Controlling Spin Qubits in Quantum Dots C. M. Marcus Harvard University 1
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
The modern transistor 3
Quanta 4
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
Quantum Entanglement: Spooky Action at a Distance helium S 6
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
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 2006 8
making controllable qubits ion traps Josephson devices Electron Spins in Dots 9
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 93106-4030 2 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 10598 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. S1050-2947 98 04501-6 10
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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
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
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 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) 1.4 1.2 1.0 180 200 220 Magnetic Field (mt)!v QPC (nv) 30 20 10 0 Magnet 15
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 " " $, $! ε '(+* " ɛ store test store ɛ store sense store τ dj dɛ 0 dj dɛ πd eτ dj dɛ 0 16
(a) Inject/eject electron Spin shuttle gates Qubit (in transit) Classical control circuits Static gate Qubit A SET/QPC couple MW gate MW gate 2-qubit couple MW gate Static gate Static gate MW gate MW gate unit A SET/QPC couple Qubit B MW gate Static gate la t a t la t Control circuit oding unit B (b) Classical control circuity cu l n ncilla Data bloc a ock Encoding unit A Ancilla block Data block Ancilla block Control circuit Encoding unit B (c) 17
Electrostatic Two-Qubit Gate 18
Single-shot S-T detection ~ scope (a) (b) V T SINGLET TRIPLET (c) ΔBZ S T0 19
nuclear state preparation PRL 100, 067601 (2008) P H Y S I C A L R E V I E W L E T T E R S week ending 15 FEBRUARY 2008 a) T Dynamic Nuclear Polarization with Single Electron Spins J. R. Petta, 1,2 J. M. Taylor, 1,3 A. C. Johnson, 1 A. Yacoby, 1 M. D. Lukin, 1 C. M. Marcus, 1 M. P. Hanson, 4 and A. C. Gossard 4 1 Department of Physics, Harvard University, 17 Oxford St., Cambridge, Massachusetts 02138, USA 2 Department of Physics, Princeton University, Princeton, New Jersey 08544, USA 3 Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 4 Materials Department, University of California, Santa Barbara, California 93106, USA (Received 6 September 2007; published 11 February 2008) 1 "m b) (0,2)S S T - T 0 T + b) Prepare Singlet (0,2)S T - T 0 T+ c) -470 (1,1) V L (mv)!$% L R g S S (1,2) P', M -474 (0,2) (0,1) P V R (mv) -345-341 0gS (10-3 e2/h) 60 40 20 Energy d) B 0 (mt) S 100 50 0-50 -100-1.0! # E Z =g*" B B tot (0,2)S 0! 1.0 0.8 0.6! 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
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. www.sciencemag.org SCIENCE VOL 321 8 AUGUST 2008 21
Nuclear Zamboni 22
some mostly-zero-nuclear-spin materials 23
Si/Ge Nanowire with Integrated Charge Sensor 20-2.95 0 gdd (10-3 e2/h) 40-2.94 a -2.94 15 b 0-10 -2.95 dgs/dvlp (a.u.) VLP (V) -2.96-2.96-2.89-2.88-2.87-2.86-2.85-2.84 VRP (V) 0 0.004 e2/h 0 0.05 e2/h 0 0.12 e2/h Si Ge VLP (V) -2.86-2.87-2.88-2.89-3.04-3.03-3.02-3.01-3.04-3.03-3.02-3.01-3.04-3.03-3.02-3.01 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.) -2 2-20 dgs / dvlp (a.u.) (M+1, N+1) -2873 a -2876 (M+1,N) -3038-3035 VRP (mv) 0.5 20 Temperature 1.0 K 0.5 K 0.15 K (fit) -2.90-2.92 VLP (V) 0.0 1.0 (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) -2.85-2.84 VRP (V) -2.83-1.0-0.5 0.0 ε (mv) 0.5 1.0 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 0.5 0 1000 2000 3000 4000 or 5000 6000 coupling to nuclei: resource headache? Measurement Cycle 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 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