Photonic implementation of the one-way model of quantum computation

The one-way model of quantum computation (QC) uses a particular type of entangled state as its initial resource, which are called graph states. The computation is then performed by measuring single qubits in various bases. These bases depend on the algorithm that is being implemented and the results of the previous measurements. Hence, the qubits need to be stored in some way, while the results of the previous measurements are being processed.;For the photonic implementation of this model, optical fibers are the most practical choice for storing the qubits. The arrival time of each photon at the detector, referred to as the time-bin qubit, is the most robust physical degree of freedom of photons in optical fibers. In order to make the initial entangled resource, one first produces EPR-type entangled pairs of photons, which are fully indistinguishable in all their degrees of freedom, but the one that is encoding the logical qubits. Using fusion gates, these photon pairs are combined to produce larger graph states. Fusion gates are not deterministic and have a finite probability of success. For them to be scalable, one further requires storage of photons. For the implementation of this model by time-bin qubits, one uses a special combination of all-fiber 50 : 50 couplers and electro-optical modulators to perform the fusion gates, in addition to the arbitrary single qubit gates necessary for performing the computation itself. Both these steps, namely the production of graphs using fusion gates and performing the quantum computation, require storage of time-bin qubits, which is implemented naturally in the proposed scheme that takes advantage of optical fibers.;One of the questions that has been addressed by the mathematicians working on the one-way model is how to figure out what computations are possible, if any, by a given graph state and the choices of input and output qubits on this graph state. These studies have led to the development of an algorithm for finding a proper pattern of measurements and corrections that leads to deterministic quantum computation on the graph state. This pattern is said to be a flow on the graph. Recently this algorithm is generalized to finding the generalized flow, which are computation patterns on graphs with interesting geometries, such as graphs that contain loop structures. We experimentally realize a 4-qubit loop graph with an input qubit that renders it to be the smallest graph with a generalized flow and no flow. Such graphs with a loop structure result into a time-like loop and thus a circuit that is not runnable. Using generalized flow, however, allows us to find an equivalent to the loop graph that respects the ordinary time line and is runnable.;Bennett, Schumacher and Svetlichny (BSS) have proposed using quantum teleportation and post-selection to simulate time-like loops. It is shown that time-like loops arise naturally in the frame work of the one-way model of QC with graph states and the equivalent circuit to the created 4-qubit loop graph is equivalent to the proposal of BSS, provided that the post-selection in the BSS model has succeeded. Hence, our 4-qubit loop graph simulates a time-like loop without the use of post-selection.;For the experimental realization of this graph, we use the polarization and path degrees of freedom of two photons. A pair of polarization entangled photons are first generated using Spontaneous Parametric Down Conversion in a PPKTP crystal. The path qubits are then added using 50 : 50 beam splitters. A novel combination of half-wave plates then applies the required controlled- Z gate between the polarization degree of freedom of one photon and the path degree of freedom of the other one. This experiment is the first reported experiment that is performing a 2-qubit operation between degrees of freedom of different photons using only linear optics. Using other strategically placed half-wave plates, controlled-Z operations are added to the polarization and path degrees of freedom on the same photon and the 4-qubit loop graph is thus created. (Abstract shortened by UMI.).