1/30 University of Toronto, 28 March 2005 Quantum Information Processing with Atoms and Light Daniel F. V. James Group T-4, Los Alamos National Lab University of Toronto, Canada Monday, 28 March 2005

2/30 University of Toronto, 28 March realizing quantum gates and detectors Research Interests - coherence-induced changes in spectra (and other things) - novel synthetic aperture imaging techniques - properties of polarized light and ellipsometry - characterizing quantum states and processes - physical boundaries of entanglement and entropy (MEMS states) - quantum dynamics of trapped ions (modes, heating, motion...) - quantum algorithms: teleportation, factoring... - scalable architectures - quantum simulations (chaos, phase transitions etc.) Classical optics and Coherence Theory Quantum Optics Trapped Ions and Quantum Information Processing Solid State quantum technologies - spin-based quantum solid-state quantum computing architectures - read-out techniques (optics, MRFM,cantilevers) and tomography

3/30 University of Toronto, 28 March 2005 Collaborators -LANL Postdocs John Grondalski Sergey Ponomarenko -Los Alamos Summer School David Etlinger, Rochester/Northwestern David Hume, Kentucky/Colorado Miho Ishibashi, Salisbury/Stanford Matt Krems, Missouri Rolla -Quantum Optics Experiments Paul Kwiat Andrew White Michael Di Rosa, Fio Omenetto -Ion Trap Experiments Rainer Blatt Ferdinand Schmidt-Kaler -Solid State Quantum Technology Marilyn Hawley Robert Clark -Classical and Quantum Optics Theory Emil Wolf Gerard Milburn Peter Milonni, Eddy Timmermans, Gennady Berman, Gerardo Ortiz, Juan-Pablo Paz, James Gubernatis

4/30 University of Toronto, 28 March 2005 Quantum Computers : Each register (“qubit”) can be in a superposition of two states  0  and  1  Quantum Computing: Basic Ideas Classical digital computers : Each register is either 0 or 1ProsCon BIG memory: n qubits  2 n “bits” of data MASSIVE Parallelism Readout: n-bits Difficult to make

5/30 University of Toronto, 28 March 2005 Quantum Memories State of one quantum data register (“qubit”): a  + b  1   c  1  + d  1  1  a, b  c and d etc. are the probability amplitudes. n qubits = 2 n pieces of information Quantum memories are BIG State of two qubits: a  + b  1  a  + b  1   c  1  + d  1  1  +e  1  + f  1  1   g  1  1  + h  1  1  1  State of three qubits:

6/30 University of Toronto, 28 March 2005 Quantum Parallelism Operations on one qubit effect ALL of the data in the quantum register. Quantum computers perform complex operations on very large registers very efficiently Example: bit flip on second qubit: a  + b  1   c  1  + d  1  1   b  + a  1   d  1  + c  1  1 

7/30 University of Toronto, 28 March 2005 You can do ANYTHING if you can do the following two things: Unitary operations on any individual qubit: A  + B  1   A  + B  1  '' U Two qubit gates such as the “Controlled Z gate” a  + b  1   c  1  + d  1  1   a  + b  1   c  1  - d  1  1  Z Quantum Logic Gates Notation:  1  0  etc.

8/30 University of Toronto, 28 March 2005 Measurement and Readout N qubits store 2 N bits of information and process them efficiently, BUT you can only read out N bits to get the final answer. Restricts types of algorithms that can be executed on a quantum computer: ‘global’ mathematical properties like periodicities. Projective measurement of each qubit: i.e.A  0  + B  1    0  (probability P 0 =|A| 2 ) ORA  0  + B  1    1  (probability P 1 =|B| 2 )

9/30 University of Toronto, 28 March 2005 Example: n = 77; x = 8;, ( GCD(x,n) =1 ), is periodic, period r. Either or is a factor of n. Shor’s Algorithm: what are the factors of the integer n ? From data, r = 10; Period Finding  Factoring Killer App: Factoring

10/30 University of Toronto, 28 March L operations replaced by 1 operation entangled state! Quantum Factoring Classical factoring: evaluate f n,x (a) for a large number (~ 2 L-1 ) of values of a until you can find r. Quantum parallelism: Quantum Fourier Transform and measurement gives r.

11/30 University of Toronto, 28 March 2005 Ion Traps Cannot trap ions electrostatically (Earnshaw’s Theorem) Do it dynamically (Paul trap) Effective harmonic well (in all three directions) oscillating saddle potential

12/30 University of Toronto, 28 March 2005 Phonon Modes Ions coupled by Coulomb force  ions’ oscillations have normal modes. D.F.V. James, Appl Phys B 66, (1998) Lowest mode: center-of-mass (CM): Next mode is “stretch” mode: Number of modes in each direction = number of ions.

