All-Silicon Quantum Computer Phys. Rev. Lett. Vol. 89, (2002) Kohei M. Itoh. Dept. Applied Physics, Keio University

Size: px

Start display at page:

Download "All-Silicon Quantum Computer Phys. Rev. Lett. Vol. 89, (2002) Kohei M. Itoh. Dept. Applied Physics, Keio University"

Easter Morris
5 years ago
Views:

1 All-licon Quantum Computer Phys. Rev. Lett. Vol. 89, (2002) Kohei M. Itoh Dept. Applied Physics, Keio University January 20, 2003 University of New South Wales Contents 1. Introduction 2. Isotope Engineering of semiconductors 3. All-licon Quantum Computer 4. Experimental situations MBE growth of silicon isotopes Micro-magnet fabrication 5. Summary

2 Quantum computation with spins 1. Initialization 2. Operation 3. Read-out qubit #1 qubit #2 S N qubit #3 qubit #4 qubit #5 qubit #6 Rotation Controlled NOT Spin-polarized probe # of qubits # of operation Spin quantum bits Classical bit with spins 0 1 Quantum bit with spins B I1> 1 2 ( ) 0 nor 1 (error) I0> Quantum spin allows for equal probability of 0 and 1

3 Quantum parallelism multaneous processing of 2 n numbers Binary numbers Decimal numbers Candidates for qubits Hydrogenic model Electronic orbital N nucleus S S 1.Nuclear spin 2.Electronic spin N electron long decoherence time needed

4 Figures of merits 1.Scalable # of qubits (n) 2 n states 2.Large # of total operation Phase decoherence time T 2 Switching time t s qubit T 2 (sec) t s (sec) # of operation Electronic state Electronic spin Ion state Nuclear spin photon Neutral Atoms in Optical Lattices Solution NMR Trapped Ions Atomic Cavity QED Solid-State Systems All-licon Quantum Computer Optically Driven Electronic States in Quantum Dots Optically Driven Spin States in Quantum Dots Electronically Driven Electronic States in Quantum Dots Flux States in Superconductors Charge States in Superconductors Electrons Floating on Liquid Helium ngle-spin MRFM Impurity Spins in Semiconductors Electronically Driven Spin States in Quantum Dots Others: Nonlinear Optics, STM,...

5 Experimental situation * # gates and gate network Chuang Nature 98 Vandersypen APL 00 Vandersypen PRL 99 Vandersypen PRL 00 Vandersypen Nature 2001 factoring Delft 02 NEC Number of qubits 4. Measurement is facilitated by huge ensemble of independent copies 1. A small number of stable qubits provided by distinct spin 1/2 nuclei B 5. Decoherence times are long since nuclei interact only weakly with environment RF 3. Dipolar interactions controllable by RF 2. Perfect initialization is not possible. Instead, pseudopure states must be used N. A. Gershenfeld and I. Chuang, Science 275, 350 (1997) D. G. Cory, A. F. Fahmy, and T. F. Havel, Proc. Natl. Acad. Sci. USA 94, 1634 (1997)

B. E. Kane, Nature 393, 133 (1998) 1. Isolated impurity nuclei provide qubits 2. Low temperature electrons allow initialization 3. Electron-mediated interactions controlled by gates 4.

6 B. E. Kane, Nature 393, 133 (1998) 1. Isolated impurity nuclei provide qubits 2. Low temperature electrons allow initialization 3. Electron-mediated interactions controlled by gates 4. ngle-spin measurement via nuclear-electron coupling is proposed 5. Well-separated impurities have long decoherence times Solution NMR QC Solid-State Impurity QC N. A. Gershenfeld and I. Chuang, Science 275, 350 (1997) D. G. Cory, A. F. Fahmy, and T. F. Havel, Proc. Natl. Acad. Sci. USA 94, 1634 (1997) Advantages: Ensemble measurement Natural (chemical) fabrication Disadvantages: Challenging to scale to many qubits and/or gates Initialization difficult B. E. Kane, Nature 393, 133 (1998) R. Vrijen, et al., Phys. Rev. A 62, (2000) G.P. Berman, G. D. Doolen, P. C. Hammel, and V. I. Tsifrinovich, Phys. Rev. B 61, (2000). Advantages: Scalable! Can cool to low temperatures for initialization Disadvantages: Need single-spin measurement Challenging fabrication All licon QC uses advantages of both!

