Transcript Folie 1
Experimental one-way quantum computing Student presentation by Andreas Reinhard Outline 1. Introduction 2. Theory about OWQC 3. Experimental realization 4. Outlook 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 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 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? Entanglement of qubits with CPhase operations • Computational basis: • Notation: 1 0, 1 2 • Prepare "physical" 2-qubit state (not entangled) 1 1 1 0 1 0 1 00 10 01 11 1 1 2 2 2 2 2 • CPhase operation => highly entangled state 1 00 10 01 – 11 2 Cluster states • Prepare the 4-qubit state 1 0 1 2 1 0 1 2 + where • and connect "neighbouring" qubits with CPhase operations. The final state is highly entangled: 00 1 0 1 2 1 0 11 Cluster state • Nearest neighbour interaction sufficient for full entanglement! Operations on qubits • Prepare cluster state • We can measure the state of qubit j in an arbitrarily chosen basis B j + j , j where j 1 0 j ei 1 2 j • Consecutive measurements on qubits 1, 2, 3 disentangle the state and completely determine the state of qubit 4. • The state of "output" qubit 4 is dependent on the choses bases. • That‘s the way a OWQC works! A Rotation • Disentangle qubit 1 from qubits 2, 3, 4 2 03 4 0 1 0 1 1 2 3 4 0 1 2 2 2 4 • and project the state on 4 i 2 3 e i sin 2 2 i 2 3 e cos 2 4 i 2 3 e i sin 2 2 ( ) ( ) R R x z 3 i 2 3 e cos 2 e i e 4 4 i 2 2 e e other 3 terms 2 3 => post selection Single qubit rotation i sin i sin i i 2 cos 2 cos 2 2 2 2 SU(2) rotation & gates • A general SU(2) rotation and 2-qubit gates • CPhase operations + single qubit rotations = universal quantum computer! A one-way Quantum Computer • Initial cluster structure <=> algorithm Clusters are subunits of larger clusters. • The computation is performed with consecutive measurements in the proper bases on the physical qubits. • Classical feedforward makes a OWQC deterministic 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) Experimental setup • Parametric down-conversion with a nonlinear crystal • PBS transmits H photons and reflects V photons • 4-photon events: • => Highly entangled state HHHH HHVV VVHH VVVV • Entanglement achieved through post-selection • Equivalent to proposed cluster state under unitary transformations on single qubits State tomography • Prove successful generation of cluster state => density matrix • Measure expectation values 2 Cluster A B C D with A , B , C , D in order to determine all elements • Fidelity: F Cluster Cluster 0.63 0.02 V , 1 H V , 2 1 H i V 2 H , Realization of a rotation and a 2-qubit gate • Output characterized by state tomography • Rotation: 0.86 0.03 2 4 2 F 0.85 0.04 0.83 0.03 0 • 2-qubit CPhase gate: 0 F 0.84 0.03 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 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)