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Whither Quantum Computing?

Daniel F. V. JAMES. Department of Physics and Center for Quantum Information and Quantum Control (CQIQC) University of Toronto. Whither Quantum Computing?. 2007 CQCT ANNUAL WORKSHOP Sydney, Australia 8 February 2007. funding by ARO, NSERC gratefully acknowledged.

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Whither Quantum Computing?

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  1. Daniel F. V. JAMES Department of Physics and Center for Quantum Information and Quantum Control (CQIQC) University of Toronto Whither Quantum Computing? 2007 CQCT ANNUAL WORKSHOP Sydney, Australia 8 February 2007 funding by ARO, NSERC gratefully acknowledged

  2. DiVincenzo’s Five Commandments* 1. Scalable, well-characterized qubits. 2. Ability to initialize qubits in some pure state. 3. Long decoherence time compared to gate time. 4. Universal set of quantum gates. 5. Measurement capability. *D. P. DiVinzenco, Fortschr. Phys.48 (2000) 771-783 Are these obsolescent? • Strong vs. Weak measurement in #5? • KLM redefines #4. • Cluster states redefines #2, #4

  3. Roadmap Traffic-Light Diagram (Apr 2004) -updated 4. Quantum Gates 1. Scalable qubits 5. Measurement 2. Initialization 3. Coherence NMR No know approach Trapped Ions Theoretical possibility Neutral Atoms Photons Experimental reality Solid State Superconductors Cavity QED NMR Algorithmic cooling Clock states, DFS SET detectors (> 80%) QLD, APL gates Entanglement at UCSB

  4. oscillating saddle potential Trapped Ions • Cannot trap ions electrostatically (Earnshaw’s Theorem) • Do it dynamically (Paul trap) • Effectively a harmonic well in all 3D

  5. Phonon Modes Ions coupled by Coulomb force  ions’ oscillations have normal modes. • Lowest mode: center-of-mass (CM): •Next mode is “stretch” mode: Number of modes in each direction = number of ions. D.F.V. James, Appl Phys B66, 181-190 (1998)

  6. Harmonic potential Trapped Ion QC* Laser pulses can: • Perform Rabi flips between and . • Excite phonons of the longitudinal vibration modes. *J. I. Cirac and P. Zoller , Phys Rev Lett74, 4091 (1995)

  7. B (collective operator) average over random B field Dephasing due to Magnetic Fields • Random drift of the ‘static’ magnetic field (the “Britney Spears effect”)

  8. Linear response to a zero mean, stationary B field: White noise limit : Two Qubits

  9. B0 = 119.4 Gauss = effective hyperfine B field I = nuclear spin = magnetic quantum numbers of levels chose B0 so this term is zero bias field random field Fixes 1: NIST 1. “Magic” Magnetic Fields* Breit-Rabi Formula: T2 > 10 seconds *C. Langer, et al. [die Winelandern], "Long-lived qubit memory using atomic ions," Phys. Rev. Lett.95, 060502 (2005)

  10. Fixes 2: IQOQI (Innsbruck) 2. Decoherence Free Spaces* Consider dephasing of 2 ions: there are two eigenstates with zero eigenvalue: they don’t dephase, regardless of the value of B: -use this pair of two-qubit states as a single logical qubit. -use sub-levels of 2S1/2 to avoid spontaneous decay. T2 = 34 ± 3 seconds *H. Häffner, et al. [die Blattern], "Robust Entanglement", Appl. Phys. B81, 151 (2005).

  11. Large detuning + temporal averaging of dynamics*: Non-resonant gates • remove Stark-shift term by destructive interference with another field at -: Mølmer-Sørensen gate. *DFVJ and J. Jerke, "Effective Hamiltonian Theory and Its Applications in Quantum Information,” Can. J. Phys., in the press (2007)

  12. Logical CZ Gate* Phase shift, realized by A.C. Stark effect Quantum A.C. Stark gate *L. Wu and DFVJ, in preparation

  13. • Logical gates between logical qubits • Small scale factoring: 5 qubits, 3 CNOTs. • Comparisons of different error mitigation techniques in the same environment. • Proof-of-principal for parallel operations. • Cluster state preparation/p.o.p. experiment. So: Near-term prospects • $64,000,000 question: Is it scalable?