7 Semiconductor Isotope Engineering licon: Germanium:Ge licon-germanium: Ge Semiconductor Isotope Engineering (2) List of stable isotopes 92.2% 4.7% % 70 Ge 20.5% 72 Ge 27.4% 73 Ge 7.8% 74 Ge 36.5% 76 Ge 7.8% 1/2 (nuclear spin) 9/2 (nuclear spin) 69 Ga 60.1% 71 Ga 39.9% 75 As 100% 3/2 3/2 (nuclear spin) 3/2 Nuclear spin control through manipulation of stable isotopes

8 NMR Intensity (a.u.) Relaxation time of (Sasaki) NMR in natural silicon at T=300K 1000sec 3000sec 5000sec 7000sec T sec MHz 90 pulse 1.0μsec coadding 10 times T 2 6.5msec decoupling 0 1 khz Pulse delay time T 2 >> 100 msec nuclear spin quantum computer Qubit #1 ω 1 Qubit #2 ω 2 Qubit #3 ω 3 Qubit #4 ω 4 Copies Position ω n+1 - ω n ~20kHz large field gradient 1.5 Tesla/µm B

9 Elimination of background spins 31 P e - qubits: phosphorus donors in and Ge Kane: nuclear spin of 31 P Yablonovitch: electron spin Elimination of (s=1/2) and 73 Ge(s=9/2) in the background is important! Kane s nuclear spin quantum computer Ref. B.Kane,Nature 393,133(1998) Constant fileld (=2T) Insulator A-gate A-gate J-gate Energy of 31 P(I=1/2) 1> 0> ΔE=gβH Mono isotopic without with I=1/2 T=100mK RF magnetic field (~10-3 T) Qubit:nuclear spins of 31 P(I=1/2) Operation:A- and J-gates

10 Yablonovitch s ESR quantum computer Vrijen et al, Phys. Rev. A, (2000) Ge hetero structures (ESR trasistor) Band structures g-values Bohr radius and Ge without (I=1/2) and 73 Ge (I=9/2) Qubit:Spins of bound electrons of 31 P(I=1/2) Operation:A-gate nuclear spin quantum computer Qubit #1 ω 1 Qubit #2 ω 2 Qubit #3 ω 3 Qubit #4 ω 4 Copies Position ω n+1 - ω n ~20kHz large field gradient 1.5 Tesla/µm B

An ensemble of copies, orthogonal to the gradient direction, allow measurement by MRFM. Decoherence times are limited by pulse sequence design, crystal purity, and cantilever stability.

11 An all silicon quantum computer Qubits are spin-1/2 nuclei in a crystal. They are distinguished by a one-dimensional field gradient. Initialization is accomplished by cooling, optical pumping, boosting, and pseudo-pure state techniques. Qubit interactions (decoupling and recoupling) are accomplished with RF pulse sequences. An ensemble of copies, orthogonal to the gradient direction, allow measurement by MRFM. Decoherence times are limited by pulse sequence design, crystal purity, and cantilever stability. wires embedded in the matrix nuclear spins cantilever Dy magnet Phys. Rev. Lett. Vol. 89, (2002).[ Alternative configuration Bridge L= 400 µm W = 4 µm H = 10 µm s = 2.1 µm l = 300 µm t = 0.25 µm w = 4 µm db z /dz = 1.4 T/µm B 0 = 7 T (111) Active Region: 100µm x 0.2µm

12 Initialization Polarization = tanh(ħγb 0 /k B T s ) Boosting by Schulman-Vazirani scheme Polarization by optical pumping Fraction of cold qubits kept 1 O(T 1 ) O(n log n) Higher polarization Lower T s More logically labeled qubits 1 p o 1-H(p o ) t Long T 1 means nuclei may be cooled much lower than lattice temperature (Optical Pumping) Then, excess qubits may be sacrificed to cool a subset (Boosting) L. J. Schulman and U. V. Vazirani, Proc. 31st ACM Symp. on Theory of Computing, 322 (1999) D. E. Chang, L. M. K. Vandersypen, and M. Steffan, quant-ph/ (2001) Finally, logical labeling may be used to establish an effective pure state N. A. Gershenfeld and I. L. Chuang, Science 275, 350 (1997) L. M. K. Vandersypen, C.S. Yannoni, M. H. Sherwood, and I. L. Chuang, Phys. Rev. Lett. 83, 3085 (1999) Polarization by optical pumping Circularly Polarized Light Spin polarized current III-V Spin-Injected current polarizes chains of nuclei Pump The spin-polarized conduction electrons are cleared away after polarization, removing them as decoherence source Nuclear spin state Electron spin state Contact Hyperfine Interaction T 1e process G. Lampel, Phys. Rev. Lett. 20, 491 (1967) R. Tycko, Solid State Nuclear Magnetic Resonance 11, 1 (1998) Recombination Preferentially Populated State

