Controlling Spin Qubits in Quantum Dots. C. M. Marcus Harvard University

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1 Controlling Spin Qubits in Quantum Dots C. M. Marcus Harvard University 1

2 Controlling Spin Qubits in Quantum Dots C. M. Marcus Harvard University GaAs Experiments: David Reilly (Univ. Sydney) Edward Laird Christian Barthel Jason Petta (Princeton) Amir Yacoby Nanotubes: Hugh Churchill Ferdinand Kuemmeth Jennifer Harlow (Boulder) Andrew Bestwick (Stanford) Michael Biercuk (NIST) Nadya Mason (UIUC) Theory: Jacob Taylor (MIT) Mikhail Lukin Michael Stopa Material: Art Gossard (UCSB) Loren Pfeiffer (Alcatel-Lucent) Financial Support: DoD IARPA/ARO NSF 2

3 The modern transistor 3

4 Quanta 4

5 Mesoscopic Electronics and Quantum Interference OFF ON A transistor is a switch controlled by a voltage. If the transistor can be in more than one state at a time, then it can control another switch that can be in more than one state at a time, etc. 5

6 Quantum Entanglement: Spooky Action at a Distance helium S 6

7 A universal quantum computer A universal quantum computer can be made from 2-bit XOR s and 1-bit U s (from Bennett and DiVincenzo, Nature) 7

8 Comparing quantum and classical computation time to factor a product of two primes QC at 1 Hz QC at 1 khz QC at 1 MHz QC at 1 GHz bits van Meter et al

9 making controllable qubits ion traps Josephson devices Electron Spins in Dots 9

10 PHYSICAL REVIEW A VOLUME 57, NUMBER 1 JANUARY 1998 Quantum computation with quantum dots Daniel Loss 1,2, * and David P. DiVincenzo 1,3, 1 Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California Department of Physics and Astronomy, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland 3 IBM Research Division, T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York Received 9 January 1997; revised manuscript received 22 July 1997 We propose an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier between neighboring dots. Several measures of the gate quality are computed within a recently derived spin master equation incorporating decoherence caused by a prototypical magnetic environment. Dot-array experiments that would provide an initial demonstration of the desired nonequilibrium spin dynamics are proposed. S

11 11

12 S State Preparation (0,2)S T- S T+ T 0 Energy T- T0 S (1,1) is GS T+ (0,2)S Voltage-controlled tilt (0,2) is GS 12

13 S State Preparation (0,2)S T- S T+ T 0 Energy T- T0 S (1,1) is GS T+ (0,2)S Voltage-controlled tilt (0,2) is GS 13

14 The fully controlled singlet-triplet qubit Eigenstates of exchange ΔBZ S J T 0 Eigenstates of magnetic field difference 14

PRL 99, 246601 (2007) P H Y S I C A L R E V I E W L E T T E R S week ending 14 DECEMBER

Barthel, 1 E. I. Rashba, 1,2 C. M. Marcus, 1 M. P. Hanson, 3 and A. C. Gossard 3 1 a) c) Magnet 2!

15 PRL 99, (2007) P H Y S I C A L R E V I E W L E T T E R S week ending 14 DECEMBER 2007 Hyperfine-Mediated Gate-Driven Electron Spin Resonance E. A. Laird, 1 C. Barthel, 1 E. I. Rashba, 1,2 C. M. Marcus, 1 M. P. Hanson, 3 and A. C. Gossard 3 1 a) c) Magnet 2!m b) Frequency (GHz) Magnetic Field (mt)!v QPC (nv) Magnet 15

16 Electrostatic Two-Qubit Gate $ 710A>10 ε > 0 4 ) 8 BC" 40A>1>B0 $ " C% D ε < 0 S BCτ 4 ".:;<:0 ε < 0 5&'µ0+*, =0>?@10 ε > 0!!"" #" %&'()* " $#" $!"" 4 $, $! ε '(+* 5 5&'µ0+* " T0 " " $, $! ε '(+* " ɛ store test store ɛ store sense store τ dj dɛ 0 dj dɛ πd eτ dj dɛ 0 16

(a) Inject/eject electron Spin shuttle gates Qubit (in transit) Classical control circuits Static gate Qubit A SET/QPC couple MW gate MW gate 2-qubit couple MW gate Static gate Static gate MW gate MW

17 (a) Inject/eject electron Spin shuttle gates Qubit (in transit) Classical control circuits Static gate Qubit A SET/QPC couple MW gate MW gate 2-qubit couple MW gate Static gate Static gate MW gate MW gate unit A SET/QPC couple Qubit B MW gate Static gate la t a t la t Control circuit oding unit B (b) Classical control circuity cu l n ncilla Data bloc a ock Encoding unit A Ancilla block Data block Ancilla block Control circuit Encoding unit B (c) 17

18 Electrostatic Two-Qubit Gate 18

19 Single-shot S-T detection ~ scope (a) (b) V T SINGLET TRIPLET (c) ΔBZ S T0 19

nuclear state preparation PRL 100, 067601 (2008) P H Y S I C A L R E V I E W L E T T E R S week ending 15 FEBRUARY 2008 a) T Dynamic Nuclear Polarization with Single Electron Spins J. R. Petta, 1,2 J.

