Periodic Reporting for period 1 - ClusterQ (Scalable quantum computing with continuous variable cluster states)
Reporting period: 2023-01-01 to 2025-06-30
Measurement-based quantum computation is a highly promising approach to quantum computing as it simply performs quantum processing directly through the measurements of a multi-partite entangled cluster state and thereby circumvents the complex unitary dynamics of conventional gate-based quantum computers. However, despite significant progress over the last decade in devising new strategies for measurement-based quantum computing, significant conceptual and technical challenges still remain for realizing up-scaled versions that reach the quantum advantage regime where it outperforms classical computation. In ClusterQ we aim to overcome these challenges using continuous variable three-dimensional entangled cluster states. Based on our recent work on generating and exploiting extremely large two-dimensional clusters states we aim to make conceptual breakthroughs along three different directions. First, we deterministically generate highly scalable three-dimensional cluster states of different topological structures, and explore their many-body behavior and usefulness for quantum computing. Next, we use the three-dimensional cluster states combined with hybrid detection technologies to demonstrate new quantum boson sampling algorithms – a near-term quantum computing algorithm allowing for a demonstration of quantum computational supremacy – and finally, we explore, theoretically and experimentally, a novel strategy for fault-tolerant measurement-based quantum computation using surface-codes in 3D cluster states. ClusterQ aims to position the continuous variable measurement-based approach to quantum information processing in the field of front-running candidates for NISQ (noisy, intermediate-scale quantum) computing and, in the longer term, fault-tolerant quantum computing.
The project has made key advancements in continuous-variable (CV) quantum computing, focusing on scalable cluster states, quantum advantage applications, and fault tolerance.
1. Generation and study of 3D CV cluster states
We developed the Octo-Rail Lattice, a novel four-dimensional CV cluster state architecture, extending the 2D Quad-Rail Lattice into higher dimensions. This new structure combines the flexibility and low-noise characteristics of its 2D predecessor with the ability to support topological error-correcting codes for fault-tolerant quantum computing. Our theoretical analysis confirmed that, when combined with GKP states, this structure meets the fault-tolerance threshold of 9.75 dB squeezing without requiring additional non-Gaussian resources. While theoretical work has been concluded, the experimental setup is under construction, with results expected by the end of 2025.
2. Application of 3D cluster states to boson sampling
As the primary achievement under this objective, we developed measurement-induced multimode squeezed light interferometers, a scalable and low-loss approach for Gaussian Boson Sampling (GBS). This technique enables entanglement across hundreds of modes while avoiding exponential loss accumulation, a common challenge in large-scale interferometers. We successfully built a 6-mode interferometer and designed a 400-mode scalable architecture. In parallel, we achieved an additional milestone by demonstrating a quantum learning advantage on a scalable photonic platform, showing an exponential speedup in learning a bosonic displacement process compared to classical methods.
3. CV fault-tolerant quantum computing using 3D cluster states
We introduced new error correction protocols tailored to CV systems, including a teleportation-based GKP error correction scheme that eliminates the need for quantum-limited amplification. This improves performance under realistic noise conditions. We also developed an all-optical cat-code error correction protocol, which detects and corrects single-photon loss errors while restoring the amplitude of the cat states, a key advancement toward practical optical error correction.
Taken together, the project has delivered key results across all objectives. We have developed scalable architectures for high-dimensional CV cluster states, advanced protocols for GBS implementation with measurement-induced entanglement, and introduced experimentally viable CV error correction schemes. An additional achievement, demonstrating quantum learning advantage on a photonic platform, further underscores the versatility and potential of the technologies developed within this project. Together, these outcomes mark a significant step toward scalable, fault-tolerant, and practical quantum computing using CV optical systems.
1. Generation and study of 3D CV cluster states
We developed the Octo-Rail Lattice, a novel four-dimensional CV cluster state architecture, extending the 2D Quad-Rail Lattice into higher dimensions. This new structure combines the flexibility and low-noise characteristics of its 2D predecessor with the ability to support topological error-correcting codes for fault-tolerant quantum computing. Our theoretical analysis confirmed that, when combined with GKP states, this structure meets the fault-tolerance threshold of 9.75 dB squeezing without requiring additional non-Gaussian resources. While theoretical work has been concluded, the experimental setup is under construction, with results expected by the end of 2025.
2. Application of 3D cluster states to boson sampling
As the primary achievement under this objective, we developed measurement-induced multimode squeezed light interferometers, a scalable and low-loss approach for Gaussian Boson Sampling (GBS). This technique enables entanglement across hundreds of modes while avoiding exponential loss accumulation, a common challenge in large-scale interferometers. We successfully built a 6-mode interferometer and designed a 400-mode scalable architecture. In parallel, we achieved an additional milestone by demonstrating a quantum learning advantage on a scalable photonic platform, showing an exponential speedup in learning a bosonic displacement process compared to classical methods.
