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Beyond Stellar Rank: Control Parameters for Scalable Optical Non-Gaussian State Generation

Fumiya Hanamura1, Kan Takase1,2,3, Hironari Nagayoshi1, Ryuhoh Ide1, Warit Asavanant1,2,3, Kosuke Fukui1, Petr Marek4, Radim Filip4, and Akira Furusawa1,2,3,*

  • 1Department of Applied Physics, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
  • 2Optical Quantum Computing Research Team, RIKEN Center for Quantum Computing, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
  • 3OptQC Corp., 3-28-13 Nishi-Ikebukuro, Toshima-ku, Tokyo, Japan
  • 4Department of Optics, Palacky University, 17. listopadu 1192/12, Olomouc, 77146, Czech Republic

  • *Contact author: akiraf@ap.t.u-tokyo.ac.jp
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Phys. Rev. X 16, 021034 – Published 13 May, 2026

DOI: https://doi.org/10.1103/ldbf-vbyp

Abstract

Advanced quantum technologies rely on non-Gaussian states of light, essential for universal quantum computation, fault-tolerant error correction, and quantum sensing. Their practical realization, however, faces hurdles: Simulating large multimode generators is computationally demanding, and benchmarks such as the stellar rank do not capture how effectively photon detections yield useful non-Gaussianity. We address these challenges by introducing the non-Gaussian control parameters (s0,δ0), a continuous and operational measure that goes beyond stellar rank. Leveraging these parameters, we develop a universal optimization method that reduces photon-number requirements and greatly enhances success probabilities while preserving state quality. Applied to the Gottesman-Kitaev-Preskill state generation, for example, our method cuts the required photon detections by a factor of 3 and raises the preparation probability by nearly 108. Demonstrations across cat states, cubic phase states, Gottesman-Kitaev-Preskill states, and even random states confirm broad gains in experimental feasibility. Our results provide a unifying principle for resource-efficient non-Gaussian state generation, charting a practical route toward scalable optical quantum technologies and fault-tolerant quantum computation.

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Advanced quantum technologies rely on non-Gaussian states of light for universal quantum computation, fault-tolerant error correction, and quantum sensing. We address the hurdles of multimode simulation and inadequate benchmarking by introducing non-Gaussian control parameters, which provide a continuous and operational measure of non-Gaussianity beyond traditional stellar rank. Using these parameters, we develop a universal optimization method that preserves state quality while significantly reducing photon-number requirements and boosting success probabilities. For example, when applied to Gottesman-Kitaev-Preskill state generation, our approach reduces the number of photon detections needed by three and raises preparation probability by orders of magnitude. These results provide a unifying principle for resource-efficient state engineering and establish a practical route toward scaling optical quantum technologies for fault-tolerant computation.

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Phys. Rev. X 16, 021034– Published 13 May, 2026
  • Received 7 September 2025
  • Revised 26 January 2026
  • Accepted 9 April 2026
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