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Experimental one-way quantum computing

Experimental one-way quantum computing. Student presentation by Andreas Reinhard. Outline. Introduction Theory about OWQC Experimental realization Outlook. Introduction. Standard model: Computation is an unitary (reversible) evolution on the input qubits

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Experimental one-way quantum computing

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  1. Experimental one-way quantum computing Student presentation by Andreas Reinhard

  2. Outline • Introduction • Theory about OWQC • Experimental realization • Outlook

  3. Introduction • Standard model: • Computation is an unitary (reversible) evolution on the input qubits • Balance between closed system and accessibility of qubits=> decoherence, errors • Scalability is a problem

  4. Introduction • A One-Way Quantum Computer1 proposed for a lattice with Ising-type next-neighbour interaction • Hope that OWQM is more easlily scalable • Error threshold between 0.11% and 1.4% depending on the source of the error2 (depolarizing, preparation, gate, storage and measurement errors) • Start computation from initial "cluster" state of a large number of engangled qubits • Processing = measurements on qubits => one-way, irreversible 1R. Raussendorf, H. J. Briegel, A One-Way Quantum Computer, PhysRevLett.86.5188, 2001 2R. Raussendorf, et al., A fault-tolerant one-way quantum computer, ph/050135v1, 2005

  5. Cluster states • Start from highly entangled configuration of "physical" qubits.Information is encoded in the structure: "encoded" qubits • quantum processing = measurements on physical qubits • Measure "result" in output qubits • How to entangle the qubits?

  6. Entanglement of qubits with CPhase operations • Computational basis: • Notation: • Prepare "physical" 2-qubit state (not entangled) • CPhase operation =>highly entangled state –

  7. Cluster states • Prepare the 4-qubit state • and connect "neighbouring" qubits with CPhase operations.The final state is highly entangled: • Nearest neighbour interaction sufficient for full entanglement! Cluster state

  8. Operations on qubits • Prepare cluster state • We can measure the state of qubit j in an arbitrarily chosen basis • Consecutive measurements on qubits 1, 2, 3 disentangle the state and completely determine the state of qubit 4. • The state of "output" qubit 4 isdependent on the choses bases. • That‘s the way a OWQC works!

  9. A Rotation • Disentangle qubit 1 from qubits 2, 3, 4 • and project the state on => post selection Single qubit rotation

  10. SU(2) rotation & gates • A general SU(2) rotation and 2-qubit gates • CPhase operations + single qubit rotations = universal quantum computer!

  11. A one-way Quantum Computer • Initial cluster structure <=> algorithm • The computation is performed with consecutive measurements in the proper bases on the physical qubits. • Classical feedforward makesa OWQC deterministic Clusters are subunits of larger clusters.

  12. Experimental realization1 • A OWQC using 4 entangled photons • Polarization states of photons = physical qubits • Measurements easily performable. Difficulty: Preperation of the cluster state 1P. Walther, et al, Experimental one-way quantum computing, Nature, 434, 169 (2005)

  13. Experimental setup • Parametric down-conversion with a nonlinear crystal • PBS transmits H photons and reflects V photons • 4-photon events: • => Highly entangled state • Entanglement achieved through post-selection • Equivalent to proposed cluster state under unitary transformations on single qubits

  14. State tomography • Prove successful generation of cluster state => density matrix • Measure expectation valuesin order to determine all elements • Fidelity:

  15. Realization of a rotationand a 2-qubit gate • Output characterized by state tomography • Rotation: • 2-qubit CPhase gate:

  16. Problems of this experiment • Noise due to imperfect phase stability in the setup (and other reasons). => low fidelity • Scalability: probability of n-photon coincidence decreases exponentially with n • No feedforward • No storage • Post selection => proof of principle experiment

  17. Outlook • 3D optical lattices with Ising-type interacting atoms • Realization of cluster states on demand with a large number of qubits • Cluster states of Rb-atoms realized in an optical lattice1 • Filling factor a problem • Single qubit measurements not realized (adressability) 1O. Mandel, I. Bloch, et al., Controlled collisions for multi-particle entanglement of optically trapped atoms, Nature 425, 937 (2003)

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