Quantum Information Science Q with Trapped Ions

Home , Rainer Blatt

Quantum Information Science with Trapped Ions 4 Quantum Information Science EitlExperimental IlImplement ttiation with TdTrapped Ions

Rainer Blatt Institute of Exppy,y,erimental Physics, University of Innsbruck, Institute of Quantum Optics and Quantum Information, Austrian Academy of Sciences

Lectures:

3. Advance d procedures and operations teleportation, entanglement swapping etc.

4. Scaling up the ion trap quantum processor segmented traps; complex, fast procedures 3. Quantum information processing with trapped Ca+ ions

2.1 Deutsch-Jozsa algorithm with a single Ca+ ion 222.2 Cirac-Zoll er CNOT gate operation with two ions 2.3 Entanglement and Bell state generation 2.4 State tomography 2.5 Process tomography of the CNOT gate 2.6 Tripartite entanglement (W-states, GHZ-states) 2.7 Multipartite entanglement 3.0 Advanced Procedures and Operations 3.1 Teleportation 3.2 Entanglement Swapping 3.3 Metrology with entangled states 4.0 Scaling the ion trap quantum computer Teleportation

recover input state measurement in Bell basis ALICE

unknown input state rotation

Bell state BOB

M. Riebe et al., Nature 429, 734 (2004) M.D. Barrett et al., Nature 429, 737 (2004) Teleportation

M. Riebe et al., Alice‘s input state New J. Phys. 9, 211(2007)

Alice and Bob share the state joint three-qubit quantum state can be written as

rearrange

with Quantum teleportation protocol

classical communication Ion 1

Ion 2 C Bell Ion 3 state

CNOT operation, conditional check BllbBell bas is #2 and #3 rotations on #3 #3 entangled Bell recovered initialize state measurement on #3 #1, #2, #3 prepared on #1 QCSL: Quantum Computer Script Language Quantum teleportation protocol, details

conditional rotations Ion 1 using electronic logic,  B B B B C C H triggered by PM signal

Ion 2 C B B B C H U H

Ion 3  C H U C H U C C C C 

spin echo sequence blue sideband B pulses full sequence: carrier pulses 26 pulses + 2 measurements C Teleportation procedure, analysis

Initial Input state Output state Final

U TP U-1

Fidelities Teleportation with atoms: results

83 %

class. : 67 % no cond. op. 50 %

- no post -selection - teleportation at "any" choice of time - it work s " al ways " M. Riebe et al., New J. Phys. 9, 211(2007) - only 10 m Process tomography of quantum teleportation

M. Riebe et al., New J. Phys. 9, 211(2007) Process tomography of quantum teleportation

represent input/output states with Bloch spheres:

inppput sphere

output sphere

M. Riebe et al., New J. Phys. 9, 211(2007) 3. Quantum information processing with trapped Ca+ ions

► entanglement swapping : distribution of entanglement

 two atoms that never interacted become entangled  atom – light entanglement

by postselection: expect:

/2

Bell yy pair ograph

Bell mm pair To measurement of qubits 2 and 3 finds either and leave qubits 1 and 4 in one of the Bell states Entanglement swapping: action upon measurement

conditional rotations of qqpgubit 3 depending on outcome of measurement of qubits 1 and 4

deterministic entanglement of qubits 2 and 3

Bell /2 pair raphy gg Z X Bell pair Tomo

M. Riebe et al., Nature Physics 4, 839 (2008) Pulse sequence for entanglement swapping

Bell12 CNOT 

C B B B C C’ C’

B C’ C C’ C C’

B C’ C C’ C C’ C C C

C B C B B B C C’ C’

hide states spin Bell 34 (protect) echoes Entanglement swapping: result

tomography analysis of final state:

still violates Bell inequality:

M. Riebe et al., Nature Physics 4, 839 (2008) 3. Quantum information processing with trapped Ca+ ions

….using entanglement for precision measurements

 Detection enhancement using entangling operations T. Schätz et al., Phys. Rev. Lett. 94, 010501 (2005) Enhancing the S/N ratio using more entangled atoms/ions D. Leibfried et al., Science 304, 1476 (2004), Nature 438, 639 (2005)  Entangling spectroscopy ions with logic ions using quantum information processing P. Schmidt et al., Science 309, 749 (2005)  Designing entangled atoms for precision measurements C. F. Roos et al., Nature 443, 316 (2006) Ion clocks with entangled states

