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Stochastic One-Way Quantum Computing with Ultracold Atoms in Optical Lattices

Stochastic One-Way Quantum Computing with Ultracold Atoms in Optical Lattices. Michael C. Garrett David L. Feder (supervisor). CQISC August 16, 2006. OUTLINE. The Quantum Circuit Model One-Way Quantum Computing Cluster States from Ultracold Atoms in Optical Lattices

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Stochastic One-Way Quantum Computing with Ultracold Atoms in Optical Lattices

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  1. Stochastic One-Way Quantum Computing with Ultracold Atoms in Optical Lattices Michael C. Garrett David L. Feder (supervisor) CQISC August 16, 2006.

  2. OUTLINE The Quantum Circuit Model One-Way Quantum Computing Cluster States from Ultracold Atoms in Optical Lattices PROBLEM: Imperfect Cluster States SOLUTION: Stochastic Protocol SUMMARY

  3. The Quantum Circuit Model (the standard) m1 U U 1 m2 U U U 2 m3 U U 3 m4 U 4 Time {U} Universal set of gates (eg. {CZ, R(x,h,z)} )

  4. One-Way Quantum Computing 1) Initialize qubits:

  5. “cluster state” One-Way Quantum Computing 2) Entangle qubits: Apply CZ gates to nearest neighbors

  6. “real-space quantum circuit” One-Way Quantum Computing 3) Remove unwanted qubits: Z-basis measurements

  7. horizontal chains = logical qubits vertical links = 2-qubit gates One-Way Quantum Computing 4) Computation via XY measurements & feedforward:

  8. “one-bit teleportation” x-basis measurement (the key identity) HRZ(x) x m By-product operator “Classical feedforward” Sufficient for arbitrary single-qubit rotations One-Way Quantum Computing =

  9. One-Way Quantum Computing Single qubit rotation:

  10. One-Way Quantum Computing Single qubit rotation:

  11. One-Way Quantum Computing Single qubit rotation:

  12. One-Way Quantum Computing Single qubit rotation:

  13. One-Way Quantum Computing Single qubit rotation:

  14. Universal set of operators One-Way Quantum Computing x z h j

  15. JILA UHH Bose-Einstein Condensate Optical Lattice Superfluid Mott Insulator IQO Cluster States from Ultracold Atoms in Optical Lattices Goal: One atom per lattice site

  16. Ideally, In practice, j f j+1 imperfect cluster states Cluster States from Ultracold Atoms in Optical Lattices • Ising interactions • Heisenberg interactions • collisional phase shifts

  17. x m Fidelity loss is small if q«p Over a series of teleportations, fidelity losses add up M. S. Tame, et al., PRA72, 012319 (2005). PROBLEM: Imperfect cluster states HRZ(x) q = S(p+q)

  18. HRZ(x) m ; m' = 0 (failure) ; m' = 1 (success) m' x 0 q= 0: max entangled q=p: unentangled SOLUTION: Stochastic protocol q q H S(p+q) X = S(p+q) X

  19. j S(f) X j+1 D. Jaksch, et al., PRL82, 1975 (1999). SOLUTION: Stochastic protocol

  20. HRZ(x) m ; m' = 0 (failure) ; m' = 1 (success) m' x 0 H? q= 0: max entangled q=p: unentangled SOLUTION: Stochastic protocol q q H S(p+q) X = S(p+q) X

  21. H SOLUTION: Stochastic protocol ; m' = 0 (failure) ; m' = 1 (success) H can be inserted manually (single atom addressing)

  22. q q q q x 0 0 0 , Improved success rates SOLUTION: Stochastic protocol Repair via concatenation • flag success in advance (Clifford measurements) • physically rearrange good/bad chains

  23. SUMMARY • Systematic phase errors expected (imperfect cluster states) • Stochastic protocol can perform perfect teleportation • Success determined by X-basis measurements (Clifford) • Success increased via concatenation and physical manipulation Can prepare error-free algorithm-specific graph states in advance!

  24. S(p+q) X Referee’s Report… (recent update) ; m' = 0 (failure) ; m' = 1 (success) H can be inserted manually (single atom addressing) cannot H

  25. q q q q 0 0 Z Z H H Referee’s Report… (recent update) Distillation perspective Not universal…?

  26. Thank You! David Feder (supervisor) Peter Hoyer (co-supervisor) Nathan Babcock (CQISC organizer)

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