13 Optical initialization of electron (and nuclear) spins 3.53~5.16 ev SHG Generator Parametric amplifier amplifier 1.77~2.58 ev 0.77~1.12 ev Parametric amplifier Solid laser 1.45~1.65 ev Ti:Al 2 O 3 laser PL intensity (arb. units) T=11.3 K p- ρ=0.5-7 Ohm.cm EH-TO (1.1 ev) Ar + (514.5 nm) P ex =25 mw E g =1.17 ev 0 Various excitation of electrons in Energy (ev) PL Operation (decoupling) WHH, etc. Broadband decoupling sequence for homonuclear decoupling Narrowband selective π-pulses for heteronuclear decoupling ω 1 ω 2 ω 3 RF ω 1 ω 2 ω 3 -X Y -Y X -X Y -Y X -X Y -Y X -X Y -Y X -X Y -Y X -X Y -Y X -X Y -Y X -X Y -Y X

14 Operation (recoupling) D. W. Leung, I. Chuang, F. Yamaguchi and Y. Yamamoto, Phys. Rev. A, 61(4) /1 (1999) Qubits may be selectively recoupled Add single spin rotations to make controlled-not ω 1 ω 2 ω 3 RF ω 1 ω 2 ω 3 -X Y -Y X -X Y -Y X -X Y -Y X -X Y -Y X -X Y -Y X -X Y -Y X -X Y -Y X -X Y -Y X Read-out by the MRFM cantilever Qubit #1 ω 1 ω Read out of the qubit #2 Qubit #2 ω 2 ω 2 Qubit #3 ω 3 Qubit #4 ω 4 Resonance ω c (10-100kHz) of the cantilever ω c (10-100kHz) time

15 SNR and number of qubits Force resolution for a cantilever in the thermal limit: Fmin = B 0 4kk TB ω Q n 100 Number of qubits (n) for SNR = 1 vs. nuclear polarization 1 1+ P F ~ n 1 P Force generated from a single atomic plane: Magnetization for nuclear spins in plane: M z 1+ P = γhin 2 B F( t) = M z( r, t) z n z 1 P 2 n 10 1 F ~ n n 2 P 20% 40% 60% 80% 100% nuclear polarization (P) N = number of qubit copies n = number of qubits in QC Decoherence and th emaximum operation step Primary Decoherence Sources: DC spectral density of local fluctuating field Second Moment due to residual dipolar couplings Clock period t c =Ln 2 / ω set by pulse sequence. Number of logic gates T 2 /t c is limited Residual Dipolar Couplings Reversible in principle Present sequence: T 2 ~ 10 ms Cantilever Drift Thermal equilibrium: T 2 ~ 200 ms Feedback control T 2 ~ 1 hour Paramagnetic Impurites Assuming very dilute impurities, T 2 ~ (ω 0 T 1e ) -1/2 T 1 ~ 1 minute, but much shorter for nuclei near impurity LT 2 /t c (# of operation) T 0 2 =1000 s T 0 2 =10 s T 20 =100 ms T 0 2 =1 ms Number of qubits n n

wire fabrication Form regular step arrays on slightly miscut (111)7 7 surface (~ 1º from normal)

chains formed by Step Decoration from steps Angle of miscut controls chain spacing 40 70nm 2 340

, JAP 84, 255 (1998) Row-by-row growth The step-flow growth was observed as the appearance of

16 wire fabrication Form regular step arrays on slightly miscut (111)7 7 surface (~ 1º from normal) Steps are straight, with about 1 kink in sites. chains formed by Step Decoration from steps Angle of miscut controls chain spacing 40 70nm nm 2 J.-L. Lin, et al., JAP 84, 255 (1998) Row-by-row growth The step-flow growth was observed as the appearance of new adatoms at the edge Short rows are thermally diffused to form a longer row which is energetically stable < 11 2 > T sub 350 Growth rate BL/min T. Hasegawa, et al., Phys. Rev. B48, 1943 (1995). U(5)

