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arXiv:2505.16816 · Physical Review Applied

Fusion for high-dimensional linear-optical quantum computing with improved success probability

Gözde Üstün, Eleanor Gilbert Rieffel, Simon J. Devitt, Jason Saied

Published Aug 28, 2025• 2 citations
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Abstract

Type-II fusion is a probabilistic entangling measurement that is essential to measurement-based linear-optical quantum computing and can be used for quantum teleportation more broadly. However, it remains under-explored for high-dimensional qudits. Our main result gives a Type-II fusion protocol with proven success probability approximately 2 / d 2 for qudits of arbitrary dimension d . This generalizes a previous method that only applied to even-dimensional qudits. We believe this protocol to be the most efficient known protocol for Type-II fusion, with the d = 5 case beating the previous record by a factor of approximately 723 . We discuss the construction of the required ( d − 2 ) -qudit ancillary state using a silicon spin-qudit ancilla coupled to a microwave cavity through time-bin multiplexing. We then introduce a general framework of extra-dimensional corrections, a natural technique in linear optics that can be used to nondeterministically correct nonmaximally entangled projections into Bell measurements. We use this method to analyze and improve several different circuits for high-dimensional Type-II fusion and compare their benefits and drawbacks.

DOI
10.1103/l7bg-hc8c

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Type-II fusion is a probabilistic entangling measurement that is essential to measurement-based linear-optical quantum computing and can be used for quantum teleportation more broadly. However, it remains under-explored for high-dimensional qudits. Our main result gives a Type-II fusion protocol with proven success probability approximately 2 / d 2 for qudits of arbitrary dimension d . This generalizes a previous method that only applied to even-dimensional qudits. We believe this protocol to be the most efficient known protocol for Type-II fusion, with the d = 5 case beating the previous record by a factor of approximately 723 . We discuss the construction of the required ( d − 2 ) -qudit ancillary state using a silicon spin-qudit ancilla coupled to a microwave cavity through time-bin multiplexing. We then introduce a general framework of extra-dimensional corrections, a natural technique in linear optics that can be used to nondeterministically correct nonmaximally entangled projections into Bell measurements. We use this method to analyze and improve several different circuits for high-dimensional Type-II fusion and compare their benefits and drawbacks.
We propose a quantum measurement that probabilistically projects a pair of qudits of dimension d onto a Bell state in a two-qubit subspace. It can be implemented using linear-optical circuits with the success probabilities of 1-d^{-1} without ancilla photons and 1-d^{-(k+1)} with 2(2^{k}-1) ancilla photons. It allows us to entangle two independently prepared high-dimensional entangled states two dimensionally with higher success probabilities than ones of linear-optical fusion gates on qubits. As an application, we propose a fast quantum repeater protocol with three-qudit GHZ states and quantum memories.
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%50\%50% to 1−1/d1-1/d1−1/d for qudits of dimension ddd 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.
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 MMM, the total number of measured qudits including ancillae. Consequently, a correct qudit fusion which requires rank ddd is impossible without ancillae and requires at least d−2d-2d−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 1/21/21/2. Existing 3/43/43/4-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 5/85/85/8, while a distillation protocol converts partially entangled outcomes into additional successful events, raising the total success probability to 11/1611/1611/16 after one stage and asymptotically to 3/43/43/4. 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.
Probabilistic and destructive Bell-measurements, also known as fusions, constitute a fundamental primitive for photonic quantum technologies. These operations rely only on pairwise photonic interference, whereas the computational power of photonic quantum systems originates from many-body interference. Here, we introduce a family of high-efficiency linear-optical GHZ measurements based on four-mode interferometers and show that incorporating many-body interference into this ubiquitous primitive leads to more efficient entangling operations. For the four-photon case, the success probability is 9/329/329/32, and adaptive variants ensure that unsuccessful events project onto useful stabilizer states. We further show that the approach naturally generalizes to larger GHZ measurements, yielding an exponentially higher success probability than previous linear-optical schemes. Finally, we demonstrate practical advantages for graph-state resource generation, entanglement distribution between remote spin-photon interfaces, and fusion-based quantum computing. Our results establish high-efficiency many-body measurements as a new primitive for scalable photonic quantum information processing.
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.