400 nm Solid State Qubits (1) Daniel Esteve GROUP. SPEC, CEA-Saclay

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1 400 nm Solid State Qubits (1) S D Daniel Esteve QUAN UM ELECT RONICS GROUP SPEC, CEA-Saclay

2 From the Copenhagen school (1937) Max Planck front row, L to R : Bohr, Heisenberg, Pauli,Stern, Meitner, Ladenburg, Jacobsen

3 To quantum machines for computing Alan Turing A universal (Turing) machine can implement any algorithm John von Neumann sequential computing thy of complexity Richard Feynman quantum ressources!! David Deutsch Richard Jozsa the breakthrough: algorithmic complexity depends on hardware!

4 The art of quantum computing the illusion of quantum parallelism I X > + I X > + I X> +... U U I X > + U I X > + U I X> +... restored by distillation I X > I X > I X > I X > I X > I SOL > Factorisation of N : O[ (Log N) 3 ] Peter Shor Search through an unstructured data base size N : O[ N 1/2 ] Lov Grover

5 Schematic blueprint of a quantum processor 2 level systems: qubits 2 qubit gates: Controlled interactions Readout ? 1 U 1 U 1 Single qubit gates

6 DiVincenzo criteria Robust scalable qubits with long coherence times Universal set of unitary gates (1 & 2 qubits) U efficient reset 1 0 U 1 high fidelity Readout TE = α 0 + β 1 projective measurement 0 1 & readout: 0 with prob. or & readout: 1 with prob. 2 α 2 β Note and discuss: QND not mandatory for QC

Implementations: micro versus Macro Quantum

qubits Innsbrück (Innsbruck,NIST) Atoms in

7 Implementations: micro versus Macro Quantum optics Trapped ions Liquid NMR solid state qubits Innsbrück (Innsbruck,NIST) Atoms in cavity ( LKB) semiconductor circuits superconducting circuits quantum!! scalability? atom/ion/molecule chips? (Oxford, Stanford, IBM,MIT ) limited scalability and slow solid state NMR? scalable, quantum? decoherence free circuits?

8 Hardware: from abacus to quantum processor? electronic circuits quantum circuits?? ENIAC (Eckert & Mauchlie) quantum processors Solid state quantum bit circuits?

SOLID STATE QUANTUM BIT CIRCUITS Two strategies

global quantum states of superconducting Josephson

impurities in Si Chalmers NEC Quantronics U.

Schoelkopf et al, Yale 6/ 65 B1) Charge: NTT B2)

states: flying qubits QHE edge states: LPA (ENS

9 SOLID STATE QUANTUM BIT CIRCUITS Two strategies single particle states in semiconductor structures global quantum states of superconducting Josephson circuits (A) Kane s proposal : nuclear spins of P impurities in Si Chalmers NEC Quantronics U. Of New South Wales (B) Electrons in quantum dots Schoelkopf et al, Yale 6/ 65 B1) Charge: NTT B2) Spin: TU Delft, Harvard, 1,67 (C) Propagating states: flying qubits QHE edge states: LPA (ENS Paris) TU Delft Z e / e From charge states to phase states this lecture next lectures

10 (A) Kane s proposal : a silicon-based nuclear spin quantum computer B.E. Kane : (1998) nuclar spins of donors in Si : P, Te, NMR qubit manipulation using gate controlled resonance hyperfine coupling through electrons charge readout

11 hyperfine interaction (simplified) + = $ σ σ + $ σ σ + -σ σ 1 Q. 1H 2 Q. 2H 1 H. 2H 1 2 Overlap of wavefunctions magnetic interaction between s electron and nucleus Contact interaction $ = (8 / 3) πµ J µ Ψ(0) % Exchange interaction Single qubit gate: NMR with small ac field 2 qubit gates: Indirect coupling between nuclear spins SWAP GATE 75 khz for 4 - / K = 30*+] at B=2T

passage On l-r transition Charge transfer to probe well probe

12 Charge readout of nuclear spins (II) 3 donors and 2 electrons SET Charge readout l r probe Strong coupling Adiabatic fast passage On l-r transition Charge transfer to probe well probe charge with a Single Electron Transistor not demonstrated yet

13 SOLID STATE QUANTUM BIT CIRCUITS single particle states in semiconductor structures (A) Kane s proposal : nuclear spins of P impurities in Si (B) electrons in quantum dots n-algaas AlGaAs channel GaAs depletion 6 / 6 5 B1) Charge B2) Spin (C) Propagating states: flying qubits