20 nuclear state preparation PRL 100, (2008) P H Y S I C A L R E V I E W L E T T E R S week ending 15 FEBRUARY 2008 a) T Dynamic Nuclear Polarization with Single Electron Spins J. R. Petta, 1,2 J. M. Taylor, 1,3 A. C. Johnson, 1 A. Yacoby, 1 M. D. Lukin, 1 C. M. Marcus, 1 M. P. Hanson, 4 and A. C. Gossard 4 1 Department of Physics, Harvard University, 17 Oxford St., Cambridge, Massachusetts 02138, USA 2 Department of Physics, Princeton University, Princeton, New Jersey 08544, USA 3 Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 4 Materials Department, University of California, Santa Barbara, California 93106, USA (Received 6 September 2007; published 11 February 2008) 1 "m b) (0,2)S S T - T 0 T + b) Prepare Singlet (0,2)S T - T 0 T+ c) -470 (1,1) V L (mv)!$% L R g S S (1,2) P', M -474 (0,2) (0,1) P V R (mv) gS (10-3 e2/h) Energy d) B 0 (mt) S ! # E Z =g*" B B tot (0,2)S 0! ! S (mv) 0 P S 0 S Energy Energy (0,2)S " "* 0 Rapid Adiabatic Passage (0,2)S T - T 0 T+ " S (0,2)S " 0 Slow Adiabatic Passage (0,2)S T - T 0 T+ t=0 t=! S Bex ~ ΔBnu Energy 0 " F (0,2)S " 20

For few-electron quantum dots made from gallium arsenide (GaAs), fluctuating nuclear spins in the host lattice are the dominant source of spin decoherence.

21 nuclear state preparation Suppressing Spin Qubit Dephasing by Nuclear State Preparation D. J. Reilly, 1 J. M. Taylor, 2 J. R. Petta, 3 C. M. Marcus, 1 * M. P. Hanson, 4 A. C. Gossard 4 Coherent spin states in semiconductor quantum dots offer promise as electrically controllable quantum bits (qubits) with scalable fabrication. For few-electron quantum dots made from gallium arsenide (GaAs), fluctuating nuclear spins in the host lattice are the dominant source of spin decoherence. We report a method of preparing the nuclear spin environment that suppresses the relevant component of nuclear spin fluctuations below its equilibrium value by a factor of ~70, extending the inhomogeneous dephasing time for the two-electron spin state beyond 1 microsecond. The nuclear state can be readily prepared by electrical gate manipulation and persists for more than 10 seconds. SCIENCE VOL AUGUST

22 Nuclear Zamboni 22

23 some mostly-zero-nuclear-spin materials 23

24 Si/Ge Nanowire with Integrated Charge Sensor gdd (10-3 e2/h) a b dgs/dvlp (a.u.) VLP (V) VRP (V) e2/h e2/h e2/h Si Ge VLP (V) VRP (V) Yongjie Hu, Hugh O. H. Churchill, David J. Reilly, Jie Xiang, Charles M. Lieber, Charles M. Marcus, Nature Nanotechnology 2, 622 (2007). 24

Si/Ge Nanowire with Integrated Charge Sensor 25 10 1.0 gs (10-3 e2/h) (M,N) (M,N+1) VLP (mv) m -M ε dgs / dvlp (a.u.

0 (M,N+1) 2t -2.92 m -M -2.94 (M+1,N) (M+1,N) b (M,N+1) 0.5-2.94-2.96 a -2.88 VRP (V) t (µev) -863 58-855 31-851 -850 18 ~0 0.0 b -2.89 V3 (mv) -2.

25 Si/Ge Nanowire with Integrated Charge Sensor gs (10-3 e2/h) (M,N) (M,N+1) VLP (mv) m -M ε dgs / dvlp (a.u.) dgs / dvlp (a.u.) (M+1, N+1) a (M+1,N) VRP (mv) Temperature 1.0 K 0.5 K 0.15 K (fit) VLP (V) (M,N+1) 2t m -M (M+1,N) (M+1,N) b (M,N+1) a VRP (V) t (µev) ~0 0.0 b V3 (mv) VRP (V) ε (mv) Yongjie Hu, Hugh O. H. Churchill, David J. Reilly, Jie Xiang, Charles M. Lieber, Charles M. Marcus, Nature Nanotechnology 2, 622 (2007). 25

Summary TRIPLET -0.4 ens_b_singleshot_766-0.8 2.5 2.0-1.0 SINGLET Scope Voltage (V) Triplet probability -0.6 1.5-1.2 1.0-1.4 0.

0 0 100 200 300 Separation time ts 400 500ns quantum bits on a chip Spin shuttle gates Inject/eject electron Static gate MW gate MW gate MW gate Static gate Static gate MW gate MW gate MW

26 Summary TRIPLET -0.4 ens_b_singleshot_ SINGLET Scope Voltage (V) Triplet probability or coupling to nuclei: resource headache? Measurement Cycle Separation time ts ns quantum bits on a chip Spin shuttle gates Inject/eject electron Static gate MW gate MW gate MW gate Static gate Static gate MW gate MW gate MW gate Static gate Ancilla unit Control circuit co u SE Data unit le up Qubit B co Q PC PC Qubit A T/ Ancilla unit Q T/ pl e 2-qubit couple SE Classical control circuits Qubit (in transit) nuclear spin free materials for quantum spin how to build a quantum processor Encoding unit A unit B with error correction Ancilla block 26 cuit cuit Ancilla

Lecture 2: Double quantum dots

Lecture 2: Double quantum dots Basics Pauli blockade Spin initialization and readout in double dots Spin relaxation in double quantum dots Quick Review Quantum dot Single spin qubit 1 Qubit states: 450