Clock experiments with maximally entangled states

(Wine lan d e t a l., PRA 46, R6797(‘92), Bo llinger e t a l., PRA 54, R4649 (‘96))

/2 pulses + parity measurement

measurement uncertainty 3. Quantum information processing with trapped Ca+ ions

2.1 Deutsch-Jozsa algorithm with a single Ca+ ion 2.2 Cirac-Zoller CNOT gate operation with two ions 2.3 Entanglement and Bell state generation 2.4 State tomography 2.5 Process tomography of the CNOT gate 2.6 Tripartite entanglement (W-states, GHZ-states) 2.7 Multipartite entanglement 3.0 Advanced Procedures and Operations 3.1 Teleportation 323.2 Entanglement Swapping 3.3 Metrology with entangled states 404.0 Scaling the ion trap quantum computer 4.1 More complex and faster procedures Scaling the ion trap quantum computer ….

 more ions, larger traps, phonons carry quantum information Cirac-Zoller, slow for many ions (few 10 ions maybe possible)  move ions, carry quantum information around

Kielpinski et al., Nature 417, 709 (2002)

requires small, integrated trap structures,

miniaturized optics and electronics Multiplexed trap structure: NIST Boulder

D. Leibfried, D. Wineland et al., NIST Operating a quantum algorithm on an ion chip

Movie: © Isaac Chuang, MIT Operating a quantum algorithm on an ion chip

Movie: © Isaac Chuang, MIT The development of a quantum microprocessor

Innsbruck ion trap since 2000 ion trap chip 2008, microtrap Scaling the ion-trap quantum computer: CHIPS

Planar chip traps: Wineland group (J. Chiaverini, S. Seidelin)

Lucent: DSlhD. Slusher e t a l. Ion Chip Trap Quantum Microprocessors: worldwide efforts

d ~ 40µm d ~ 250µm

MIT, USA NIST, USA Ulm + Microtrap

d ~ 200µm d ~ 200µm U Michigan, U Maryland, USA USA

d ~ 60µm U Innsbruck Advanced chip traps at NIST

2-layer, 2-D, X-junction, 18 zones (Au on Al2O3)

 Transport through junction (9Be+,24Mg+)  minimal heating ~ 20 quanta  transport error < 3 x 10-6

R. B. Blakestad transport in 40-zone, surface-electrode trap (Au on quartz)

 multi-layer leadouts

 louvers for back-side loading 4 mm (prevents electrode shorting)

J. Amini

Next (?) 200 – zone “racetrack” Scaling the ion trap quantum computer: CHIPS

Monroe group Scaling the ion trap quantum computer ….

 cavity QED: atom – photon interface, use photons for networking J. I. Cirac et al., PRL 78, 3221 (1997) P. Schmidt et al., Univ. Innsbruck

 trap arrays, using single ion as moving head motion

head I. Cirac und P. Zoller, Nature 404, 579 (2000)

target pushing  ion – solid state qubits (e.g. charge qubit) laser L. Tian et al., PRL 92, 247902 (2004) H. Häffner et al., IQOQI Innsbruck  …more ideas …? 3. Quantum information processing with trapped Ca+ ions

Toffoli gate (Tommaso Toffoli, 1980):

…… is a universal reversible logic gate, i.e. any reversible circuit can be constructed from Toffoli gates. also known as the controlled-controlled-NOT or CCNOT-gate operation

useful, e.g. for error correction Toffoli gate: pulse sequence use 2-phonon excitation Th. Monz et al., Phys. Rev. Lett. 102, 040501 (2009)

B B B B B B B B

B B

C B B B C effective  for n=1,2 result: n=1 iff SS undo encoding, reverse phases CNOT iff n=1 Toffoli gate: experimental truth table density matrix

State Fidelity

Th. Monz et al., Phys. Rev. Lett. 102, 040501 (2009) Toffoli gate: process tomography

