Extensible universal photonic quantum computing with nonlinearity

TL;DR

An extensible photonic computer that supports a universal gate set by seamlessly combining fully programmable, scalable linear optical networks with integrated nonlinear modules is reported, which enables a broad range of quantum computing and simulation tasks.

Abstract

Universal quantum computing requires an architecture that supports both linear circuits and, crucially, strong nonlinear resources. For quantum photonic systems, integrating such nonlinearities with scalable linear circuitry has been a major bottleneck, leaving most optical experiments without nonlinear operations and, consequently, incapable of achieving universality. Here, we report an extensible photonic computer that supports a universal gate set by seamlessly combining fully programmable, scalable linear optical networks with integrated nonlinear modules. This platform enables a broad range of quantum computing and simulation tasks. We demonstrate the quasi-deterministic generation of optical Gottesman-Kitaev-Preskill states, which are essential resources for bosonic error correction, yet had previously been realized only probabilistically. Furthermore, we simulate complex many-body quantum dynamics, exemplified by the Bose-Hubbard model. Such quantum simulation tasks have long been considered beyond the reach of photonic hardware limited to linear operations. These capabilities, enabled by our extensible architecture, establish a viable route towards photonic quantum simulation and fault-tolerant quantum computing.

Figures (4)

• Figure 1: An extensible quantum photonic architecture and example applications. (a) Schematic of the architecture. Clavina features jigsaw-like extensibility. A central control unit provides phase control, synchronization, and long-fiber delay lines that serve as a cache; the LOU, inline squeezing unit Miwa2014, and nonlinear unit Costanzo2017 can be plugged into this control unit to expand the system's scale and functionality. Different types of light sources (blue pieces) and detectors (red pieces) can also be connected individually or simultaneously. This design achieves extensibility by combining mode-count scalability with modular composability. (b) Several example applications offered by Clavina. Tasks such as sampling Yu2023Madsen2022, and cluster-state generation Larsen2019Asavanant2019 can be directly implemented on its linear circuits. By integrating non-Gaussian resources, more advanced applications, for example, QONNs Yu2024QONN, error-correction codes Konno2024Winnel2024, and Hamiltonian simulation Yang2020 also become achievable. Further details about these applications are provided in Supplementary Information Section VI. The diagram on the right provides a detailed illustration of how the "cores" enable interactions among qumodes.
• Figure 2: Scalability and nonlinearity through modular functional units. (a) Large-scale linear transformations using the LOU. (b) By comparing sampling patterns acquired at different times with the initial pattern, we tracked the fidelity over nearly two hours, clearly demonstrating the platform's stability. Error bars denote the standard error. (c) Participation coefficients for all nodes in a 100-node network are extracted from Gaussian boson sampling data. (d and e) Quadrature correlation of the cluster state indicates strong $x$- and $p$-quadrature correlations between modes $A$ and $B$ across the first 200 time-bin modes. The measurements below show nullifier variances consistently below the -3 dB inseparability threshold over 8,000 modes, confirming sustained multimode entanglement in both quadratures. (f) Top: An inline squeezer acting on a single-photon state Miwa2014 could serve as a resource for generating GKP codes. Bottom: A Kerr gate Costanzo2017 with Hamiltonian $\hbar\kappa\hat{n}(\hat{n}-1)$ (where $\hat{n}$ is the bosonic number operator) directly introduces nonlinearity, demonstrated by the Wigner negativity (the blue regions). These plug-in units (including photon-number-state inputs) provide practical tools for achieving universality.
• Figure 3: Non-Gaussian state engineering and quasi-deterministic GKP state generation. (a) Schrödinger cat state breeding outcomes. An initial small cat state is prepared by inline squeezing of a single-photon Fock state with squeezing parameter $r \approx 0.3$. It is then expanded into a larger-amplitude cat state through iterative breeding (middle: after one round; bottom: after two rounds). (b) The Wigner function of the optical compass state is reconstructed from the interference of two cat states, prepared with inline squeezing $r=0.6$. (c) Quasi-deterministic generation of the GKP grid state. The marginal probabilities, shown as a solid blue line for the full dataset and a gray dashed line for the subset filtered to $|x|<0.75$, reveal a phase-space lattice of peaks and troughs characteristic of a logical grid state. The initial cat state is prepared using inline squeezing with $r=0.48$. (d) Measured quadrature probability distributions for the GKP state along two orthogonal phase quadratures (0 and $\pi/2$ cuts). More details are given in Supplementary Information Sec.VII B.
• Figure 4: Nonlinear resource for simulating Bose-Hubbard Hamiltonian. (a) Kerr-gate fidelity on the low-photon Fock subspace. The corresponding fidelity reaches $0.820\pm 0.033$ compares with ideal value. Here, input is coherent state with $\alpha=0.5$, and the Kerr nonlinearity $\Phi=\pi/3$. (b) A diagrammatic sketch of the one-dimensional Bose-Hubbard model shows bosons (e.g., photon) hopping between nearest-neighbor sites of a linear lattice while experiencing an on-site interaction. This model can be simulated with photonic quantum circuits, which can be realized on Clavina with connecting Kerr module to main QPU. The hopping term is realized by the QPU, which couples time-bin modes in direct analogy to particle tunneling between neighboring lattice sites. The on-site interaction term, describing boson-boson collisions, is implemented via the Kerr module. (c) Occupation probabilities after a fixed evolution time ($t=0.5$) while the interaction-to-tunneling ratio $U/J$ is swept from 0.5 to 3.0. Each bar is stacked according to the six two-photon Fock configurations. Left and right sub-panels correspond to the initial states $|200\rangle$ and $|110\rangle$, respectively. (d) Time resolved evolution at $U/J = 1$. Heat maps display the same set of Fock-state probabilities as a function of time for the two initial states used in Fig. 4(c). Top: Experimental results. Bottom: Ideal numerical simulations densely sampled across $U/J$ and $t$. The observed agreement, within experimental uncertainty, demonstrates that Clavina accurately captures the dynamics.