS, USA Dr Fahd Mohiyaddin Kohei Itoh Keio University, Japan Dr Juha Muhonen Mikko Möttönen Aalto, Finland Dr Arne Laucht A/Prof Andrea Morello Floris Zwanenburg Twente, Netherlands
Spin Qubits in Semiconductors Si:P Donors: Electron & Nuclear Spin Qubits in 28Si
J. Muhonen et al., Nature Nanotechnol. 9, 986 (2014) SiMOS Quantum Dot: Electron Spin Qubit in 28Si
M. Veldhorst et al., Nature Nanotechnol. 9, 981 (2014) Spin Qubits in Semiconductors 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 Single Atom Nanotechnologies: Top-Down & Bottom-Up
Jamieson, Yang, Hopf, O'Brien, Schofield, Hearne, Pakes, Prawer, Simmons, Clark, ASD, Mitic, Gauja, Andresen, Curson, Kane, McAlpine, Hudson, ASD and Clark, Hawley and Brown, Appl. Phys. Lett. 86, Phys.Rev. B 64, 202101 (2005). R161401 (2001)
1 nm Progress in Atomically Precise STM-fabricated Devices
Nano Letters Nature Nanotechnology Nature Materials 13, 605 (2014) 14, 1830 (2014) 9, 430 (2014)
40 Simmons Group
0
)
pA 0 150 (
UNSW
SET I 40
0
0 150 Time (ms) Nature Communications 4, 2017 (2013)
Nature Nature Nanotechnology Science Nanotechnology Nano Letters 7, 242 (2012) 335 64 (2012) 5, 502 (2010) 11, 4376 (2011) Ion Implanted Qubits in Silicon
Jamieson, Yang, Hopf, Hearne, Pakes, Prawer, Mitic, Gauja, Andresen, Hudson, ASD and Clark, Appl. Phys. Lett. 86, 202101 (2005). Ion-Implanted Counted Atom Devices
2 DP3 Chip Map 2
2
2
5 4
1.2 mm 2 Fabrication Pathway
2 2 mm
Detector Atom Complete fabrication implantation measurement Single Atom Nanoelectronics : Top Down Nanofab
UNSW U Melbourne S.J. Angus et al., Nano Letters 7, 2051 (2007)
Readout Device: Si-MOS SET Charge Sensing: 100% Contrast
ISET
donor
N-1 N N+1
Electron on P-donor ISET = 0 (Coulomb blockade)
P-donor Empty ISET > 0
Vtop gate
ISET
Vtop gate
Vplunger
A. Morello et al., Phys. Rev. B 80, 081307(R) (2009) Si:P e-Spin Qubit: Single-Shot Readout
A. Morello et al., Nature 467, 687 (2010) Andrea Morello et al. Phys. Rev. B 80, 081307R (2009)
Hans Huebl et al., Phys. Rev B 81, 235318 (2010)
Andrea Morello et al., Nature 467, 687 (2010)
T1e = 6s (at 1.5T) Fidelity > 90% Qubit Gate Operations: P-Donor ESR & NMR On-chip microwave transmission line: 31P:Si J.P. Dehollain et al., Nanotechnology 24, 015202 (2013) P-Donor Electron/Nuclear Spin Levels
B0
Bac
= Electron Spin, S H = gBB0Sz – nB0Iz + A I S = Nuclear Spin, I
Si:P e-Spin Qubit: Coherent Control via ESR
Single P Donor:
T2e = 206 µs
Cf. Bulk:
T2e = 240 µs Gordon and Bowers, PRL 1, 368 (1958) Si:P Nuclear Spin Qubit
J.J. Pla et al., Nature 496, 334 (2013) Lattice Nuclear Spin Noise in natSi
28Si,30Si Lattice 29Si (~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 31P o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 28 T2e > 1 s in Si [A.M. Tyryshkin et al., Nature Materials 11, 143 (2011)] Ultra-Long Coherence: Avogadro Project 28Si Redefine kilogram based on lattice constant and density of 28Si 5 kg crystal Enrichment: 99.995% Dislocation free Image courtesy of Mike Thewalt, Simon Fraser University
31P Nuclear Spin - in 99.995% 28Si wafer - optical readout via electron spin (bound exciton)
13C Nuclear Spin - in 99.99% 12C diamond - optical readout via NV centre
Si:P Donors: Electron & Nuclear Spin Qubits in 28Si
J. Muhonen et al., Nature Nanotechnol. 9, 986 (2014) Si:P Donor Qubits: Scalability Concepts
Classical CMOS circuitry
Spin transport rails
1-qubit & 2-qubit Gates
Spin Readout & Initialization (spincharge conversion) L. Hollenberg et al., PRB 74, 045311 (2006) Electron Transport via Quantum Dots
Rossi et al., Nano Letters 14, 3405 (2014) N e 1 e 1 e N e SET Dot Dot SET
I. LOAD (SPIN DOWN)
