From Three-Photon Greenberger-Horne-Zeilinger States to Ballistic Universal Quantum Computation

Single photons, manipulated using integrated linear optics, constitute a promising platform for universal quantum computation. A series of increasingly efficient proposals have shown linear-optical quantum computing to be formally scalable. However, existing schemes typically require extensive adaptive switching, which is experimentally challenging and noisy, thousands of photon sources per renormalized qubit, and/or large quantum memories for repeat-until-success strategies. Our work overcomes all these problems. We present a scheme to construct a cluster state universal for quantum computation, which uses no adaptive switching, no large memories, and which is at least an order of magnitude more resource efficient than previous passive schemes. Unlike previous proposals, it is constructed entirely from loss-detecting gates and offers a robustness to photon loss. Even without the use of an active loss-tolerant encoding, our scheme naturally tolerates a total loss rate $\sim 1.6\%$ in the photons detected in the gates. This scheme uses only 3 Greenberger-Horne-Zeilinger states as a resource, together with a passive linear-optical network. We fully describe and model the iterative process of cluster generation, including photon loss and gate failure. This demonstrates that building a linear-optical quantum computer needs to be less challenging than previously thought.

Figure 1

Boosted type-II fusion gate. Photons 1 and 2 represent the photons on which the gate is applied; the rest are ancillary photons. The implementation based on [13] requires a pair of maximally entangled photons, while the implementation based on [14] requires four single photons. The boosted gates have the exact same success and failure outcomes as the original type II but with a higher success probability. Note that all photons are measured. Here and in subsequent figures we will represent the boosted fusion by the hexagon marked “F”.

Figure 2

Full layout of a layer of the diamond graph using three-photon Greenberger-Horne-Zeilinger (GHZ) states as input. The legend at the bottom of the figure shows the role of each photon. There are two types of rotated fusion type-II gates used; their effect on the GHZ states is described in Figs. 3 and 4.

Figure 3

Probabilistic creation of star microclusters.

Figure 4

Fusion of five-quoit microclusters to form the final lattice.

Figure 5

Instance of the percolated cluster ($10\times 3\times 3$), highlighted in blue is the spanning cluster. In addition to the orthogonal bonds which are expected in the canonical brickwork lattice, we see some diagonal bonds—these are the result of failed fusions during the creation of microclusters.

Figure 6

Results for simulations on a bulk of cluster of $L=15,20,25$. Each cluster contain $L^3$ sites and has been generated from $3L^3$ GHZ states.

Figure 7

Percolation probabilities as a function of the length, for lattices of square cross section $L^2$. The length of the cluster correlates to the computational depth of the lattice. The exponential decay shown has a decay constant which depends quadratically on $L$.

Figure 8

Loss tolerance (blue) for a cubic lattice of linear dimension $L=25$.