ABSTRACT Measurement‐based quantum computing relies on the preparation of large‐scale multipartite entanglement, typically realized through cluster states. Quantum frequency combs provide a naturally multimode platform for constructing such states, yet prior pulse‐shaping methods are inherently sequential, thereby hindering scalability and making the reconstructed state vulnerable to system drifts. Here, we address this limitation by developing a multipixel homodyne detection scheme that enables the parallel characterization of quantum noise across multiple frequency modes and the single‐step reconstruction of the full covariance matrix, ensuring high measurement stability independent of long‐term system drifts. In an eight‐mode quantum frequency comb system, we experimentally determine sixteen entangled bipartitions (out of 127 possible bipartitions) and extract three squeezed supermodes via eigenmode decomposition of the covariance matrix. Through constructing linear optical networks in classical post‐processing, these resources enable the deterministic construction of cluster states ranging from one‐dimensional chains based on supermodes to three‐dimensional topological graphs formed by bipartite entangled pairs. The synergy between the parallel measurement capability of multipixel homodyne detection and the scalability of quantum frequency combs provides a compact and versatile platform for large‐scale, reconfigurable quantum information processing.
ABSTRACT Measurement‐based quantum computing relies on the preparation of large‐scale multipartite entanglement, typically realized through cluster states. Quantum frequency combs provide a naturally multimode platform for constructing such states, yet prior pulse‐shaping methods are inherently sequential, thereby hindering scalability and making the reconstructed state vulnerable to system drifts. Here, we address this limitation by developing a multipixel homodyne detection scheme that enables the parallel characterization of quantum noise across multiple frequency modes and the single‐step reconstruction of the full covariance matrix, ensuring high measurement stability independent of long‐term system drifts. In an eight‐mode quantum frequency comb system, we experimentally determine sixteen entangled bipartitions (out of 127 possible bipartitions) and extract three squeezed supermodes via eigenmode decomposition of the covariance matrix. Through constructing linear optical networks in classical post‐processing, these resources enable the deterministic construction of cluster states ranging from one‐dimensional chains based on supermodes to three‐dimensional topological graphs formed by bipartite entangled pairs. The synergy between the parallel measurement capability of multipixel homodyne detection and the scalability of quantum frequency combs provides a compact and versatile platform for large‐scale, reconfigurable quantum information processing.
Multimode entanglement is an essential resource for quantum information processing and quantum metrology. However, multimode entangled states are generally constructed by targeting a specific graph configuration. This yields to a fixed experimental setup that therefore exhibits reduced versatility and scalability. Here we demonstrate an optical on-demand, reconfigurable multimode entangled state, using an intrinsically multimode quantum resource and a homodyne detection apparatus. Without altering either the initial squeezing source or experimental architecture, we realize the construction of thirteen cluster states of various sizes and connectivities as well as the implementation of a secret sharing protocol. In particular, this system enables the interrogation of quantum correlations and fluctuations for any multimode Gaussian state. This initiates an avenue for implementing on-demand quantum information processing by only adapting the measurement process and not the experimental layout.
Continuous-variable (CV) multipartite entangled states, particularly Greenberger–Horne–Zeilinger (GHZ) states, are an indispensable resource for quantum networks and quantum information processing. Conventional approaches to generating CV GHZ states rely on combining multiple independently prepared squeezed lights through complex interferometric networks, which impose significant challenges in scalability and stability. Here, we experimentally demonstrate a compact and resource-efficient scheme for generating a tripartite CV GHZ state from a single quantum frequency comb produced by a synchronously pumped optical parametric oscillator. By employing multipixel homodyne detection, we simultaneously measure quadrature fluctuations across multiple frequency bands and reconstruct the full multimode covariance matrix in a single measurement. Through eigenmode decomposition, we extract a set of independent squeezed supermodes, which are subsequently transformed via a tailored linear unitary operation implemented in post-processing. Using this approach, we deterministically construct a tripartite GHZ state from three supermodes and verify its entanglement via the van Loock–Furusawa criteria, with the corresponding correlation variances measured to be 0.57, 0.75, and 0.57, all below the shot noise limit. This method effectively realizes a scalable entanglement generation scheme within a single optical beam, eliminating the need for complex interferometric networks. Our results provide a scalable and versatile platform for multimode quantum information processing.
