Applications of quantum walks can depend on the number, exchange symmetry and indistinguishability of the particles involved, and the underlying graph structures where they move. Here, we show that silicon photonics, by exploiting an entanglement-driven scheme, can realize quantum walks with full control over all these properties in one device. The device we realize implements entangled two-photon quantum walks on any five-vertex graph, with continuously tunable particle exchange symmetry and indistinguishability. We show how this simulates single-particle walks on larger graphs, with size and geometry controlled by tuning the properties of the composite quantum walkers. We apply the device to quantum walk algorithms for searching vertices in graphs and testing for graph isomorphisms. In doing so, we implement up to 100 sampled time steps of quantum walk evolution on each of 292 different graphs. This opens the way to large-scale, programmable quantum walk processors for classically intractable applications.
In this paper, two novel schemes for deterministic joint remote state preparation (JRSP) of arbitrary single- and two-qubit states are proposed. A set of ingenious four-particle partially entangled states are constructed to serve as the quantum channels. In our schemes, two senders and one receiver are involved. Participants collaborate with each other and perform projective measurements on their own particles under an elaborate measurement basis. Based on their measurement results, the receiver can reestablish the target state by means of appropriate local unitary operations deterministically. Unit success probability can be achieved independent of the channel’s entanglement degree.
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