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 do not capture how effectively photon detections yield useful non-Gaussianity. We address these challenges by introducing the ( s 0 , δ 0 ) , 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 10 8 . 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.
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 do not capture how effectively photon detections yield useful non-Gaussianity. We address these challenges by introducing the ( s 0 , δ 0 ) , 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 10 8 . 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.
Quantum technologies, encompassing communication, computation, and metrology, rely on the generation and control of non-Gaussian states of light. These states enable secure quantum communication, fault-tolerant quantum computation, and precision sensing beyond classical limits, yet their practical realisation remains a major challenge due to reliance on high-photon-number Fock states or strong non-linearities. Here we introduce a unified optical framework that removes this constraint, using only Gaussian inputs, optical parametric amplification, and heralded photon detection. Within a single architecture, we demonstrate the generation of photon-added squeezed states with near unit fidelity, cubic-phase-like states with strong non-linearities and fidelities above 98.5%, and squeezed-cat states exceeding 99% fidelity that can be iteratively bred into GKP grid states surpassing the 9.75 dB fault-tolerance threshold. Operating entirely below 3 dB of input squeezing, the approach provides a scalable, experimentally accessible platform that unites the state resources required for quantum communication, metrology, and computation within one coherent optical framework.
Bosonic quantum error correction (QEC) relies on non-Gaussian bosonic encodings whose preparation cost is a central practical constraint. In this work, we use stellar rank as a resource measure to design and benchmark bosonic codes under finite non-Gaussian resources. For fixed cat and Gottesman--Kitaev--Preskill (GKP) code families, we show that finite stellar rank creates a trade-off among state approximability, energy, and logical protection under photon loss and photon-number dephasing, evaluated with optimal recovery. This trade-off implies that codewords with better ideal error-correction properties need not be optimal once finite-rank preparation constraints are imposed. Going beyond fixed-target codewords, we directly optimize bosonic encodings at fixed stellar rank, revealing noise-adapted code structures and concrete resource thresholds. Grid-like encodings emerge under photon loss, whereas approximately rotation-symmetric encodings arise under dephasing. In the optimized search, stellar rank k=2 suffices to surpass break-even for all dephasing strengths considered, while under photon loss the required rank increases with the loss rate. These results establish stellar rank as an operationally meaningful resource measure for bosonic QEC under practical state-preparation constraints.
Abstract Quantum technologies, encompassing communication, computation, and metrology, rely on the generation and control of non-Gaussian states of light. These states enable secure quantum communication, fault-tolerant quantum computation, and precision sensing beyond classical limits, yet their practical realisation remains a major challenge due to reliance on high-photon-number Fock states or strong non-linearities. Here we introduce a unified optical framework that removes this constraint, using only Gaussian inputs, optical parametric amplification, and heralded photon detection. Within a single architecture, we demonstrate the generation of photon-added squeezed states with near unit fidelity, cubic-phase-like states with strong non-linearities and fidelities above 98.5%, and squeezed-cat states exceeding 99% fidelity that can be iteratively bred into GKP grid states surpassing the 9.75 dB fault-tolerance threshold. Operating entirely below 3 dB of input squeezing, the approach provides a scalable, experimentally accessible platform that unites the state resources required for quantum communication, metrology, and computation within one coherent optical framework.
Non-Gaussian quantum states and operations constitute essential resources for achieving quantum computational advantage and enabling quantum error correction in bosonic platforms. However, their generation in optical settings remains a challenging experimental task, often relying on probabilistic heralded protocols. Here, we present an in-depth analysis of the suitability of photon catalysis between low number Fock states and squeezed states for the generation of squeezed coherent state superpositions. We employ the stellar rank formalism to characterize the non-Gaussian complexity of input resources (including both states and measurements) and the generated states. This enables a systematic comparison of the fidelity between the catalyzed output and the target states to the maximum fidelity achievable by any protocol with the same non-Gaussian input resources. In this sense, we identify instances where the catalysis protocols considered here are provably optimal. We identify parameter regimes in which high-fidelity approximations of the target states can be achieved with minimal resources. Furthermore, we benchmark the performance of photon catalysis against Gaussian boson sampling-inspired protocols in terms of success probability and state quality, highlighting the advantages of deterministic Fock state sources. We also investigate the generation of related non-Gaussian resources including squeezed Fock states, relevant for quantum error correction. To account for experimental imperfections, we model losses across all optical modes using a Hilbert space truncation approach in the Fock basis and analyze the robustness of the generated states under realistic conditions. Our results quantify the trade-offs between non-Gaussian resource complexity, achievable fidelity, and losses in photon catalysis protocols, providing practical guidelines for near-term photonic implementations.
Non-Gaussian quantum states are crucial to fault-tolerant quantum computation with continuous-variable systems. Usually, generation of such states involves trade-offs between success probability and quality of the resultant state. For example, injecting squeezed light into a multimode interferometer and postselecting on certain patterns of photon-number outputs in all but one mode, a fundamentally probabilistic task, can herald the creation of cat states, Gottesman-Kitaev-Preskill (GKP) states, and more. We consider the addition of a non-Gaussian resource state, particularly single photons, to this configuration and show how it improves the qualities and generation probabilities of desired states. With only two modes, adding a single-photon source improves GKP-state fidelity from 0.68 to 0.95 and adding a second then increases the success probability eightfold; for cat states with a fixed target fidelity, the probability of success can be improved by factors of up to four by adding single-photon sources. These demonstrate the usefulness of additional commonplace non-Gaussian resources for generating desirable states of light.
Optical quantum computing is a promising approach for achieving large-scale quantum computation. While Gaussian operations have been successfully scaled, the inherently weak nonlinearity in optics makes generating highly non-Gaussian states a critical challenge for universality and fault tolerance. Here, we propose and experimentally demonstrate a scalable method to generate optical non-Gaussian states with a resonator-based quantum memory that supports continuous-time storage and retrieval, in contrast to conventional loop-based memories. We introduce a dual-mode operation of the memory, enabling both storage and entangling functionalities within a single device. By employing a time-domain-multiplexed approach, we successfully demonstrate both cat and Gottesman-Kitaev-Preskill breeding protocols in a scalable fashion, marking a key step toward quantum error correction. Our experiment also marks the first full demonstration of an optical resonator memory performing writing, storage, and readout operations. We validate the memory by storing squeezed single-photon states with up to 93% total efficiency, and measure an energy relaxation time T 1 = 2.3 μ s and dephasing time T ϕ = 0.96 μ s . These results establish a scalable pathway to generating complex non-Gaussian states required for fault-tolerant optical quantum computing. Beyond computation, our techniques provide new tools for enhancing quantum communication, sensing, and metrology.