  14. • State of the Factoring Art with Conventional Computers: RSA-640 (640 bits) factored on a distributed network with a number field sieve in 5 months (1.3 107 sec) [1]. • Quantum factoring (without error correction) of a N-bit number requires ~ 544 N3 two qubit quantum gates [2]; • Can we do it in, say, 5 minutes? • Sixth Commandment: for quantum computers to be really useful, quantum gates need to take ~1 nanosecond. [2] R. J. Hughes, D. F. V. James, E. H. Knill, R Laflamme and A. G. Petschek, Phys. Rev. Lett. 77, 3240 (1996), eq.(7). [1] www.rsasecurity.com Do we need a 6th Commandment? • Shor’s Algorithm is the the “killer app”.

  15. Roadmap Traffic-Light Diagram (+ 6th Commandment) 1. Scalable qubits 4. Quantum Gates 5. Measurement 2. Initialization 3. Coherence 6. Speed NMR No know approach Trapped Ions Theoretical possibility Neutral Atoms Photons Experimental reality Solid State 5 nsec coincidence window in QLD gate Superconductors 22 nsec root-SWAP in UCSB exp. Cavity QED

  16. • Resolve modes in frequency [1]:  • Resolve ions spatially [2]: [1] D. F. V. James, Appl. Phys. B 66, 181 (1998). [2] R. J. Hughes, D. F. V. James, E. H. Knill, R Laflamme and A. G. Petschek, Phys. Rev. Lett. 77, 3240 (1996). What’s the Speed Limit for Trapped Ions? • Bottom line: Tgate> ~10 sec.

  17. BUT: • individual pulses ~ spontaneous decay rate of upper level (i.e. ~10 nsec). • Results of Monroe et al: 5 nsec Rabi oscillations; psec non-deterministic atom-photon entanglement High Speed Gates* • Ultrafast pulses interacting with two trapped ions. CM and stretch modes interfere to create a CZ gate. • No need for spatial resolution; insensitive to heating. • Cost: considerable increase in complexity Npulses ~ (Tgateftrap)-3/2 ; if Tgate~ 1 nsec, ftrap ~ 10 MHz, Npulses ~ 103 : can this be handled if need be? *J.J. Garcia-Ripoll, P. Zoller and J. I. Cirac, Phys. Rev. Lett. 91, 157901 (2003)

  18. It gets worse... • Gates in multi-trap architectures have five-steps: 1. Extract two ions from “storage” trap. 2. Move ions to “logic” trap. 3. Sympathetic cooling. 4. Perform logic gate. 5. Return ions to “storage” trap. • Speed issues in moving ions around: 1. Move fast + sympathetic cooling OR move slow. 2. Steep potentials  small traps  heating.

  19. Ground State Fidelity: Moving Trapped Ions Quickly displacement of trap center

  20. Are cluster states the answer?* Definitions: • Number of qubits in a circuit = breadth, m • Number of gates in a circuit = depth, n Claim: For any quantum circuit there exists a pure state (m,n) such that: • (m,n) involves O(m.n) qubits • (m,n) can be prepared with poly(m.n) resources • Local measurement in an appropriate basis + feed forward simulates the quantum circuit. * R. Raussendorff and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001).

  21. Cluster States: Good: • Create 2D cluster state with only 4 CZ gates (6 for a 3D cluster) done in parallel. • Do not worry about heating after Cluster State created. Bad: • readout time and memory give new speed limit. • Need a bunch more qubits. Ugly: • Cannot make a 3D cluster needed (?) for fault-tolerance.

  22. Conclusion • Progress in the decade since publication of Cirac-Zoller proposal has been excellent, but there is still a still a long, long way to go... • My bet with Andrew White (made in 1998): will there be a quantum computer which can break 64 bit encryption in 30 minutes by 2023? (Anyone want a piece of the action?)

  23. “The English always win one battle... ...the last” E. Venizelos, 1919 Parthian shot (cricket)

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