We study an architecture for fault-tolerant measurement-based quantum computation (FT-MBQC) over optically-networked trapped-ion modules. The architecture is implemented with a finite number of modules and ions per module, and leverages photonic interactions for generating remote entanglement between modules and local Coulomb interactions for intra-modular entangling gates. We focus on generating the topologically protected Raussendorf–Harrington–Goyal (RHG) lattice cluster state, which is known to be robust against lattice bond failures and qubit noise, with the modules acting as lattice sites. To ensure that the remote entanglement generation rates surpass the bond-failure tolerance threshold of the RHG lattice, we employ spatial and temporal multiplexing. For realistic system timing parameters, we estimate thecode cycle timeof the RHG lattice and the ion resources required in a bilayered implementation, where the number of modules matches the number of sites in two lattice layers, and qubits are reinitialized after measurement. For large distances between modules, we incorporate quantum repeaters between sites and analyze the benefits in terms of cumulative resource requirements. Finally, we derive and analyze a qubit noise-tolerance threshold inequality for the RHG lattice generation in the proposed architecture that accounts for noise from various sources. This includes the depolarizing noise arising from the photonically-mediated remote entanglement generation between modules due to finite optical detection efficiency, limited visibility, and presence of dark clicks, in addition to the noise from imperfect gates and measurements, and memory decoherence with time. Our work thus underscores the hardware and channel threshold requirements to realize distributed FT-MBQC in a leading qubit platform today—trapped ions.
We study an architecture for fault-tolerant measurement-based quantum computation (FT-MBQC) over optically-networked trapped-ion modules. The architecture is implemented with a finite number of modules and ions per module, and leverages photonic interactions for generating remote entanglement between modules and local Coulomb interactions for intra-modular entangling gates. We focus on generating the topologically protected Raussendorf–Harrington–Goyal (RHG) lattice cluster state, which is known to be robust against lattice bond failures and qubit noise, with the modules acting as lattice sites. To ensure that the remote entanglement generation rates surpass the bond-failure tolerance threshold of the RHG lattice, we employ spatial and temporal multiplexing. For realistic system timing parameters, we estimate thecode cycle timeof the RHG lattice and the ion resources required in a bilayered implementation, where the number of modules matches the number of sites in two lattice layers, and qubits are reinitialized after measurement. For large distances between modules, we incorporate quantum repeaters between sites and analyze the benefits in terms of cumulative resource requirements. Finally, we derive and analyze a qubit noise-tolerance threshold inequality for the RHG lattice generation in the proposed architecture that accounts for noise from various sources. This includes the depolarizing noise arising from the photonically-mediated remote entanglement generation between modules due to finite optical detection efficiency, limited visibility, and presence of dark clicks, in addition to the noise from imperfect gates and measurements, and memory decoherence with time. Our work thus underscores the hardware and channel threshold requirements to realize distributed FT-MBQC in a leading qubit platform today—trapped ions.
Fault-tolerant quantum computing requires architectures that simultaneously address scalability, connectivity, and error correction under realistic noise constraints. We present a compound photonic-atomic quantum computing platform that uses cavity QED to realize near-deterministic entangling operations between flying photonic qubits and stationary atomic qubits. Photons provide long-range connectivity and scalability via measurement-based quantum computing (MBQC), while atoms supply reusable, near-deterministic resources for photon generation and entanglement, overcoming the inefficiency of purely photonic platforms. The core primitive is a symmetrized Duan-Kimble photon-atom controlled-phase (CZ) gate, robust to experimental imperfections and high-fidelity. Using single 87Rb atoms coupled to optical cavities, we give protocols for state preparation, measurement, photon generation, and entangling gates on tens-of-nanosecond timescales, and show how large-scale cluster states with effectively unrestricted connectivity and reduced overhead can be generated through atomic reuse. We analyze fault tolerance on the Raussendorf-Harrington-Goyal (RHG) lattice with a hardware-aware noise model capturing asymmetric loss and correlated photonic-atomic errors. Logical memory simulations yield a photon-loss threshold near 2.6% per physical gate ($\sim$15\% total per trajectory). The full Clifford set -- Hadamard, phase, CNOT -- is implementable transversally or fold-transversally at thresholds matching the identity channel, and we propose two non-Clifford resource-state routes (code teleportation and magic state cultivation) within the foliated cluster-state architecture.
Hybridizing different physical systems or degrees of freedom offers significant advantages for realizing practical, universal, scalable, and fault-tolerant quantum computation (FTQC). Here, we propose optical FTQC schemes with low squeezing thresholds by leveraging the strengths of both discrete-variable (DV) and continuous-variable (CV) systems while utilizing frequency, time, and orbital angular momentum degrees of freedom. First, we design an optical entanglement generator (OEG) capable of producing various types of entangled pairs, including cluster pairs, hybrid entangled pairs, and GKP Bell pairs, which can be flexibly chosen by adjusting the measurement basis. Additionally, the OEG features extra ports for directly inputting (outputting) data (result) states via quantum teleportation, eliminating the need for optical switches. Secondly, large-scale one-dimensional, two-dimensional, and three-dimensional (3D) hybrid cluster states, composed of DV Gottesman-Kitaev-Preskill (GKP) qubits and CV squeezed states, are deterministically generated using the entangled pairs passed through a time-delay system. Moreover, we optimize the surface-GKP code to further reduce logical errors during the stabilizer measurements in the surface code. By combining the 3D cubic hybrid cluster state with the modified surface-GKP code and accounting for full circuit-level noise, FTQC is achieved with a squeezing threshold of 10 dB. Moreover, our method can also generate a 3D macronode Raussendorf-Harrington-Goyal (RHG) cluster state, facilitating an alternative FTQC scheme via the RHG-GKP code. Our work provides a viable pathway toward future optical FTQC architectures.
