Stochastic OneWay Quantum Computing with Ultracold Atoms in
- Slides: 26
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 PROBLEM: Imperfect Cluster States SOLUTION: Stochastic Protocol SUMMARY
The Quantum Circuit Model (the standard) U 1 m 1 U U m 2 2 U U 3 m 3 U U U 4 m 4 Time {U} Universal set of gates (eg. {CZ, R(x, h, z) } )
One-Way Quantum Computing 1) Initialize qubits:
One-Way Quantum Computing 2) Entangle qubits: Apply CZ gates to nearest neighbors “cluster state”
One-Way Quantum Computing 3) Remove unwanted qubits: Z-basis measurements “real-space quantum circuit”
One-Way Quantum Computing 4) Computation via XY measurements & feedforward: horizontal chains = logical qubits vertical links = 2 -qubit gates
One-Way Quantum Computing “one-bit teleportation” (the key identity) x-basis measurement HRZ(x) x m = By-product operator “Classical feedforward” Sufficient for arbitrary single-qubit rotations
One-Way Quantum Computing Single qubit rotation:
One-Way Quantum Computing Single qubit rotation:
One-Way Quantum Computing Single qubit rotation:
One-Way Quantum Computing Single qubit rotation:
One-Way Quantum Computing Single qubit rotation:
One-Way Quantum Computing x z h j Universal set of operators
Cluster States from Ultracold Atoms in Optical Lattices JILA Bose-Einstein Condensate Superfluid UHH Optical Lattice Mott Insulator Goal: One atom per lattice site IQO
Cluster States from Ultracold Atoms in Optical Lattices • Ising interactions • Heisenberg interactions • collisional phase shifts Ideally, j f j+1 In practice, imperfect cluster states
PROBLEM: Imperfect cluster states x q HRZ(x) m = S(p +q) Fidelity loss is small if q «p Over a series of teleportations, fidelity losses add up M. S. Tame, et al. , PRA 72, 012319 (2005).
SOLUTION: Stochastic protocol HRZ(x) x q 0 q = S(p +q) m m' H X S(p +q) X ; m' = 0 (failure) ; m' = 1 (success) q = 0 : max entangled q = p : unentangled
SOLUTION: Stochastic protocol j j+1 S(f) X D. Jaksch, et al. , PRL 82, 1975 (1999).
SOLUTION: Stochastic protocol HRZ(x) x q 0 q = S(p +q) m m' H X S(p +q) X ; m' = 0 (failure) ; m' = 1 (success) H? q = 0 : max entangled q = p : unentangled
SOLUTION: Stochastic protocol ; m' = 0 (failure) ; m' = 1 (success) H can be inserted manually (single atom addressing) H
SOLUTION: Stochastic protocol Repair via concatenation x q 0 q 0 q , • flag success in advance (Clifford measurements) • physically rearrange good/bad chains Improved success rates
SUMMARY ØSystematic phase errors expected (imperfect cluster states) ØStochastic protocol can perform perfect teleportation ØSuccess determined by X-basis measurements (Clifford) ØSuccess increased via concatenation and physical manipulation Can prepare error-free algorithm-specific graph states in advance!
Referee’s Report… (recent update) ; m' = 0 (failure) ; m' = 1 (success) H can be inserted manually (single atom addressing) cannot H S(p +q) X
Referee’s Report… (recent update) q 0 q Distillation perspective Z H Not universal…?
Thank You! David Feder (supervisor) Peter Hoyer (co-supervisor) Nathan Babcock (CQISC organizer)
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