17 MBE fabrication of wire copies Progress at Keio

18 Progress on Isotope Engineering at Keio 99.92% single crystal J. Mater. Res. 8, 1341 (1993) Jpn. J. Appl. Phys. 38, L1493 (1999) Isotopically controlled fabrication Natural abundance % 4.7% 3.1% 99.92% single crystal 96% single crystal 10mm 99.2% 30 single crystal

19 / 30 Isotope Superlattices Depth profile of and 30 of the [( ) 16 /( 30 ) 16 ] 50 superlattice layer 30 layer layer 30 layer layer Concentration [arb. unit] Depth [nm] Phonons of ( ) n /( 30 ) n SLs Phonons in SLs Ex) (. ) 4 /( 30 ) 4 Γ ω LO TO X Calculation of Phonon Frequency Planar-Bond Charge (PBC) Model P. Molinàs-Mata, A. J. Shields, and M. Cardona, Phys. Rev. B 47, 1866 (1993) 30 Bond charge LA TA 0 π/4a k [100] π/a Fig. phonon dispersion relation ( : bulk, : ( ) 4 /( 30 ) 4 ) r q f m-th unit cell

20 Raman spectroscopy Raman Spectrum of SL [( nat. ) 16 /( 30 ) 16 ] 50 Conditions Laser: nm Temp.: ~ 4 K Intensity (arb. unit) LO 3 ( nat. ) LO 1 ( 30 ) LO 1 ( nat. ) Phonon folded mode can be confirmed Wavenumber (cm -1 ) Fig. Raman spectrum of [( nat. ) 16 /( 30 ) 16 ] 50 superlattice Expected Raman Peaks Ex) (. ) 16 /( 30 ) 16 Oscillation (a. u.) cm cm -1 Oscillation of atoms cm -1 Number of Layers LO 1 ( nat. ) LO 3 ( nat. ) LO 5 ( nat. ) LO 7 ( nat. ) LO 9 ( nat. ) LO 1 ( 40 ) Phonon Freqency (cm -1 ) Expected Raman peaks of ( nat. ) n /( 30 ) n superlattices calculated by PBC model (n: even numbers)

21 Micro-magnet fabrication Ferro magnet (I=0) Qubit#1 ω 1 (I=1/2) シリコン基板 substrate 磁性体 Micro-magnet Qubit#2 ω 2 substrate Homogeneity and Strong gradient Magnetic field B Magnetic field simulation width Distance (μm) distance and gradient 2µm gradient (T/μm) Width 磁性体の幅 of magnet [μm] (μm) Width 磁性体の幅 of magnet [μm](μm)

substrate 2μm Optical pumping and NMR シリコン基板 Sputter growth growth and reactive

22 Field simulation and micro-fabrication NH NH3/CO/Xeリアクティブイオンエッチング 3 reactive etching of NiFe チタン Ti シリコン基板 SF SF6リアクティブイオンエッチング 6 reactive etching of シリコン基板 substrate 2μm Optical pumping and NMR シリコン基板 Sputter growth growth and reactive ion etching of NiFe NiFe 2µm Ti buffer 80A substrate After reactive ion etching 10µm

23 Next-step: / isotope superlattice Proof of concepts (I=0) (I=1/2) substrate Qubit #1 ω 1 Qubit #2 ω 2 B Magnetic field In-plane coupling of may severely limit the scaling Summary Semiconductor Isotope Engineering New quantum computation scheme exclusively with silicon Fabrication of the all silicon quantum computer at Keio

24 Collaborators Eisuke Abe (Keio University) Takeharu Sekiguchi (Keio Univeristy) Ryusuke Nebashi (Keio University) Yoshinori Matsumoto (Keio University) Hideo Ohno (Tohoku University) Yuzo Ohno (Tohoku University) Susumu Sasaki (Nigata University) Yoshhisa Yamamoto (Stanford University) Thaddeus Ladd (Stanford University) Jonathan Goldman (Stanford University)

Experimental Realization of Shor s Quantum Factoring Algorithm

Experimental Realization of Shor s Quantum Factoring Algorithm M. Steffen1,2,3, L.M.K. Vandersypen1,2, G. Breyta1, C.S. Yannoni1, M. Sherwood1, I.L.Chuang1,3 1 IBM Almaden Research Center, San Jose, CA