Percolation thresholds for photonic quantum computing
2019
Despite linear-optical fusion (Bell measurement) being probabilistic, photonic cluster states for universal quantum computation can be prepared without feed-forward by fusing small n-photon entangled clusters, if the success probability of each fusion attempt is above a threshold, $${\mathrm{\lambda }}_{\mathrm{c}}^{(n)}$$
λ
c
(
n
)
. We prove a general bound $${\mathrm{\lambda }}_{\mathrm{c}}^{(n)} \ge 1/(n - 1)$$
λ
c
(
n
)
≥
1
∕
(
n
-
1
)
, and develop a conceptual method to construct long-range-connected clusters where $${\mathrm{\lambda }}_{\mathrm{c}}^{(n)}$$
λ
c
(
n
)
becomes the bond percolation threshold of a logical graph. This mapping lets us find constructions that require lower fusion success probabilities than currently known, and settle a heretofore open question by showing that a universal cluster state can be created by fusing 3-photon clusters over a 2D lattice with a fusion success probability that is achievable with linear optics and single photons, making this attractive for integrated-photonic realizations.
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