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One-Way Quantum Computation

One-Way Quantum Computation. Andrew Lopez. Overview. Introduction to OWQC Simple 2-qubit example Simple 4-qubit example Recent developments Questions. Introduction to OWQC. The computation is performed by a series of single- qubit measurements. (inherently irreversible)

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One-Way Quantum Computation

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  1. One-Way Quantum Computation Andrew Lopez

  2. Overview • Introduction to OWQC • Simple 2-qubit example • Simple 4-qubit example • Recent developments • Questions

  3. Introduction to OWQC • The computation is performed by a series of single-qubit measurements. (inherently irreversible) • As such it requires a certain type of entangled state, called a graph state. • A graph state |G> is associated with a graph, G, in which every qubitis represented by a vertex and each edge represents the interaction between respective qubits. • A graph state in a square lattice is called a cluster state. Generally they require more qubits but are easier to make.

  4. Simple 2-qubit example • Initially: • Qubit 1: • Qubit 2: • Apply CZ operation: • Perform a measurement on qubit 1 in the basis, , which corresponds to • Define a binary digit • Final state Qubit 2: • Conclusion: any desired unitary transformation can be implemented up to a random but known Pauli Transformation

  5. Simple 4-qubit example • Let’s perform that same two-qubit measurement protocol three times for three arbitrary angles • Define 3 binary digits for measurements 1,2, and 3 respectively. • The net unitary transformation applied to qubit 2 is: • Which can be rewritten as: • Only deterministic if • The dependency that these angles have on previous measurements introduced a time-ordering to the measurements. • In other words there is a limit to how quickly a OWQC can be performed.

  6. Recent Developments • In 2013, B. A. Bell and his collaborators characterized the Hadamard, T, and CNOT gates for OWQC. • To create the resource state, they used two photonic crystal fibre sources to produce pairs of Bell states and then fused the pairs with a polarisingbeamsplitter to generate an entangled four-photon ‘star’ cluster state. • The ‘star’ cluster state is advantageous because they can be combined by performing a fusion operation to generate a resource state of the desired size.

  7. Recent Developments

  8. Recent Developments • Bell used State tomography to reconstruct the density matrix and then calculated the error-probability per gate for each gate. • H gate: • T gate: • CNOT gate: • Next they simulated a SWAP gate by linking 3 CNOT gates together • The limitations of this experiment are due to the multiphoton count rates and the interference visibilities of the photonic crystal fibre sources.

  9. Questions?

  10. References • Quantum Computation and Quantum Information, by Michael A. Nielsen and Isaac L. Chuang, Cambridge University Press. • One-way Quantum Computation. Dan Browne and Hans Briegel. arXiv:quant-ph/060322v2 3 Oct 2006 • Experimental characterization of universal one-way quantum computing. B.A. Bell, M.S. Tame, et al. arXiv:1305.0212v1 [quant-ph] 1 May 2013

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