Multimode entanglement is quintessential for the design and fabrication of quantum networks, which play a central role in quantum information processing and quantum metrology. However, an experimental setup is generally constructed with a specific network configuration in mind and therefore exhibits reduced versatility and scalability. The present work demonstrates an on-demand, reconfigurable quantum network simulator, using an intrinsically multimode quantum resource and a homodyne detection apparatus. Without altering either the initial squeezing source or experimen- tal architecture, we realize the construction of thirteen cluster states of various size and connectivity as well as the implementation of a secret sharing protocol. In particular, this simulator enables the interrogation of quantum correlations and fluctuations for a Gaussian quantum network. This initi- ates a new avenue for implementing on-demand quantum information processing by only adapting the measurement process and not the experimental layout.
Scalability is a key challenge in advancing quantum technologies such as quantum computing, communication, and metrology. Photonic systems offer a promising route to scalability by enabling the deterministic generation of large-scale entangled states. Homodyne detection is an essential quantum measurement to exploit such entangled states, enabling quantum-enhanced measurement, deterministic quantum teleportation, GKP-state breeding, and quantum error correction. Despite the recent progress in generating large-scale quantum states, realizing quantum measurement at scale remains a major challenge. Here we realize scalable and efficient homodyne detection by leveraging a large number of pixels in a charge-coupled-device (CCD) camera. Our approach enables shot-noise-limited quadrature measurements of 60 optical modes simultaneously, while requiring only nanowatt-level local oscillator power per mode -- a six-order-of-magnitude reduction compared to conventional methods. The system achieves clearance exceeding 24 dB for all modes with negligible crosstalk. We demonstrate its compatibility with a large-scale quantum state by directly observing squeezing and entanglement in 60 optical modes. Furthermore, we showcase applications in verifying multipartite entanglement and in the conditional preparation of multimode states. This work provides a scalable method for quantum measurement, paving the way for large-scale quantum information processing.
This paper theoretically demonstrates a compact method for the production of cluster states, based on recent experiments with multimode cavities, by using a so-called multi-pixel homodyne detection (MPHD) system and classical post-processing. This effectively allows to incorporate the linear optic network in the stage of the measurement. The physical transformations which the modes undergo due to the measurement (i.e., propagation from the cavity to the multipixel homodyne detector and multipixel homodyne detection) can be modeled by symplectic matrices, acting on the vector which regroups the annihilation operators associated to the various input squeezed mode. The method proposed can mimic the action of a desired matrix Uthif there exists a suitable combination of the experimental parameters such that UMPHD= Uth. It is therefore important to characterize from a theoretical point of view the class of unitary operations which are experimentally implementable by the use of this method. A condition which allows to test the implementability of a given unitary matrix Uth, and to find the experimental parameters to use in order to emulate it is determined. Some examples of cluster state generation by this method are presented. Finally, how this procedure can be generalized to perform Gaussian quantum computation is further analyzed. In particular, the possibility of implementing the elementary operations which compose a Gaussian universal set, including the Fourier transform of a single-mode input state and a two-mode CZinteraction, is studied.
Multimode Gaussian states are a versatile resource for quantum information technologies and have been realized across a wide range of physical platforms. Recent progress in the large-scale generation of such states provides a key ingredient for scalable quantum technologies. Despite the importance of accurately characterizing these states, conventional tomography methods are often impractical because they require large sample sizes and can yield unphysical states. Here we present a reliable and efficient tomography method for multimode Gaussian states based on maximum-likelihood estimation. By directly operating on covariance matrices, the method avoids the exponential overhead associated with density-matrix reconstruction. We consider two commonly used detection schemes--single and joint homodyne detection--and systematically analyze the reconstruction performance. Our method outperforms conventional approaches by ensuring physical covariance matrices and achieving better agreement with the true states. To demonstrate the experimental applicability of the method, we experimentally generate various multipartite entangled states--six-mode graph states with different connectivity, a six-mode GHZ state, and a fully connected ten-mode graph state--and reconstruct their covariance matrices. Using the reconstructed covariance matrices, we quantify fidelities, detect entanglement, and reveal the multimode structure of squeezing and noise. Our technique offers a practical diagnostic tool for developing scalable quantum technologies.