Semiconductor qubits for adiabatic quantum computing

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Silicon P donor qubit structure Spin read-out & Rabi oscillations

[us] Semiconductor qubits for adiabatic quantum computing Malcolm

National Laboratories is a multi-program laboratory managed and

Lockheed Martin Corporation, for the U.S.

1 Silicon P donor qubit structure Spin read-out & Rabi oscillations Adiabatic inversion DQD qubits for QA ~10 P Local ESR P Ramp time [us] Semiconductor qubits for adiabatic quantum computing Malcolm Carroll Sandia National Labs, Albuquerque June 11 th, 2014 Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy s National Nuclear Security Administration under contract DE-AC04-94AL85000.

2 Outline Motivation for Si qubit research in adiabatic QC and QA Single electron spin qubit and adiabatic operation Semiconductor qubit approaches to quantum annealing Summary 2

3 Motivations and research direction What are the limits and extensions of adiabatic control of one or several qubits? (e.g., adiabatic inversion) Questions about quantum annealing Are there tests with one and a few qubits that inform the black box testing approach What are the microscopic dynamics and how does it break? o Is fast relaxation helpful? (what dependence?) o kt >> E gap? o What role does T2 play? What makes a good qubit for quantum annealing? Our approach: o Is there benefit to using a semiconductor qubit for QA? Examine silicon (or semiconductor) qubits in context of adiabatic quantum computation (or annealing)? 4

4 Outline Motivation for Si qubit research in adiabatic QC and QA Single electron spin qubit and adiabatic operation Semiconductor qubit approaches to quantum annealing Summary 5

Qubit approach using donors in Si Kane, Nature, 1998 Kane-like (electron spin only): Single donor for qubit One electrode on/off frequency tuning to NMR or ESR u-waves Second electrode on/off

5 Qubit approach using donors in Si Kane, Nature, 1998 Kane-like (electron spin only): Single donor for qubit One electrode on/off frequency tuning to NMR or ESR u-waves Second electrode on/off overlap electrons for exchange (sqrt[swap]) Lot s of progress in this area recently Not clear how people will couple donors but focus of this talk is context of adiabatic control for single spin 6

6 Concept SET or QD detects nearby charge center ionization Single donor spin read-out concept Read sequence (spin up) donor SET E C 3. Unload Spin dependent ionization 2. Read 1. Load Charge state is static Charge state is changing in time due to tunneling 7 Morello et al., Nature 2010

7 Poly silicon quantum dot 0 V 0 V Single dot current 1.2V LP 0 V RP 500 nm S/D E= q C Poly-Si SiO 2 Si Simplify SET for donor read-out o Implant will be self-aligned 8 Harvey-Collard

8 Poly silicon quantum dot 0 V 0 V Single dot current 1.2V LP 0 V RP 500 nm S/D E= q C Poly-Si SiO 2 Si Simplify SET for donor read-out o Implant will be self-aligned Relatively regular period Coulomb blockade achieved in poly silicon SET Wire width ~50-60 nm with gaps between wire and plunger of ~40-50 nm This structure can regularly be used for read-out 9 Harvey-Collard

Semi-classical modelling of lithographic dot

~5x10 10 /cm 2 Gate to quantum dot capacitances

9 Semi-classical modelling of lithographic dot Dot location QCAD is semi-classical simulation capability developed at SNL 1.1x10 17 /cm 3 charge fits 4K threshold Order of ~5x10 10 /cm 2 Gate to quantum dot capacitances are similar to QCAD predictions in multiple devices Shirkhorshidian 10

10 Gate wire with implant QD coupling to donor Implant window T ~ 2K Poly-Si SiO 2 Si Sb Typical implant conditions: 120 kev implant, range ~28 nm below SiO 2 /Si interface, 18 nm vertical straggle 4e11/cm -2 dose ~ 14 Sb donors in 60 x 60 nm 2 window Charge offsets are seen in these implanted poly-mos devices 11

11 Tuning spin readout Load Reservoir Ez Spin bump with 256 averages Load Measure Unload up Read Reservoir Ez Donor All down would have no bump Ez Reservoir Unload 12 Lilly

12 ESR pulse sequence two level pulse (a) plunge and ESR (b) read Ez Reservoir Reservoir Ez Donor Donor 1. At the end of the readout pulse, a spin down is loaded. (b) 2. Pulse energy levels down to manipulate. (a) 3. Apply microwaves. (a) 4. Spin readout (b) 13

13 Electron spin resonance of single spin Hold/u-waves Read/initialize level Time [ms] B=1.3T P = 0 dbm o Two level test with ESR detects spin resonance o Phosphorus implanted sample (~ 400 nm from center) o Similar approach to Al-Si SET devices [Pla et al. (2012)] Nguyen 14 14

14 Resonance frequency drifts These two scans were taken 10 min apart. Electron spin p Nuclear spin bath o 29 Si can reorient over timescales of ~sec, and the electron resonance frequency shifts due to hyperfine coupling. o ~5-10 MHz line width or equivalent of ~ mt o B ac max ~0.1 mt 15 Lilly