14 B1) First demonstration of coherent oscillations in a double dot Coherent charge oscillations in a double dot (NTT, Hayashi HWDO. 2003) R> L> + R> L> L> R> 7 2 (charge qubit) ~ 1 ns But charge too much coupled to the environment! spin expected better

15 B2) Spin qubits % Z 6 / 6 5 Initial ideas: Loss & DiVincenzo (1998) (= JPB% 1-qubit control: magnetic (ESR) electric (modulate effective g-factor) 2-qubit coupling: exchange interaction between 2 dots 5HDGRXWWKURXJKFKDUJH -W Expts: TU Delft, Harvard

16 Single electron qubit : Zeeman splitting in an artificial Hydrogen atom TU Delft Team L.Kovenhouven L. Vandersypen DRAIN, DOT T SOURCE energy ES GS '( = '( 25% '( = M P R TU Delft % = 0 % > 0 % // magnetic field SDUDOOHOto 2DEG Single-shot readout achieved qubit-qubit interaction: exchange in double dot Lectures by Lieven Vandersypen

17 b) 2e spin qubit in a double dot (NEW) Harvard U. C. Marcus team, Nature, june 2005, & Petta et al., in prep. GD Charge sensor GSL Two electron spin qubit 0 GSR Harvard charge readout (1,1) 6 (1,1) 7 P = with QPC # e in dot

18 Bloch sphere in (1,1) S - T0 subspace

19 Measuring Spin Dephasing (T2) (0,2)S (1,1)S (1,1)T0 2t (1,1)S (0,2)S (electrostatic energy difference) Move from (0,2)S to (1,1) s & let evolve

20 Measuring Spin Dephasing (T2) (0,2)S (1,1)S (1,1)T0 2t (1,1)S (0,2)S dephasing causes failure to return to (0,2) spin T2 ~ 10 ns

21 Short coherence time : 10 ns due to nuclei B Nuclear B Total B Zeeman

22 But coherence restored by spin echo model experiment ε PRELIMINARY ε 0 40 ns tflip 0 40 ns tflip pattern still observed at long times: coherence time TE =1.2 Ps

23 SOLID STATE QUANTUM BIT CIRCUITS single particle states in semiconductor structures (A) Kane s proposal : nuclear spins of P impurities in Si Gates beam splitter: (B) Electrons in quantum dots (C) Propagating states: flying qubits electron waveguides Coulomb coupler rail 1 a H From R. Ionicioiu, P. Zanardi, & F. Rossi, PRA rail 1 b H

24 Flying qubits : propagating electrons in QHE edge states the e-qbit project (LPA, ENS Paris) Propagating electrons in QHE edge states O ϕ > 120 µ m C. Glattli, B. Plaçais, JM Berroir, J. Gabelli, G. Feve LPA -ENS Paris, (2005) encoding : e 0 quantum rail 0 quantum rail quantum rail 1 quantum rail e

25 controlled injection of single electrons capacitor plate (&J) ( & ( & 2 H ( & = 2& quantum Dot QPC e 2D electrons Vg(t), ( W) GW = H Vg(t) & J 9 J H & J electronic wavepacket length of injected electrons: O :. 3. G 1 ' 4. GRW π G is the dot diameter for a 0.5 micron Q.Dot: O.. 15 µ m : 3 ( ) τ = = / ' WLPH τ = 500 ps for =1 K and transmission D =0.1 Readout: detection of passing e with cold amp.

26 qubit gates - constant phase shift 0 quantum rail - the controlled phase shifter : 1 quantum rail 0 quantum rail qubit (a) 1 quantum rail static gate used to providephase shift - Hadamard gate qubit (b) e Z 1 quantum rail / e 0 quantum rail QPC ( D=1/2 ) 0 quantum rail 0 quantum rail 1 quantum rail 1 quantum rail Φ H K 2 % HQ H /RJ (// Z) π 2 π 2 1

27 VLQJOH particle qubits in semiconducting nanostructures : main advantage : compatibility with semiconductor circuits fab. techniques achieved results: P in Si : e in dots : not yet demonstrated charge qubits: Rabi oscillations in coupled dots spin qubits: coupling demonstrated, readout in single electron spin qubit Rabi oscillations demonstrated in 2e spin qubit with short T2 & long Techo (limited by nuclear spins), Flying qubits: simple gates, but timing, readout & scalability difficult Thanks to L. Vandersypen, C. Marcus, C. Glattli

Semiconductors: Applications in spintronics and quantum computation. Tatiana G. Rappoport Advanced Summer School Cinvestav 2005

Semiconductors: Applications in spintronics and quantum computation Advanced Summer School 1 I. Background II. Spintronics Spin generation (magnetic semiconductors) Spin detection III. Spintronics - electron