Distributed quantum computing with solid state systems

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1 Workshop on Quantum Information Processing and Nanoscale Systems NSF/EMT, September 10-11, 2007 Distributed quantum computing with solid state systems Lu J. Sham University of California San Diego Supported by ARO/NSA-LPS, DARPA/AFOSR, NSF We see further because we stand on the shoulders of giants - Bernard of Chartres 12c A quantum network as a paradigm for the interaction between microscopic and macroscopic systems mediated by mesoscopic ones. It leads to a question whether there is not a fertile regime for exploration between the classical and the quantum. L J Sham 9/10/07 1

2 Classical and quantum technologies Classical (ITR 2006) Quantum (atom-optics) Classical algorithms Quantum algorithms 15 nm (projected 2010 channel length) 1 THz (projected NMOS switch speed) 1 ps (capacitive delay) 10 4 nm 2 (DRAM area) 1 terabit/in 2 =2 petabit/m 2 (magnetic memory) nm 0.1 GHz ~1 µm 2 (opt lattice cell) 100 petabit/m 2 (1 n-spin/ lattice const) The end is nigh Wasteland? A bridge too far L J Sham 9/10/07 2

3 What is in the middle? Classical systems Classical algorithms 15 nm (projected 2010 channel length) 1 THz (projected NMOS switch speed) 1 ps (capacitive delay) 10 4 nm 2 (DRAM area) 1 terabit/in 2 =2 petabit/m 2 (magnetic memory) Meso/Nano systems Median algorithms Quantum w/ lots of noise? Mixed-state entanglement? nm GHz (operation speed) 10 nm 2-1 µm 2 (q-dots, JJ) 1-10 petabit/m 2 (nanomagnets) Quantum (atomoptics) Quantum algorithms nm 0.1 GHz (operation speed) ~1 µm 2 (opt lattice cell) 100 petabit/m 2 (1 n-spin/ lattice const) L J Sham 9/10/07 3 Opportunity knocks?

4 Scaling - by quantum network Motivation: An obstacle to scaling is the time of & coherence preservation of qubit exchange to distance parts. Copsey, Oskin, Impens, Metodiev, Cross, Chong, Chuang, & Kubiatowicz, IEEE Journal of Selected Topics in Quantum Electronics, 9, 1552 (2003). Distributed computation at each node connected by flying qubits channel is the key idea. Atoms-Cavity Quantum Electrodynamics/photons Cirac, Zoller, Kimble & Mabuchi, PRL 78, 3221 (1997). Control - deterministic process may be helpful Adiabatic: Fleischhaeur, Yelin & Lukin (2000), Duan, Kuzmich & Kimble (2003) Non-adiabatic: Yao, Liu & Sham (2005) Reason for cavity and wave guide: intermediary between micro (spin) and macro (laser pulses) L J Sham 9/10/07 4

A solid-state network: cavity-dot-wave guide Cavity containing a cluster of dots Z Spin-photon state swap B X Y + vac α C (4) (3) cpl Τ trion (2) Y (1) spin states Deterministic process driven by Y

5 A solid-state network: cavity-dot-wave guide Cavity containing a cluster of dots Z Spin-photon state swap B X Y + vac α C (4) (3) cpl Τ trion (2) Y (1) spin states Deterministic process driven by Y pulse (2) 1. Pulse moves Τ to resonance with C 2. Y pulse (macro) transforms + to Τ 3. Τ evolves to C generating a photon 4. Photon (micro) moves along wave guide + Cf. Microwave control in SC qubit (Yale) Yao, Liu, Sham, PRL 95, (2005) L J Sham 9/10/07 5

6 Consequences of spin-photon swap A stationary qubit & a flying qubit exchanging info. Initialization Reduce an unpolarized state to a spin state,, say. Basic process: Wave guide as conduit to entropy dump Entanglement: spin and photon QND - The spin state unchanged after photon emission. Hence, can be cycled many times to collect photons. For imperfect detector, analyze results by POVM and Baysian Th Liu, Yao, Sham, PRB 72, (R) (2005) + vac α [β β ] vac [β + α + β vac ] + vac [ + vac + α ]/ 2 trion cpl spin states L J Sham 9/10/07 6 (1) X Τ+ (3) + + C (2) (4)

7 Solid state quantum computing network Cavity containing a cluster of dots Laser pulse control AC Stark shift Sending No actual gap Photon packet Send & Receive: entangle two spins via a photon Basis for distributed computation to scale up a Q computer Receiving Q & A: What could be gained by controlling an ensemble of dots in each node? Lessen requirements on optical control, timing, readout, noise, Gain not as much as the quantum algorithm but more than classical. An evolutionary step towards quantum technology Waiting for Godot L J Sham 9/10/07 7