- matrix for ideal TOFFOLI gate operation

III IIX IIY IIZ ZZZ IXI

ZZZ III Toffoli gate: process tomography

- matrix for the real TOFFOLI gate operation

Mean Process Fidelity

Th. Monz et al., Phys. Rev. Lett. 102, 040501 (2009) Quantum procedures and fidelities

► single qubit operations > 99 %

► 2-qubit CNOT gate ~ 93 %

► Bell states 93-95 %

► W and GHZ states 85-90 %

► Quantum teleportation 83 %

► Entanglement swapping ~ 80 %

► Toffoli gate operation 71 %

BUT: for fault-tolerant operation needed > 99 % ! Mølmer - Sørensen gate - operation

K. Mølmer, A. Sørensen, bichromatic laser excitation Phys. Rev. Lett. 82, 1971 (1999) close to upper and lower C. A. Sackett et al., sidebands induces collective Nature 404, 256 (2000) state changes (spin flips) Measuring entanglement

C. A. Sackett et al., Nature 404, 256 (2000) measure the parity :

/2 CNOT /2 Ion 1   /2 Ion 2  oscilla tes w ith 2  54% visibility Fidelit y =

0.5(PSS+PDD+visibility) =

71(3) %

F. Schmidt-Kaler et al., Nature 422, 408 (2003) Deterministic Bell states using the Mølmer-Sørensen gate

entangled J. Benhelm, G. Kirchmair, C. Roos Theory: C. Roos, New Journ. of Physics 10, 013002 (()2008)

measure entanglement via ppyarity oscillations

gate duration averaggye fidelity Multiple Mølmer-Sørensen gate operations in sequence corroborates average fidelity J. Benhelm et al. Nature Physics 4, 463 (2008) Theory: C. Roos, NJP 10 (2008)

maximally entangled states Multiple gate operations

after 21 consecutive gate operations

Fidelity

80 %

J. Benhelm et al., Nature Physics 4, 463 (2008) Collective entangling gates + individual light shifts

N ions Basic set of operations:

Mølmer-Sørensen gate individual light shift gates collective spin flips + + + + +

● favorable ion addressing by light shifts (~2) ● no interferometric stability between beams required

 Arbitrary unitary operations can be achieved !

...but how ? Optimal control for arbitrary quantum gates

V. Nebendahl et al., Quantum optimal control: Phys. Rev. A 79, 012312 (2009)

Find such that

Gradient ascent algorithm: N. Khaneja et al.,,g J. Magn. Res. 172,,() 296 (2005)

Modification of search algorithm: ● no simultaneous application of several Hamiltonians ● sequence of pulses with variable length

Example: quantum Toffoli gate

2 =

3    Optimal control : Quantum Error Correction

Quantum Error Correction: 3 qubits encode logical qubit (protection against spin flips)

spin flip errors spin flip errors

encoding reset ancillas

error syndrome correction detection step

V. Nebendahl et al., Phys. Rev. A 79, Implementation : 34 laser pulses (11 entangling pulses) 012312 (2009) Future goals and developments

 more qubits (~20 – 50)  better fidelities  faster gate operations cryogenic trap, micro-structured traps  faster detection  development of 2-d trap arrays, onboard addressing, electronics etc.  entangling of large(r) systems: characterization ?  implementation of error correction, keep „„qubitqubitalive“ alive“  applications - small scale QIP (e.g. repeaters) - quantum metrology, enhanced S/N, tailored atoms and states - quantum simulations - quantum computation The international Team 2009

FWF MICROTRAP Industrie IQI € SFB SCALA Tirol GmbH $ The international Team 2009

H. Barros A. Stute CRC. Roos R. Gerritsma F. Splatt M. Harlander H. Häffner N. Daniidilis S. Narayanan B. Hemmerling R. Lechner W. Hänsel T. Northup F. Zähringer Th. Monz D. Nigg PShP. Schm idt J. BiBarreiro P. Schindler G. Kirchmair M. Hennrich G. Hetet B. Brandstätter S. Gerber M. Brownnutt M. Chwalla M. Kumph L. Slodička CHC. Hempe l M. Niedermair

FWF MICROTRAP Industrie IQI € SFB SCALA Tirol GmbH $