Fault tolerant quantum computation over distributed quantum computing (DQC) platforms requires careful evaluation of resource requirements and noise thresholds. As quantum hardware advances toward modular and networked architectures, various fault tolerant DQC schemes have been proposed, which can be broadly categorized into three architectural types. Type 1 architectures consist of small quantum nodes connected via Greenberger-Horne-Zeilinger (GHZ) states, enabling nonlocal stabilizer measurements. Type 2 architectures distribute a large error correcting code block across multiple modules, with most stabilizer measurements remaining local, except for a small subset at patch boundaries that are performed using nonlocal CNOT gates. Type 3 architectures assign code blocks to distinct modules and can perform fault tolerant operations such as transversal gates, lattice surgery, and teleportation to implement logical operations between code blocks. Using the planar surface code and toric code as representative examples, we analyze how the resource requirements, particularly the number of Bell pairs and the average number of generation attempts, scale with increasing code distance across different architectural designs. This analysis provides valuable insights for identifying architectures well suited to fault tolerant distributed quantum computation under near term hardware and resource constraints.
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 connectivity. 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 via quantum gate teleportation (QGT). For a scalable DQC architecture, the QGT implementation must be deterministic and repeatable; until now, no demonstration has satisfied these requirements. In this thesis, we report the first experimental demonstration of distributed quantum computing across a quantum network of two photonically interconnected trapped-ion modules. Our experimental apparatus comprises two trapped-ion modules, separated by ∼ 2 m, each co-trapping one 43Ca+ ion and one 88Sr+ ion. The 43Ca+ ions provide a robust quantum memory for the modules, while the 88Sr+ ions provide an interface to the optical quantum network, enabling the remote entanglement of 88Sr+ ions in separate modules. Using local mixed-species operations, we demonstrate the enhanced functionality of the mixed-species trapped-ion quantum network by creating more complex remotely entangled states. These include remote 88Sr+- 43Ca+ and 43Ca+-43Ca+ entanglement, as well as 3- and 4-qubit mixed-species GHZ states. Additionally, we demonstrate the storage of remote entanglement in the 43Ca+ ions for up to 10 s. Utilising these techniques, we demonstrate the distribution of quantum computations across the mixed-species trapped-ion quantum network. Using heralded remote entanglement between the 88Sr+ ions, we deterministically teleport controlled Z gates between two 43Ca+ ions in separate modules, achieving a fidelity of 86 %. We then implement distributed iSWAP and SWAP circuits, compiled with 2 and 3 instances of QGT, respectively, demonstrating the ability to distribute arbitrary two-qubit operations. Finally, we execute Grover’s search algorithm – the first implementation of a distributed quantum algorithm comprising multiple non-local two-qubit gates – and measure a success rate of 71 %. These results represent a significant step towards realising a large-scale distributed quantum computer.
Building fault-tolerant quantum computers with large numbers of logical qubits requires both scalable hardware architectures and error-correcting codes that make efficient use of physical qubits. Photonic interconnects address both of these challenges by allowing the physical qubits to be distributed across multiple processors while providing the non-local connectivity necessary to implement resource-efficient codes such as high-rate quantum low-density parity-check (qLDPC) codes. A key requirement for realising this architecture is the ability to perform stabiliser measurements between remote processors, which has not previously been demonstrated experimentally. Here we report the first experimental demonstration of distributed quantum error detection and correction. We generate entanglement between network qubits in two separate trapped-ion processors and use it to perform remote syndrome measurements on data qubits. We first realise a distributed [[2, 1, 1]] repetition code, detecting phase-flip errors on a logical qubit encoded across the two modules in real time and suppressing logical errors. We then combine these mid-circuit syndrome measurements with real-time feedforward to actively correct arbitrary single-qubit Pauli errors on a distributed Bell state. These results provide an experimental foundation for quantum error correction (QEC) across modular quantum architectures.
In this work, we introduce a method to construct fault-tolerant measurement-based quantum computation (MBQC) architectures and numerically estimate their performance over various types of networks. A possible application of such a paradigm is distributed quantum computation, where separate computing nodes work together on a fault-tolerant computation through entanglement. We gauge error thresholds of the architectures with an efficient stabilizer simulator to investigate the resilience against both circuit-level and network noise. We show that, for both monolithic (i.e., non-distributed) and distributed implementations, an architecture based on the diamond lattice may outperform the conventional cubic lattice. Moreover, the high erasure thresholds of non-cubic lattices may be exploited further in a distributed context, as their performance may be boosted through entanglement distillation by trading in entanglement success rates against erasure errors during the error-decoding process. These results highlight the significance of lattice geometry in the design of fault-tolerant measurement-based quantum computing on a network, emphasizing the potential for constructing robust and scalable distributed quantum computers.