II. ROTATE (ESR PULSE)
III. SHUTTLE
IV. READ SPIN Uncertainty < 30 ppm at f = 0.5 GHz Spin Qubits in Semiconductors Electron Spin Qubits based on Quantum Dots
Coherence times in GaAs limited by nuclear spin bath: Bluhm et al., PRL (2010) & Nature Phys. (2011) * T2 = ~ 100 ns; T2 = 30 s (Hahn); T2 = 200 s (CPMG) Si Q-Dot Qubits in Si/SiGe Heterostructures
* T2 = 360 ns
Nature 511, 70 (2014)
* T2 = 2-10 ns; T ~ 50 ps; FC = 85-94%
Nature Nanotechnology 9, 666 (2014)
* T2 = 1 s; T2 = 37 s S.J. Angus et al., Nano Letters 7, 2051 (2007)
Readout Device for P-donor qubits: Si-MOS SET Commercial SiMOS Devices
Pentium MOSFET (2005) UNSW SiMOS Devices 65nm Node ANFF @ UNSW
• 3 x EBL Systems (Raith, FEI ...) • Highest Concentration in Australia • Sub-10nm Features • Silicon MOS Process Line
TiAuPd Si-MOS Quantum Dot: Spin and Valley Level Spectra
100 nm Si-MOS Quantum Dot: Tuneable Valley Splitting, Ev
100 nm Si-MOS Quantum Dot Qubit in 28Si
Isotopically Purified 28Si Epilayer 800 ppm residual 29Si
Wafer supplied by Kohei Itoh, Keio University Silicon MOS Dots: Electron Spin Qubit in 28Si 28Si-MOS Dot: e– Spin Qubit – Coherent Control
2 2 2 f↑ = Ω / ΩR sin (ΩR τ/2) M. Veldhorst et al., Nature Nanotechnology 9, 981 (2014) 28 – Si-MOS Dot e Spin Qubit: Gate-Addressable fESR
Tunabilty = 8 MHz Cf. 2.4 kHz Linewidth M. Veldhorst et al., Nature Nanotechnology 9, 981 (2014) 28 SiMOS Dot Electron Spin Qubit in Si: Randomized Benchmarking
See: M. Veldhorst et al., Nature Nanotechnology 9, 981 (2014)
ALL 1e 1-qubit gate fidelities > 99% Average 1e 1-qubit gate fidelity = 99.6%
1-Electron Qubit 1-Electron Qubit 3-Electron Qubit 28 Si-MOS Dots: Multi-Qubit Devices
28 Si-MOS Dots: Multi-Qubit Device
Reservoir G1 G2
QC ESR G3 Drive QB QA G4 Confinement
x SET Sensor
AlOx Aluminium
x 28Si 1 Gate 1 Qubit 28 Si-MOS Dots: Two Qubit Exchange Gate
M. Veldhorst et al., arXiv:1411.5760 – submitted to Nature 28 Si-MOS Dots: Two Qubit Exchange Gate
Increased Sensitivity to Electrical / Charge Noise
M. Veldhorst et al., arXiv:1411.5760 – submitted to Nature 28 Si-MOS Dot Two-Qubit Gate: Two-Spin Correlations
M. Veldhorst et al., arXiv:1411.5760 – submitted to Nature 28 Si-MOS Dot Qubits: Scaling Up
Error Threshold for Fault-Tolerant QC with Surface Code as high as 1% Silicon-based Spin Qubits: Summary
Phosphorus Donors: Kane Concept
nat 2012 – 1-Qubit: Donor Electron in Si (ESR) T1 ~ secs; T2 ~ 0.2 ms; Fidelity ~ 50% 31 nat 2013 – 1-Qubit: P Nuclear Spin in Si (NMR) T1 ~ mins; T2 ~ 60 ms; Fidelity > 98% 28 * 2014 – 1-Qubit: Donor Electron in Si T1 ~ s; T2 ~ 0.5 s; T2 ~ 0.3 ms; Fidelity > 99% 31 28 * 2014 – 1-Qubit: P Nuclear Spin in Si T1 ~ hrs; T2 ~ 30 s; T2 ~ 0.3 s; Fidelity > 99.9% 2014 – 2-Qubit: Electron-Nuclear Hyperfine Coupling Entangling Gate Demonstrated
Si/SiGe Quantum Dots: Singlet-Triplet; Loss-DiVincenzo; Hybrid * 2012 – 1-Qubit: 2-electron Singlet-Triplet T1 ~ s; T2 ~ 400 ns * 2014 – 1-Qubit: 1-electron Spin-Charge Hybrid T2 ~ 10 ns; Fidelity = 85% – 95% * 2014 – 1-Qubit: 1-electron ESR Control T2 ~ 30 s; T2 ~ 1 s; 2015 – 1-Qubit: 3-electron Exchange-only, all-electrical control [HRL]
Si-MOS Quantum Dots: Loss-DiVincenzo
28 2012 – 1-Qubit: 1-electron ESR Control in Si T1 ~ s; T2 ~ 30 ms; Fidelity > 99% 2014 – 2-Qubit: Electron-Electron Exchange Coupling CNOT Gate Demonstrated EXTRAS Silicon Quantum Dots: Many Different Designs SOI “Nanowire” Dots Polysilicon-gated Si-MOS Si/SiGe Heterostructures H. W. Liu et al., Phys. Rev. B 77, 073310 E. P. Nordberg et al., Phys. Rev. B 80, 115331 C. B. Simmons, Appl. Phys. Lett. 91, 213103 (2008). (2009). (2007). H. W. Liu et al., Appl. Phys. Lett. 92, 222104 E. P. Nordberg et al., Appl. Phys. Lett. 95, 202102 N. Shaji et al., Nat. Phys. 4, 540 (2008). (2008). (2009). Charge Noise in SiMOS Devices