13/30 University of Toronto, 28 March 2005 Harmonic potential J. I. Cirac and P. Zoller, Phys Rev Lett 74, 4091 (1995) Perform Rabi flips between and : local gates. Trapped Ion Quantum Computers Excite phonons of the vibration modes: quantum bus for multi-qubit gates. Efficient projective measurement

14/30 University of Toronto, 28 March 2005 Theory Historical Timeline of Trapped Ion QC Cirac & Zoller differential mode heating (James; King et al.) Boulder CNOT demonstrated (ion + phonon) cooling 2 ions 2 qubit entanglement 4 qubit entanglement Innsbruck Multi-ion addressing “Hot” Gates Poyatos,Cirac & Zoller Mølmer & Sørensen Schneider, James & Milburn “Cat” motional states Cirac-Zoller gate GHZ & W states teleportation Deutsch-Jozsa Algorithm geometric gate sympathetic cooling moving qubits ion heating !!! tomography error correction

15/30 University of Toronto, 28 March 2005 Co-Authors of “Deterministic Quantum Teleportation with Atoms” at Innsbruck, 4 May Nature 429, 734 (2004)

16/30 University of Toronto, 28 March 2005 What is Quantum Teleportation? film reference beam #2 reconstructed wavefront Quantum wavefunction Reconstruction: - the quantum state of a particle is transferred to another particle by means of a classical communication and a shared correlated resource Analogy with Holography: - optical wave front reconstruction reference beam #1 object film wavefront - quantum state film - classical information correlated reference beams - entangled pair Interference on film - Bell state measurement - “Quantum mechanics is a good preparation for optics” (Denis Gabor)

17/30 University of Toronto, 28 March 2005 Quantum Teleportation: Theory the maximally entangled ‘Bell State Basis’ is: three qubits: re-write state of first two qubits using this basis:

18/30 University of Toronto, 28 March 2005 Bell state analysis: measure which Bell state the first two qubits are in, projecting third qubit into one of four possible states: Single operation on output qubit recreates input state

19/30 University of Toronto, 28 March 2005 Original Proposal Charles H. Bennett, Giles Brassard, Claude Crepeau, Richard Jozsa, Asher Peres, and William Wootters, “Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels”, Phys. Rev. Lett. 70, (1993). Dr. Daniel F.V. James MS B283, PO Box 1663, Los Alamos NM Continuous Variables: photon number rather than polarization Kimble et al., Science 282, 706 (1998). Lam et al., Phys. Rev. A 67, (2003). -NMR: no entanglement, no projective measurement, no pure states… Nielsen et al., Nature 396, 52 (1998). Experiments (so far) -Photons: can make entangled pairs; only partial Bell state measurement Zeilinger et al., Nature 390, 575 (1997); Nature 430, 849 (2004) DeMartini et al., Phys. Rev. Lett. 80, (1998). Gisin et al., Nature 421, (2003).

20/30 University of Toronto, 28 March 2005 The Tricky Part: Bell State Detection Perform the following circuit: Z π /2 π /2 = “Hadamard Gate” (give or take a phase): Measurement of the output gives a Bell state detector

21/30 University of Toronto, 28 March 2005 Teleportation Circuit 1. prepare the Bell state 2. input state to be teleported 3. Controlled-Z gate: the ‘flux capacitor’ of quantum computers 4. measurement in the computational basis 5. reconstruction 6. confirm outcome

22/30 University of Toronto, 28 March 2005 The Ca + ion D.F.V. James, Appl Phys B 66, (1998)

23/30 University of Toronto, 28 March 2005 Laser Operations Carrier pulse on n-th ion carrier (center of mass mode) (stretch mode) … … … … Blue sideband pulse: blue sideband ˆRˆR [ ] R = exp â†â† (    ) n + ii â | ||| ei  + e –i  SS D D 2 nn ( )

24/30 University of Toronto, 28 March 2005 phonon How to do a Controlled-Z gate 1Transfer state of lower qubit to the phonon mode  S   n=0    D   n=1  ;  D   n=0    D   n=0  ; 1 2  S   n=0   –  S   n=0  ;  S   n=1   –  S   n=1  ;  D   n=0    D   n=0  ;  D   n=1   –  D   n=1  ; 2 Perform Controlled Z between phonon and top qubit 3 3 Reverse 1

25/30 University of Toronto, 28 March 2005 Trapped Ion-Phonon Controlled-Z gate pulse 1 pulse 2pulse 3pulse 4 BUT:

26/30 University of Toronto, 28 March 2005 State Readout what state is the atom in? cannot detect single photons over 95% detection efficiency M.A. Rowe et al. (Wineland group) Nature 409, (2001) - detection loophole D. F. V. James and P. G. Kwiat, Phys. Rev. Lett. 89, (2002) - photon detection

27/30 University of Toronto, 28 March 2005 Results: Fidelity of Teleportation measured for 300 trials 76% 74% 73% 75% later results with Fidelities over 80% for all states

28/30 University of Toronto, 28 March 2005 What’s Next ? 15 = 5 x 3 (we hope!) π /2 Z Z Z Z argument register (2 qubits) function register (2 or 3 qubits) period r=2

29/30 University of Toronto, 28 March 2005 Prospects for Trapped Ion QIP Next year or two Scalability of ion traps? Does the final technology have to be solid state? - experiments with ~ 5 qubits: - larger entangled states - primitive versions of factoring - moving ions around (Boulder, Michigan, Ulm etc.) - connected micro-traps (Innsbruck, Michigan) - other paradigms ? - error mitigation techniques (error correction, DFS etc.) - proof-of-principle quantum simulators

30/30 University of Toronto, 28 March realizing quantum gates and detectors Research Interests - coherence-induced changes in spectra (and other things) - novel synthetic aperture imaging techniques - properties of polarized light and ellipsometry - characterizing quantum states and processes - physical boundaries of entanglement and entropy (MEMS states) - quantum dynamics of trapped ions (modes, heating, motion...) - quantum algorithms: teleportation, factoring... - scalable architectures - quantum simulations (chaos, phase transitions etc.) Classical optics and Coherence Theory Quantum Optics Trapped Ions and Quantum Information Processing Solid State quantum technologies - spin-based quantum solid-state quantum computing architectures - read-out techniques (optics, MRFM,cantilevers) and tomography