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arXiv:2407.10893 · Physical Review Letters

Linear-Optical Fusion Boosted by High-Dimensional Entanglement

Tomohiro Yamazaki, Koji Azuma

Published May 20, 2025• 6 citations
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Abstract

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.

DOI
10.1103/physrevlett.134.200801

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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.
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.
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.
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.
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.
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 1/21/21/2 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 5/85/85/8, 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%4.6\%4.6% compared with other type-I schemes. It therefore offers a resource-efficient primitive for scalable fusion-based photonic quantum information processing.
Abstract Fault-tolerant fusion-based photonic quantum computing (FBQC) greatly relies on entangling two-photon measurements, called fusions. These fusions can be realized using linear-optical projective Bell-state measurements (BSMs). These linear-optical BSMs are limited to a success probability of 50%, greatly reducing the performance of FBQC schemes. The performance of FBQC can be improved using boosting, thus achieving higher success probabilities by adding additional resources. Here, we realize a boosted BSM using a 4 × 4 multiport splitter and an additional entangled photon pair, allowing for a success probability of up to 75%. In our experiment, we obtain a success probability for our boosted BSM of (69.3 ± 0.3)%, clearly exceeding the 50% limit. We further demonstrate the significance of our boosted BSM for FBQC, showing a threefold increase in robustness to photon loss and a significant reduction of the logical error rates.