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arXiv:2410.16380 · npj Quantum Information

Boosted Bell-state measurements for photonic quantum computation

Nico Hauser, Matthias J. Bayerbach, Simone Evaldo D’Aurelio, Raphael Weber, Matteo Santandrea, Shreya P. Kumar, Ish Dhand, Stefanie Barz

Published Mar 8, 2025• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41534-025-00986-2

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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.
Fault tolerance is essential for scalable quantum technologies and is enabled by quantum error-correction codes. Bell-state measurements (BSMs) are a fundamental building block for modern quantum technologies such as measurement-based quantum computation and fusion-based quantum computation, as well as quantum networks. Therefore, performing BSMs on error-corrected qubits is a necessary step for achieving fault tolerance in these applications. In this work, we realise a logical BSM using linear optics, based on a two-qubit repetition code, an instance of a quantum parity code that allows detection of bit-flip errors, and experimentally achieve a mean success probability of (70.8 +/- 0.4)%. While standard linear-optical BSMs are fundamentally limited to a maximum success probability of 50%, this increased success probability enables higher secure key rates in quantum communication and facilitates the generation of large graph states for quantum computation. Since fault-tolerant schemes require error-correction codes regardless, this improvement comes at no additional resource overhead. Our results demonstrate that error-correction codes can be used to surpass the linear-optics limit of BSMs, which is an important step towards practical, fault-tolerant, and scalable photonic quantum technologies.
Bell state measurements (BSMs) play a significant role in quantum information and quantum computing, in particular in fusion-based quantum computing (FBQC). The FBQC model is a framework for universal quantum computing, provided that we are able to perform entangling measurements, called fusions, on qubits within small entangled resource states. Here, we analyze the usage of different linear-optical BSM circuits as fusions in the FBQC schemes and numerically evaluate hardware requirements for fault-tolerance in this framework. We examine and compare the performance of several BSM circuits with varying additional resources and estimate the requirements on losses for every component of the linear-optical realization of fusions under which errors in fusion networks caused by these losses can be corrected. Our results show that fault-tolerant quantum computing in the FBQC model is possible with currently achievable levels of optical losses in an integrated photonic implementation, provided that we can create and detect single photons of the resource states with a total marginal efficiency higher than 0.973.
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.
Abstract Quantum teleportation has proven to be fundamental for many quantum information and communication processes. The core concept can be exploited in many tasks, from the transmission of quantum states, quantum repeaters, to quantum computing. However, for linear-optical systems, the efficiency of teleportation is directly linked to the success probability of the involved Bell-state measurement (BSM). In most implementations, this is realized by linear optics with an intrinsically limited success probability of 50%. Here, we demonstrate quantum teleportation surpassing this limit. We achieve an average fidelity of the teleported states of 0.8677 ± 0.0024, leading to an overall acceptance rate of the teleportation of 69.71 ± 0.75%. We obtain this boosted success probability by generating ancillary photonic states that are interfered with the Bell states. Thus, our work demonstrates the boosting BSMs in quantum-technology applications and our scheme could directly be applied to, e.g., quantum repeaters.
Measurement-based quantum computing relies on the generation of large entangled cluster states that act as a universal resource on which logical circuits can be imprinted and executed through local measurements. A number of strategies for constructing sufficiently large photonic cluster states propose fusing many smaller resource states generated by a series of quantum emitters. However, the fusion process is inherently probabilistic with a 50% success probability in standard guise. A recent proposal has shown that, in the limit of low loss, the probability of achieving successful fusion may be boosted to near unity by redundantly encoding the vertices of linear graph states using Greenberger-Horne-Zeilinger states [Quantum 7, 992 (2023)]. Here we present a protocol for deterministically generating redundantly encoded photonic resource states using single quantum emitters, and study the impact of protocol errors and photonic losses on the generated resource states and type-II photonic fusion. Our work provides a route for efficiently constructing complex entangled photonic qubit states for photonic quantum computing and quantum repeaters.
Rotation-symmetric cat (RS-cat) codes are a bosonic-code platform for quantum information processing, combining finite-energy realizability with robustness against photon loss through their discrete rotational symmetry. For applications in long-distance quantum communication and fusion-based quantum computation (FBQC), efficient Bell state measurement (BSM) is a key primitive. In this work, we consider a BSM protocol for RS-cat codes using only a half beam splitter (HBS) and photon-number-resolving detectors (PNRDs). By exploiting the characteristic photon-number structure induced by the discrete rotational symmetry of RS-cat codes, our protocol extracts both photon-number modulo and phase information for Bell-state discrimination. We show that, under ideal loss-free conditions, the proposed BSM protocol becomes deterministic for arbitrary symmetry order NNN for sufficiently large amplitudes ααα. We further numerically evaluate the success probability under photon loss and identify the loss regime in which higher-order RS-cat codes provide an advantage. Finally, we show that post-selection can enhance the success probability.