Fusion gates enable the creation of large entangled photonic states for linear-optical quantum computing and communication protocols. However, their success probability is limited to
1/2 without additional photonic resources. Previous schemes for boosting type-I fusion have used four ancillary single photons or a two-qubit Bell state, whose preparation is probabilistic and resource intensive. Here we propose a boosted type-I fusion gate using only two independent ancillary single photons and no entangled ancillary input. It achieves a direct success probability of
5/8, matching that of the previous four-single-photon proposal while using half as many ancillary photons. The circuit is predominantly passive, with a single active element that applies a phase shift or swaps two modes according to intermediate photodetection outcomes. Unlike the previous schemes, successful outputs occupy fixed modes and require no further conditional output routing. In particular, we show that the gate is more robust to heralded ancillary-photon loss than previously proposed boosted gates and reduces the average number of single photons required to generate a six-qubit ring graph state by more than
4.6% compared with other type-I schemes. It therefore offers a resource-efficient primitive for scalable fusion-based photonic quantum information processing.
We formalize a generalized type-II fusion operation for qudit cluster states within linear optics. Two designated qudits, one from each input cluster, interfere with optional ancilla qudits via a passive linear-optical network, followed by number-resolving detection; conditioned on measurement outcome, the remaining qudits form the post-selected fused state. We prove a general rank bound: for any such interferometer and outcome, the reduced density matrix across the two parent clusters has Schmidt rank at most
M, the total number of measured qudits including ancillae. Consequently, a correct qudit fusion which requires rank
d is impossible without ancillae and requires at least
d−2 ancilla qudits. Our analysis extends previous no-go results for Bell-type qubit fusion to the qudit setting and to generalized, non-Bell projections. We analyze the probabilities and entanglement of the relevant measurement outcomes, and discuss how our lower bound aligns with existing constructive schemes. These results set a clear resource threshold for high-dimensional, fusion-based photonic MBQC.
Fusion measurements are a key primitive for linear-optical quantum computing and quantum networks. Type-I and type-II fusion gates are widely used to combine small entangled resource states into larger photonic states, but without ancillary resources their success probability is limited to
1/2. Existing
3/4-efficient type-I schemes rely on entangled Bell-pair ancillary states, whose preparation is itself probabilistic and resource-intensive. Here we propose a boosted type-I fusion gate using only four ancillary single photons and standard linear-optical primitives. For multiqubit GHZ and graph states, the gate succeeds directly with probability
5/8, while a distillation protocol converts partially entangled outcomes into additional successful events, raising the total success probability to
11/16 after one stage and asymptotically to
3/4. We quantify the practical advantage of this scheme by estimating the photonic resources required for generating representative large entangled photonic states and show that the proposed gate significantly reduces the required overhead compared with existing schemes. These results expand the set of resource-efficient linear-optical primitives and enable a substantial reduction in the resource requirements for scalable photonic quantum computing and quantum communication.
In this paper, we propose a linear-optical quantum computation scheme that starts from high-dimensionally entangled qudits but performs quantum computation on qubits defined in their subspaces. This approach enables us to increase the success probability of linear-optical fusions from
50% to
1−1/d for qudits of dimension
d without relying on existing approaches using ancilla photons and quantum codes. In particular, we show that a 2D cluster state of qubits can be generated from 5-qudit 1D cluster states using pairwise fusion gates while preserving their boosted success probability. We numerically demonstrate that this approach can improve the loss tolerance of a percolation-based scheme while keeping the photon number per resource state constant.
Linear-optical realizations of Bell state measurement (BSM) on two single-photon qubits succeed with probability
ps no higher than 0.5. However, predetection quadrature squeezing, i.e., quantum noise limited phase sensitive amplification, in the usual linear-optical BSM circuit, can yield ${p}_{s}\ensuremath{\approx}0.643$. The ability to achieve
ps>0.5 has been found to be critical in resource-efficient realizations of linear-optical quantum computing and all-photonic quantum repeaters. Yet, the aforesaid value of
ps>0.5 is not known to be the maximum achievable using squeezing, thereby leaving it open whether close-to-
100 efficient BSM might be achievable using squeezing as a resource. In this paper, we report insights on why squeezing-enhanced BSM achieves
ps>0.5. Using this, we show that the previously reported ${p}_{s}\ensuremath{\approx}0.643$ at single-mode squeezing strength
r=0.6585---for unambiguous state discrimination (USD) of all four Bell states---is an experimentally unachievable point result, which drops to ${p}_{s}\ensuremath{\approx}0.59$ with the slightest change in
r. We, however, show that squeezing-induced boosting of
ps with USD operation is still possible over a continuous range of
r, with an experimentally achievable maximum occurring at
r=0.5774, achieving ${p}_{s}\ensuremath{\approx}0.596$. Finally, deviating from USD operation, we explore a trade space between
ps, the probability with which the BSM circuit declares a ``success,'' versus the probability of error
pe, the probability of an input Bell state being erroneously identified given the circuit declares a success. Since quantum error correction could correct for some
pe>0, this tradeoff may enable better quantum repeater designs by potentially increasing the entanglement generation rates with
ps exceeding what is possible with traditionally studied USD operation of BSMs.
Quantum repeaters are necessary building blocks to realize not only long-distance quantum communication but also the quantum internet. Although quantum repeater protocols are composed of entanglement generation (between adjacent nodes) and entanglement swapping, the performance strongly depends on the success probability of the entanglement swapping. In this talk, we introduce a linear-optical “pairwise” fusion gate that probabilistically projects a pair of qudits onto a Bell state in a two-qubit subspace. The success probability of this gate increases with the dimension of the qudits. We show that the scaling of quantum repeater protocols can be improved dramatically if we use our fusion gates for the entanglement swapping, instead of conventional ones.