G. Tischler, M. E. Ware Optical spectrum provides excellent measure of charge state 1256-2.2-2.0-1.8-1.6-1.4-1.2-1.0-0.

8 A real system: electron spin in a quantum dot MBE-grown InAs/GaAs Dots AlGaAs GaAs QDs n + -GaAs AlGaAs InAs GaAs GaAs Quantum Dot: height ~ 2-4 nm width ~ nm Crosssectional STM image NRL group: D. Gammon, A. S. Bracker, M. F. Doty, M. Scheibner, E. A. Stinaff, J. G. Tischler, M. E. Ware Optical spectrum provides excellent measure of charge state VB L J Sham 9/10/07 8 PL Energy (mev) CB X + XX + X + Bias (V) X - X XX XX - X 2- X 0 X -

0 4 Transparent to the laser beam due to the optical pumping induced depletion of the spin ground states H1 & H2 degenerate

9 Expt Fast spin initialization in a singly charged quantum dot Magnetic Field 0.88T Temperature 5K Spin temp 5K => 0.06K in 4 ns VM absorption map as a function of the applied bias 0.12 I V1 H1 H2 V2 V1 H1 H2 H1 H2 V2 DC(V) 0.08 II Gt>>Gs B x Transparent to the laser beam due to the optical pumping induced depletion of the spin ground states H1 & H2 degenerate Laser Energy (mev) Xu, Wu, Sun, Huang, Cheng, Steel, Bracker, Gammon, and Emary, Sham, PRL in press L J Sham 9/10/07 9

10 Cavity and wave guide in photonic lattice Photonic double-heterostructure Q = 6 x 10 5 c = 250 nm Bong-Shik Song, Susumu Noda, Takashi Asano, Yoshihiro Akahane, Nature Materials 05 L J Sham 9/10/07 10

11 Evidence for Strong Coupling CQED Yoshie, Schere, Hendrickson, Khitrova, L J Sham 9/10/07 Gibbs,Ruppe, Ell, Shchekin. Deppe, Nature 11 04

12 Decoherence of Spin in a Bath Prepare state Initial state Quantum system Spin + Bath β + + α (β + + α ) J Time evolution Query on spin Entanglement Reduced density matrix β + J + + α J Ensemble average over bath state J population decay from ρ ++ to ρ : decoherence: coherence ρ + decay longitude relaxation time T 1 transverse relaxation time T 2 Zurek, Physics Today (1991), revised in Los Alamos Science (1992). L J Sham 9/10/07 12

Existence of a Maxwell Angel Coherence: J + J Trajectories of bath states: blue lines J + red lines J Electron spin in a dot - meso bath of nuclear spins e B Spin echo recovery of coherence Angel

13 Existence of a Maxwell Angel Coherence: J + J Trajectories of bath states: blue lines J + red lines J Electron spin in a dot - meso bath of nuclear spins e B Spin echo recovery of coherence Angel flips e spin at τ At ( 2)τ dis-entanglement not orginal state echo at 2τ Meso bath large enough for decoherence but small enough for reversal Pure coherence recovery L J Sham 9/10/07 13 Liu, Yao, Sham, PRL 98, ; New J Phys. 9, 226 (2007)

14 Give it a rest? What to do with scalability? Quantum Fourier Transform: from Wannier to Bloch state Transformation matrix j=0 1 N-2 N-1 Classical factoring with Bloch waves - Mehring et al. PRL 07, Zubairy Sci. 07 λ=0 Quantum: Shor Coppersmith n-1 n sites of TLSs N = 2 n Choose m such that n > m >> log 2 n Fowler & Hollenberg: Fault tolerant factorization of numbers up to ~ 4 m binary L J Sham 9/10/07 14 k n-1 n-m n-m-1 Phases small Sum bounded An example of the Median Way Sum n-m-1 n-m Phase = multi 2p (FFT) n-1 λ

15 With apology to Confucius The median way: less gain, less pain Meso-Nano systems Easier interface to classical systems (measurements and control) Environmental isolation and coherence recovery in meso baths "Not-quite quantum" algorithms? (instead of semiclassical) Quantum rachet or noisy quantum random walk (David Meyer, Fluctuations and Noise in Photonics and Quantum Optics, SPIE 5111, 344 (2003). Many-particle systems and ensembles Sub-diffraction limited lithography by N-photon entangled states (Boto, Kok, Abrams, Braunstein, Williams, Dowling, PRL 2000) Collective state and remote entanglement (Lukin, Fleischhauer, Cote, Duan, Jaksch, Cirac, Zoller, PRL 2001) CTRL of meso bath (Taylor, Imamoglu, Lukin, PRL 2003) Ensemble Quan. Comp. (Brion, Mølmer, Saffman, arxiv: ) There is plenty of room in the middle. With apology to Feynman. L J Sham 9/10/07 15

Lecture2: Quantum Decoherence and Maxwell Angels L. J. Sham, University of California San Diego

Michigan Quantum Summer School Ann Arbor, June 16-27, 2008. Lecture2: Quantum Decoherence and Maxwell Angels L. J. Sham, University of California San Diego 1. Motivation: Quantum superiority in superposition