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Advanced Quantum Technologies

Deterministic Entanglement as a Prerequisite for Scalable Quantum Photonic Resource State Generation

Yorick Reum, Matteo Santandrea, Rohit Prasad, Raphael Weber, Jonathan J. Finley, Tobias Huber, Andreas Theo Pfenning, Stefanie Barz, Sven Höfling

Published May 1, 2026• 1 citation
Publisher

Abstract

ABSTRACT As demonstrated experimentally by Prevedel et al., active feed‐forward can render one‐way quantum computation deterministic. An analogous principle applies to the scalable generation of photonic resource states: because each probabilistic photonic fusion operation branches the construction process, the overall success probability shrinks exponentially unless entanglement is generated deterministically. A simple comparative combinatorial resource estimate illustrates the practical consequences of this principle. State‐of‐the‐art fault‐tolerant optical quantum computing architectures incur an unreasonably high single‐photon overhead when relying solely on probabilistic fusion. In contrast, deterministic sources of entangled multi‐photon states, such as semiconductor quantum dots, can reduce the number of required attempts dramatically. Assuming realistic system efficiencies, on average only 15 attempts are needed to generate a 4‐qubit resource state (4‐star), and 89 attempts for a 6‐qubit state (6‐ring), bringing efficient resource state generation in reach with near‐term photonic systems.

DOI
10.1002/qute.70301

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ABSTRACT As demonstrated experimentally by Prevedel et al., active feed‐forward can render one‐way quantum computation deterministic. An analogous principle applies to the scalable generation of photonic resource states: because each probabilistic photonic fusion operation branches the construction process, the overall success probability shrinks exponentially unless entanglement is generated deterministically. A simple comparative combinatorial resource estimate illustrates the practical consequences of this principle. State‐of‐the‐art fault‐tolerant optical quantum computing architectures incur an unreasonably high single‐photon overhead when relying solely on probabilistic fusion. In contrast, deterministic sources of entangled multi‐photon states, such as semiconductor quantum dots, can reduce the number of required attempts dramatically. Assuming realistic system efficiencies, on average only 15 attempts are needed to generate a 4‐qubit resource state (4‐star), and 89 attempts for a 6‐qubit state (6‐ring), bringing efficient resource state generation in reach with near‐term photonic systems.
We present three schemes for constructing a (2,2)-Shor-encoded 6-ring photonic resource state for fusion-based quantum computing, each relying on a different type of photon source. We benchmark these architectures by analyzing their ability to achieve the loss tolerance threshold for fusion-based quantum computation using the target resource state. More precisely, we estimate their minimum hardware requirements for fault-tolerant quantum computation in terms of the number of photon sources to achieve on-demand generation of resource states with a desired generation period. Notably, we find that a group of 12 deterministic single-photon sources containing a single matter qubit degree of freedom can produce the target resource state near-deterministically by exploiting entangling gates that are repeated until success. The approach is fully modular, eliminates the need for lossy large-scale multiplexing, and reduces the overhead for resource-state generation by several orders of magnitude compared to architectures using heralded single-photon sources and probabilistic linear-optical entangling gates. Our work shows that the use of deterministic single-photon sources embedding a qubit substantially shortens the path toward fault-tolerant photonic quantum computation.
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Entanglement in multiphoton graph states is an important resource with various applications, such as measurement-based quantum computing and memory-less quantum repeaters. While some primitive instances have been successfully prepared, scalable generation of large-scale graph states with programmable connections remains an outstanding challenge. Fusion provides a promising "divide-and-conquer" approach by linking smaller resource states into larger, more complex graphs. However, its practical scalability has been limited by the probabilistic nature of conventional fusion protocols, which necessitates extensive hardware overhead and feed-forward resources to achieve deterministic outcomes. Here, we introduce and experimentally demonstrate a deterministic fusion operation with built-in error mitigation, capable of connecting small time-bin-encoded cluster states--originally generated on-demand from a quantum emitter--into larger, reconfigurable photonic graph states of increased sizes. The fusion operation is realized by nondestructively projecting pairs of flying microwave photonic qubits into Bell states using superconducting circuits with in-situ programmability. Crucially, the protocol features active reset and reuse of matter qubits during graph state generation, thereby circumventing the coherence constraints of the quantum emitter and enabling the generation of genuine multipartite entanglement across 13 photonic qubits. Our results establish a scalable framework for photonic graph-state synthesis, paving the way for fault-tolerant measurement-based quantum computation and distributed quantum networks.
Fusion-based quantum computing is an attractive model for fault-tolerant computation based on photonics requiring only finite-sized entangled resource states followed by linear-optics operations and photon measurements. Large-scale implementations have so far been limited due to the access only to probabilistic photon sources, vulnerability to photon loss, and the need for massive multiplexing. Deterministic photon sources offer an alternative and resource-efficient route. By synergistically integrating deterministic photon emission, adaptive repeat-until-success fusions, and an optimised architectural design, we propose a complete blueprint for a photonic quantum computer using quantum dots and linear optics. It features time-bin qubit encoding, reconfigurable entangled-photon sources, and a fusion-based architecture with low optical connectivity, significantly reducing the required optical depth per photon and resource overheads. We present in detail the hardware required for resource-state generation and fusion networking, experimental pulse sequences, and exact resource estimates for preparing a logical qubit. We estimate that one logical clock cycle of error correction can be executed within microseconds, which scales linearly with the code distance. We also simulate error thresholds for fault-tolerance considering a full catalogue of intrinsic error sources found in real-world quantum dot devices. Our work establishes a practical blueprint for a low-optical-depth, emitter-based fault-tolerant photonic quantum computer.
Fusion-based photonic quantum computing architectures rely on two primitives: i) near-deterministic generation and control of constant-size entangled states and ii) probabilistic entangling measurements (photonic fusion gates) between entangled states. Here, we demonstrate these key functionalities by fusing resource states deterministically generated using a solid-state spin-photon interface. Repetitive operation of the source leads to sequential entanglement generation, whereby curiously entanglement is created between the quantum states of the same spin at two different instances in time. Such temporal multiplexing of photonic entanglement provides a resource-efficient route to scaling many-body entangled systems with photons.
Fusion-based photonic quantum computing architectures rely on two primitives: i) near-deterministic generation and control of constant-size entangled states and ii) probabilistic entangling measurements (photonic fusion gates) between entangled states. Here, we demonstrate these key functionalities by temporally fusing resource states deterministically generated using a solid-state spin-photon interface. Repetitive operation of the source leads to sequential entanglement generation, whereby curiously entanglement is created between the quantum states of the same spin at two different instances in time. Such temporal multiplexing of photonic entanglement provides a resource-efficient route to scaling many-body entangled systems with photons.