15 Incomplete pulsed X rotations due to spin bath diffusion 128 averages per trace 150 repeats Fixed frequency ( GHz) For a fixed rotation (~pi pulse) time: sometimes the spin signal is small, sometimes large 16 Lilly

16 Microwave field dependence z z B x x B x x 0 dbm 3 dbm 6 dbm f rabi = 1.4 MHz f rabi = 2.1 MHz f rabi = 2.8 MHz 17 Lilly

17 Adiabatic inversion (pi rotation) Rotating frame k i Magnetization follows a complicated track Constant precession around Z-axis can be separated out in rotating frame ESR pulse for X rotation is notionally a diabatic pulse when on resonance Adiabatic inversion starts off resonantly and transitions slowly through resonance (LUBO) 18

18 Spin bump signal Adiabatic sweep compared to on-resonant pulse Electron spin Pulsed pi rotation on resonance Adiabatic Sweep Hold Read Hold Read p Nuclear spin bath Adiabatic approach Df/t<<f rabi 2 Df=25 MHz; t=10 us Luhman 19

19 Characterization of adiabaticity of sweep -5 dbm 0 dbm 20 Luhman

20 Outline Motivation for Si qubit research in adiabatic QC and QA Single electron spin qubit and adiabatic operation Semiconductor qubit approaches to quantum annealing Summary 21

21 What makes a good quantum annealing qubit? List of metrics for QUBO example Physics of encoding Z, ZZ, X interactions & low measurement error (also independent control) T qubit loss Metric: Max. time of computation because no error correction for leakage in quantum annealing Large (E gap ) 2 / t computation-time Measure: computation time limit before excitation error due to Landau-Zener tunneling This will be a prefactor in the scaling as gap of problem shrinks exponentially Excited state manifold of single qubit should also be well separated T excite / (E gap ) 2 at E gap ~O(kT) Measure: probability of thermal excitation error relative to computation time limit Notionally, fast adiabatic passage relative to thermal excitation time (even if kt > gap) Also details of the specific qubit interaction with its open system could be important in scaling How important is cascade of low weight Hamming error to larger Hamming error? What Hamming distance are the bath interactions for each qubit instance? Correlation length (?) Need a metric for coupling between high weight Hamming transitions Notionally, large domains coherently tunneling to find energetic minima (non-classical hopping) Engineering of encoding Parameter-tuning-range/noise High yield (uniformity variance in parameters) or accurate characterization Scalability (integration, routing, power) 22

22 What makes a good quantum annealing qubit? List of metrics for QUBO example Physics of encoding Z, ZZ, X interactions & low measurement error (also independent control) Single spin encoding B Z 0 1 ( t 0) T Two spin Hamiltonian H Bz1S1z Bz2S2z J ( S1zS2 z S1xS2 x S1yS2 y ) Hinit ( t 0) B X 1. Difficult to tune local B-field for each spin 2. Exchange is not a true ZZ term 23

23 Energy Charge qubit encoding for QUBO H 1,2 V 0 0 V R > L > L > R > Voltage H k1z l 2z m1z 2z Hinit ( t) Modulation of k and l can be accomplished with voltages on gates Negative and positive epsilon might range from -mev to +mev [~12-13 K] Can be several orders of magnitude greater than the temperature in the dot 24

24 Energy Initialization H 1,2 0 t t 0 R > 2 t L > ' ' 0 L R L > R > H k1z l 2z m1z 2z Hinit( t) Tunneling magnitude is independently tunable from possibly less than nev to 100 uev (likely greater) Only positive 25

Coulomb interaction for qubit coupling 26 L.

1342 Van Weperen, PRL, 2011 H k1z l 2z m1z 2z Hinit( t)

construction or FET couplers) & might be made larger A

25 Coulomb interaction for qubit coupling 26 L. Trifunovic et al., arxiv Van Weperen, PRL, 2011 H k1z l 2z m1z 2z Hinit( t) Interaction magnitude experimentally found to range from uev [~0.25-1K] Strength of Z1Z2 interaction tunable (by construction or FET couplers) & might be made larger A little tricky to build pure ZZ but can minimize cross terms H-litho using donors is possible path that might address both achieving high fidelity & biger ZZ 26 Bussmann

26 Other interactions for charge qubit 27 Available interactions Speculative interactions Z interaction X interaction ZZ interaction ZZ interaction XX interaction XZ interaction Donors: Superior alignment? XZ Previously proposed by Hollenberg et al. 27 Landahl, Jacobson

27 Energy Two spin approach Qubit sub-space > > J > + > B z,1 B z,2 Inductor? B poly H 1,2 J db Z db 0 Z > - > H k1z l 2z m1z 2z Hinit ( t) V Motivation: Try to leverage benefits of spin as qubit encoding (low effective kt near E-min-gaps) k,l range is defined by magnitude of J for each DQD 2-qubit coupling is similar approach as charge qubit Challenge: Possible problem with meta-stability (bigger problem for AMO approaches?) S/T- also possible Weak initialization fields for both? This sets max E of parameters (speed/size of computation limit?) 28

