Photonic systems offer a promising platform for interconnecting quantum processors and enabling scalable, networked architectures. Designing and verifying such architectures requires a unified formalism that integrates linear algebraic reasoning with probabilistic and control-flow structures. In this work, we introduce a graphical framework for distributed quantum computing that brings together linear optics, the ZX-calculus, and dataflow programming. Our language supports the formal analysis and optimization of distributed protocols involving both qubits and photonic modes, with explicit interfaces for classical control and feedforward, all expressed within a synchronous dataflow model with discrete-time dynamics. Within this setting, we classify entangling photonic fusion measurements, show how their induced Pauli errors can be corrected via a novel flow structure for fusion networks, and establish correctness proofs for new repeat-until-success protocols enabling arbitrary fusions. Layer by layer, we construct qubit architectures incorporating practical optical components such as beam splitters, switches, and photon sources, with graphical proofs that they are deterministic and support universal quantum computation. Together, these results establish a foundation for verifiable compilation and automated optimization in networked quantum computing.
Photonic systems offer a promising platform for interconnecting quantum processors and enabling scalable, networked architectures. Designing and verifying such architectures requires a unified formalism that integrates linear algebraic reasoning with probabilistic and control-flow structures. In this work, we introduce a graphical framework for distributed quantum computing that brings together linear optics, the ZX-calculus, and dataflow programming. Our language supports the formal analysis and optimization of distributed protocols involving both qubits and photonic modes, with explicit interfaces for classical control and feedforward, all expressed within a synchronous dataflow model with discrete-time dynamics. Within this setting, we classify entangling photonic fusion measurements, show how their induced Pauli errors can be corrected via a novel flow structure for fusion networks, and establish correctness proofs for new repeat-until-success protocols enabling arbitrary fusions. Layer by layer, we construct qubit architectures incorporating practical optical components such as beam splitters, switches, and photon sources, with graphical proofs that they are deterministic and support universal quantum computation. Together, these results establish a foundation for verifiable compilation and automated optimization in networked quantum computing.
Photonics offers a promising platform for implementations of measurement-based quantum computing. Recently proposed fusion-based architectures aim to achieve universality and fault-tolerance. In these approaches, computation is carried out by performing fusion and single-qubit measurements on a resource graph state. The verification of these architectures requires linear algebraic, probabilistic, and control flow structures to be combined in a unified formal language. This paper develops a framework for photonic quantum computing by bringing together linear optics, ZX calculus, and dataflow programming. We characterize fusion measurements that induce Pauli errors and show that they are correctable using a novel flow structure for fusion networks. We prove the correctness of new repeat-until-success protocols for the realization of arbitrary fusions and provide a graph-theoretic proof of universality for linear optics with entangled photon sources. The proposed framework paves the way for the development of compilation algorithms for photonic quantum computing.
Fusion-based quantum computing is an attractive model for fault-tolerant computation based on photonics requiring only finite-sized entangled resource states followed by linear-optics operations and photon measurements. Large-scale implementations have so far been limited due to the access only to probabilistic photon sources, vulnerability to photon loss, and the need for massive multiplexing. Deterministic photon sources offer an alternative and resource-efficient route. By synergistically integrating deterministic photon emission, adaptive repeat-until-success fusions, and an optimised architectural design, we propose a complete blueprint for a photonic quantum computer using quantum dots and linear optics. It features time-bin qubit encoding, reconfigurable entangled-photon sources, and a fusion-based architecture with low optical connectivity, significantly reducing the required optical depth per photon and resource overheads. We present in detail the hardware required for resource-state generation and fusion networking, experimental pulse sequences, and exact resource estimates for preparing a logical qubit. We estimate that one logical clock cycle of error correction can be executed within microseconds, which scales linearly with the code distance. We also simulate error thresholds for fault-tolerance considering a full catalogue of intrinsic error sources found in real-world quantum dot devices. Our work establishes a practical blueprint for a low-optical-depth, emitter-based fault-tolerant photonic quantum computer.
Distributed, large-scale quantum computing will need architectures that combine matter-based qubits with photonic links, but today's software stacks target either gate-based chips or linear-optical devices in isolation. We introduce Optyx, an open-source Python framework offering a unified language to program, simulate, and prototype hybrid, networked systems: users create experiments that mix qubit registers, discrete-variable photonic modes, lossy channels, heralded measurements, and real-time feedback; Optyx compiles them via ZX/ZW calculus into optimised tensor-network forms, and executes with state-of-the-art contraction schedulers based on Quimb and Cotengra. Benchmarking on exact multi-photon circuit simulations shows that, versus permanent-based methods, tensor network contraction can deliver speedups of orders of magnitude for low-depth circuits and entangled photon sources, and natively supports loss and distinguishability -- establishing it as both a high-performance simulator and a rapid-prototyping environment for next-generation photonic-network experiments.
Abstract Distributed quantum computing (DQC) combines the computing power of multiple networked quantum processing modules, ideally enabling the execution of large quantum circuits without compromising performance or qubit connectivity 1,2 . Photonic networks are well suited as a versatile and reconfigurable interconnect layer for DQC; remote entanglement shared between matter qubits across the network enables all-to-all logical connectivity through quantum gate teleportation (QGT) 3,4 . For a scalable DQC architecture, the QGT implementation must be deterministic and repeatable; until now, no demonstration has satisfied these requirements. Here we experimentally demonstrate the distribution of quantum computations between two photonically interconnected trapped-ion modules. The modules, separated by about two metres, each contain dedicated network and circuit qubits. By using heralded remote entanglement between the network qubits, we deterministically teleport a controlled-Z (CZ) gate between two circuit qubits in separate modules, achieving 86% fidelity. We then execute Grover’s search algorithm 5 —to our knowledge, the first implementation of a distributed quantum algorithm comprising several non-local two-qubit gates—and measure a 71% success rate. Furthermore, we implement distributed iSWAP and SWAP circuits, compiled with two and three instances of QGT, respectively, demonstrating the ability to distribute arbitrary two-qubit operations 6 . As photons can be interfaced with a variety of systems, the versatile DQC architecture demonstrated here provides a viable pathway towards large-scale quantum computing for a range of physical platforms.
This thesis treats networks providing quantum computation based on distributed paradigms. Compared to architectures relying on one processor, a network promises to be more scalable and less fault-prone. Developing a distributed system able to provide practical quantum computation comes with many challenges, each of which need to be faced with careful analysis in order to create a massive integration of several components properly engineered. In accordance with hardware technologies, currently under construction around the globe, telegates represent the fundamental inter-processor operations. Each telegate consists of several tasks: i) entanglement generation and distribution, ii) local operations, and iii) classical communications. Entanglement generation and distribution is an expensive resource, as it is time-consuming. The main contribution of this thesis is on the definition of compilers that minimize the impact of telegates on the overall fidelity. Specifically, we give rigorous formulations of the subject problem, allowing us to identify the inter-dependence between computation and communication. With the support of some of the best tools for reasoning -- i.e. network optimization, circuit manipulation, group theory and ZX-calculus -- we found new perspectives on the way a distributed quantum computing system should evolve.
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.