Repeat-until-success quantum computing using stationary and flying qubits

We introduce an architecture for robust and scalable quantum computation using both stationary qubits (e.g., single photon sources made out of trapped atoms, molecules, ions, quantum dots, or defect centers in solids) and flying qubits (e.g., photons). Our scheme solves some of the most pressing problems in existing nonhybrid proposals, which include the difficulty of scaling conventional stationary qubit approaches, and the lack of practical means for storing single photons in linear optics setups. We combine elements of two previous proposals for distributed quantum computing, namely the efficient photon-loss tolerant build up of cluster states by Barrett and Kok [Phys. Rev. A 71, 060310(R) (2005)] with the idea of repeat-until-success (RUS) quantum computing by Lim et al. [Phys. Rev. Lett. 95, 030505 (2005)]. This idea can be used to perform eventually deterministic two qubit logic gates on spatially separated stationary qubits via photon pair measurements. Under nonideal conditions, where photon loss is a possibility, the resulting gates can still be used to build graph states for one-way quantum computing. In this paper, we describe the RUS method, present possible experimental realizations, and analyze the generation of graph states.

Figure 1

(Color online) Experimental realization of a universal two-qubit gate for the considered network of single photon sources (stationary qubits). This requires the generation of a photon within each of the sources involved. The two photons then pass within their coherence time through a linear optics network which performs a certain photon pair measurement.

Figure 2

(Color online) Measurement-based quantum computing. The input state ${\mid \Psi ⟩}_s$ and the auxiliary state ${\mid A_0⟩}_a$ are transformed in an $N$ port that induces a unitary transformation $U_{sf}$. Given a detector outcome corresponding to a POVM ${\widehat{B}}_k$, the output state is ${\mid {{\rm Y}}_k⟩}_s$.

Figure 3

(Color online) Schematic view of a single photon (a) polarization encoder, (b) time-bin encoder, and level configuration of the source containing the qubit.

Figure 4

(Color online) Linear optics networks for the realization of a measurement of the basis states (13) after encoding the photonic qubits in the polarization degrees of two photons (a) or into four different spatial photon modes (b) involving either a beam splitter or a $4\times 4$ Bell multiport beam splitter.

Figure 5

A rectangular lattice cluster state. Each circle represents a physical qubit, and each line represents a bond between qubits. These states are sufficient for simulating arbitrary logic networks [15], with each horizontal row representing a single logical qubit, and each vertical connection representing a two-qubit gate. Note we also permit bonds between nonadjacent rows and columns (not shown), which can simulate non-nearest-neighbor two-qubit operations.

Figure 6

Dynamically growing clusters during a computation. The cluster contains three regions: the active region $\left(M\right)$ at the left of the cluster, in which the logic gate networks are being simulated via single qubit measurements; the buffer region; and the connection region, where new cluster fragments are added to the right edge of the main cluster. The connecting cluster chains have a buffer length $L_a$ to accommodate the probabilistic entangling operation.

Figure 7

Creating vertical bonds. (a) We start out with two sufficiently long cluster chains and we wish to create a vertical bond between the two qubits on the left. (b) We apply a ${\sigma }_x$ measurement to the two adjacent qubits and a Hadamard operation $H$ on the next. (c) This will result in a redundant encoding of the qubits we wish to bond together. (d) Applying the entangling operation to the dangling bonds or “cherries” will create the vertical bond. Note that we also removed the qubits in the vertical bond by applying another ${\sigma }_x$ measurement resulting in another redundant encoding. If this procedure fails we are left with a shorter chain and we can try to create a vertical bond again.