28 Outline Motivation for research in adiabatic QC and QA Single electron spin qubit and adiabatic operation Semiconductor qubit approaches to quantum annealing Summary 29

29 What makes a good quantum annealing qubit? List of metrics for QUBO example Physics of encoding Z, ZZ, X interactions & low measurement error (also independent control) T qubit loss Metric: Max. time of computation because no error correction for leakage in quantum annealing Large (E gap ) 2 / t computation-time Measures: computation time limit before excitation error due to Landau-Zener tunneling Excited state manifold of single qubit should also be well separated T 1 / (E gap ) 2 at E gap ~O(kT) Measures: probability of thermal excitation error relative to computation time limit Notionally, fast adiabatic passage relative to thermal excitation time (even if kt > gap)? 30

What makes a good quantum annealing qubit? List of metrics for QUBO example Physics of encoding Z, ZZ, X interactions & low measurement error (also independent control) T qubit loss Metric: Max.

30 What makes a good quantum annealing qubit? List of metrics for QUBO example Physics of encoding Z, ZZ, X interactions & low measurement error (also independent control) T qubit loss Metric: Max. time of computation because no error correction for leakage in quantum annealing Large (E gap ) 2 / t computation-time Measures: computation time limit before excitation error due to Landau-Zener tunneling Excited state manifold of single qubit should also be well separated T 1 / (E gap ) 2 at E gap ~O(kT) Measures: probability of thermal excitation error relative to computation time limit Notionally, fast adiabatic passage relative to thermal excitation time (even if kt > gap)? Start with Si charge qubit as test platform 31

Charge qubit encoding for QUBO (example) e

31 Charge qubit encoding for QUBO (example) e Nordberg et al., PRB 2009 Charge qubit is based on two level approximation of DQD Encoding is left / right Gap is dependent on tunnel coupling between wells Detuning established with lateral electric field L> R> 32

32 Characterization of energy dependent relaxation Non-adiabatic (fast ramp)? Adiabatic (slow ramp) Developed measurement technique and analysis to extract relaxation time and dependence on energy Related to work done by Harbusch et al. PRB Hz 860 Hz Square pulse (f & r) t ramp t measure 8600 Hz 3010 Hz 34

33 Illustrative model Jacobson Super-Ohmic model leads to peaks growing closer together with frequency Ohmic spectral leads to different qualitative signature of peak merging Super-ohmic fits experiment better good fit with acoustic phonons arxiv:

34 QIST team & external connections QIST contributors at SNL Qubit fab: M. Busse, J. Dominguez, T. Pluym, B. Silva, G. Ten Eyck, J. Wendt, S. Wolfley Qubit control & measurement: N. Bishop, S. Carr, M. Curry, S. Eley, T. England, M. Lilly, T.-M. Lu, D. Luhman, K. Nguyen, M. Rudolph, P. Sharma, A. Shirkhorshidian, M. Singh, L. Tracy, M. Wanke Advanced fabrication (two qubit): E. Bielejec, E. Bussmann, E. Garratt, A. MacDonald, E. Langlois, B. McWatters, S. Miller, S. Misra, D. Perry, D. Scrymgeour, D. Serkland, G. Subramanian, E. Yitamben Device modeling: J. Gamble, T. Jacobson, R. Muller, E. Nielsen, I. Montano, W. Witzel, R. Young Joint research efforts: o Australian Centre for Quantum Computing and Communication Technology (D. Jamieson, A. Dzurak, A. Morello, M. Simmons, L. Hollenberg) o Princeton University (S. Lyon) o NIST (N. Zimmerman) o U. Maryland (S. Das Sarma) o National Research Council (A. Sachrajda) o U. Sherbrooke (M. Pioro-Ladriere) o Purdue University (G. Klimeck & R. Rahman) o U. New Mexico (I. Deutsch, P. Zarkesh-Ha) o U. Wisconsin (M. Eriksson) o University College London (J. Morton, S. Simmons) 36

35 Summary Silicon P donor qubit structure ~10 P Spin read-out & Rabi oscillations Adiabatic inversion DQD qubits for QA Local ESR P o o o Ramp time [us] Silicon electron spin qubit is platform for ESR experiments (limits of adiabatic control?) Fairly well understood noise Adiabatic control scheme improves spin inversion probability This is the same control as LUBO Background nuclear spins in natural silicon produce diffusion of resonant frequency Discussed different encodings of semiconductor qubits for quantum annealing DQD could work (charge or spin) Possible advantages in min-gap energy, fab precision (i.e., accurate Hamiltonian) & perhaps relaxation dynamics Two pulse scheme identified as general way to characterize spectral density of relaxation processes Si MOS charge qubit spontaneous emission consistent with acoustic phonons 37

Quantum Information Processing with Semiconductor Quantum Dots

Quantum Information Processing with Semiconductor Quantum Dots slides courtesy of Lieven Vandersypen, TU Delft Can we access the quantum world at the level of single-particles? in a solid state environment?