Zimmerman et al., Nanotechnology 25, 405201 (2014) Pentium MOSFET (2005) 65nm Node 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 T1 • Longest lifetime:
T1 = 2.6 s @ B = 1.25 T • By tuning valley splitting we study two regimes:
Ez < Evs & Ez > Evs
• When Ez = Evs we see a Evs = 0.33 meV relaxation “hot spot” First exptl. observation • Interface disorder permits E = 0.75 meV vs mixing between spin & valley states via SOC 28Si-MOS Dot: e– Spin Qubit – Long Coherence Times
* Ramsey: T2 120 s Hahn: T2 1.2 ms CPMG500: T2 28 ms
M. Veldhorst et al., Nature Nanotechnology 9, 981 (2014) 28 – Si-MOS Dot Qubit: 3e Occupancy Qubit
Ne = 2 state forms singlet in valley V- 3rd electron has unpaired spin with s = ½ 3-electron state Rabi Control Experiment Model
ExperimentalExperimental Simulation,Simulation, f=300khz, f=300khz, Visibilty=0.7, Visibilty=0.7, T2=200us T2=200us Experimental Simulation, f=300khz, Visibilty=0.7, T2=200us -1 -1 Experimental -1 -1 Simulation, f=300khz, Visibilty=0.7, T2=200us -1 -1 -1 -1
-0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5
0 0 0 0
0 0 0 0
Microwave 39,170+ (Mhz) Microwave 39,170+ (Mhz) Microwave 39,170+ Microwave 39,170+ (Mhz) Microwave 39,170+
Microwave 39,170+ (Mhz) Microwave 39,170+ 0.5 0.5 Microwave 39,170+ (Mhz) Microwave 39,170+
Microwave 39,170+ (Mhz) Microwave 39,170+ 0.5 0.5 Microwave 39,170+ (Mhz) Microwave 39,170+ 0.5 (Mhz) Microwave 39,170+ 0.5 0.5 0.5 [ν , 1e] Qubit 1 1 1 1 - 1 0 1 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35 10 10 5 5 10 10 15 15 20 20 25 25 30 30 35 35 0 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35 0 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35 PulsePulse Width Width (us) (us) Pulse WidthPulse (us)Width (us) PulsePulse Width Width (us) (us) Pulse PulseWidth Width(us) (us)
ExperimentalExperimental Simulation,Simulation, f=174khz, f=174khz, Visibilty=0.73, Visibilty=0.73, T2=50us T2=50us ExperimentalExperimental Simulation,Simulation, f=174khz, f=174khz, Visibilty=0.73, Visibilty=0.73, T2=50us T2=50us -1 -1 -1 -1 -1 -1 -1 -1
-0.5 -0.5 -0.5-0.5 -0.5 -0.5-0.5 -0.5
0 0
00 0 0 0
Microwave 39,045+ (Mhz) Microwave 39,045+ (Mhz) Microwave 39,045+ Microwave 39,045+ (Mhz) Microwave 39,045+
Microwave 39,045+ (Mhz) Microwave 39,045+ 0.5 0.5
Microwave 39,045+ (Mhz) Microwave 39,045+ (Mhz) Microwave 39,045+ Microwave 39,045+ (Mhz) Microwave 39,045+ Microwave 39,045+ (Mhz) Microwave 39,045+ 0.50.5 0.5 0.5 0.5
1 1 [ν , 3e] Qubit 11 1 0 5 10 15 20 25 30 35 1 10 5 10 15 20 25 30 35 + 0 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35 0 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35 0 5 10 15 Pulse Width20 (us) 25 30 35 0 5 10 15 Pulse Width20 (us) 25 30 35 PulsePulsePulse WidthWidth Width (us) (us) PulsePulse WidthPulseWidth (us)Width(us) (us) 28 – – Si-MOS Dot Qubit: 1e cf. 3e Occupancy Qubits
Tunability of fESR using Gate Voltage (ie. Electric Field)
@ VC=-0.2V 40 1-electron & 3-electron qubits 35 g =1.9975
(GHz) 1e have: g1e=1.9975 30 distinct g-factors
freqeuency 25 opposite sign of (E)
20 Resonant 15 g3e=1.9912 Due to0.7 occupancy0.8 0.9 1 1.1 of1.2 1.3 1.4 Magnetic field (T)
40different valleys
(GHz) g =1.9912
35 3e
30
freqeuency 25
Theory with: Rusko Ruskov & Charlie Tahan (LPS) 20 Resonant
Michael Flatte (U Iowa) 15 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 Magnetic field (T) 28 Si-MOS Dots: Two Qubit Exchange Gate
M. Veldhorst et al., arXiv:1411.5760 – submitted to Nature