3. CV fault-tolerant quantum computing using 3D cluster states
We introduced new error correction protocols tailored to CV systems, including a teleportation-based GKP error correction scheme that eliminates the need for quantum-limited amplification. This improves performance under realistic noise conditions. We also developed an all-optical cat-code error correction protocol, which detects and corrects single-photon loss errors while restoring the amplitude of the cat states, a key advancement toward practical optical error correction.
Taken together, the project has delivered key results across all objectives. We have developed scalable architectures for high-dimensional CV cluster states, advanced protocols for GBS implementation with measurement-induced entanglement, and introduced experimentally viable CV error correction schemes. An additional achievement, demonstrating quantum learning advantage on a photonic platform, further underscores the versatility and potential of the technologies developed within this project. Together, these outcomes mark a significant step toward scalable, fault-tolerant, and practical quantum computing using CV optical systems.
Among the project’s significant achievements, two stand out as clear breakthroughs that advance the field of continuous-variable (CV) quantum computing well beyond the state-of-the-art: (1) the Octo-Rail Lattice proposal and (2) the quantum learning advantage experiment. Notably, both developments were unanticipated in the original project plan.
The Octo-Rail Lattice represents a major theoretical advancement in the architecture of CV cluster states. While the project initially proposed exploring 3D cluster states for topological fault-tolerance, the resulting Octo-Rail design introduces a fully scalable four-dimensional macronode-based cluster state. It not only retains the favorable properties of 2D architectures – such as low noise and gate flexibility – but also enables the embedding of topological error-correcting codes like surface and color codes in higher-dimensional structures. Its compatibility with time-domain multiplexing and static optical components makes it practical for experimental realization. Achieving a squeezing threshold of 9.75 dB for fault tolerance without requiring additional non-Gaussian resources is a critical result. This proposal opens a new pathway for scalable, fault-tolerant optical quantum computing, and clearly goes beyond the scope and ambition of the original plan.
The quantum learning advantage experiment is equally significant and unexpected. The project originally focused on computational and simulation tasks such as Gaussian Boson Sampling, and did not anticipate contributions to quantum machine learning. However, we demonstrated – both theoretically and experimentally – the CV entanglement can provide exponential sample complexity improvements in learning a multimode bosonic displacement channel. The experiment used ~5 dB of two-mode squeezing to learn a 100-mode displacement distribution with over 11 orders of magnitude fewer samples than required classically. This result establishes a new benchmark in quantum-enhanced learning and represents one of the first demonstrations of quantum advantage in a non-computational task. It also opens a promising direction for applying CV photonic platforms to quantum sensing, metrology, and adaptive protocols.
In summary, both the Octo-Rail lattice and the quantum learning experiment are clear examples of research outcomes that go beyond the state-of-the-art and were unexpected at the project's outset. Their emergence underscores the importance of maintaining adaptability in cutting-edge research, allowing for exploration of high-impact opportunities as they arise.
The Octo-Rail Lattice represents a major theoretical advancement in the architecture of CV cluster states. While the project initially proposed exploring 3D cluster states for topological fault-tolerance, the resulting Octo-Rail design introduces a fully scalable four-dimensional macronode-based cluster state. It not only retains the favorable properties of 2D architectures – such as low noise and gate flexibility – but also enables the embedding of topological error-correcting codes like surface and color codes in higher-dimensional structures. Its compatibility with time-domain multiplexing and static optical components makes it practical for experimental realization. Achieving a squeezing threshold of 9.75 dB for fault tolerance without requiring additional non-Gaussian resources is a critical result. This proposal opens a new pathway for scalable, fault-tolerant optical quantum computing, and clearly goes beyond the scope and ambition of the original plan.
The quantum learning advantage experiment is equally significant and unexpected. The project originally focused on computational and simulation tasks such as Gaussian Boson Sampling, and did not anticipate contributions to quantum machine learning. However, we demonstrated – both theoretically and experimentally – the CV entanglement can provide exponential sample complexity improvements in learning a multimode bosonic displacement channel. The experiment used ~5 dB of two-mode squeezing to learn a 100-mode displacement distribution with over 11 orders of magnitude fewer samples than required classically. This result establishes a new benchmark in quantum-enhanced learning and represents one of the first demonstrations of quantum advantage in a non-computational task. It also opens a promising direction for applying CV photonic platforms to quantum sensing, metrology, and adaptive protocols.
In summary, both the Octo-Rail lattice and the quantum learning experiment are clear examples of research outcomes that go beyond the state-of-the-art and were unexpected at the project's outset. Their emergence underscores the importance of maintaining adaptability in cutting-edge research, allowing for exploration of high-impact opportunities as they arise.