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Experimental one-way quantum computing

This student presentation provides an introduction to one-way quantum computing (OWQC), covering theories, experimental realization, and future prospects. It explores the concept of cluster states and their importance in OWQC, as well as the challenges and potential scalability of this approach. The presentation also discusses an experimental setup using entangled photons and the issues faced in achieving high fidelity. Finally, it highlights the outlook for future advancements in OWQC, such as 3D optical lattices and the realization of cluster states with a large number of 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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