A. Agrawal

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.

Sympathetic cooling of data qubits by coolant ions is an essential technique for trapped-ion quantum computing. Conventionally a second ion species is used, requiring additional lasers and complicating optical setups. We propose a scheme for sympathetic cooling using the same species and test it for $^{43}$Ca$^+$ ions. Pulsed sideband cooling and ion addressing are implemented via integrated microwave control, further simplifying optical requirements. We cool a two-ion gate mode close to its ground state ($\bar{n}\approx 0.16$) and benchmark an induced error on the data qubit of $1.7(4)\times 10^{-4}$ per cooling cycle.

We generate multipartite entangled states of two, three and four matter qubits, where the entanglement is distributed over macroscopic distances via a photonic network link. Trapped-ion ${}^{88}\text{Sr}^+$ qubits are entangled directly via the optical fibre link, and the entanglement is subsequently extended to ${}^{43}\text{Ca}^+$ memory qubits co-trapped in each network node, using local mixed-species logic gates. We create remotely entangled $\text{Sr}^+$-$\text{Ca}^+$ and $\text{Ca}^+$-$\text{Ca}^+$ states, as well as mixed-species Greenberger-Horne-Zeilinger (GHZ) states of up to four qubits. We demonstrate storage of the remotely-entangled memory qubits for $\sim10~\text{s}$, more than $100\times$ the creation time.

Distributed quantum computing (DQC) combines the computing power of multiple networked quantum processing modules, enabling the execution of large quantum circuits without compromising on performance and 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, there has been no demonstration satisfying these requirements. We experimentally demonstrate the distribution of quantum computations between two photonically interconnected trapped-ion modules. The modules are separated by $\sim$ 2 m, and each contains dedicated network and circuit qubits. By using heralded remote entanglement between the network qubits, we deterministically teleport a controlled-Z gate between two circuit qubits in separate modules, achieving 86% fidelity. We then execute Grover's search algorithm - the first implementation of a distributed quantum algorithm comprising multiple non-local two-qubit gates - and measure a 71% success rate. Furthermore, we implement distributed iSWAP and SWAP circuits, compiled with 2 and 3 instances of QGT, respectively, demonstrating the ability to distribute arbitrary two-qubit operations. As photons can be interfaced with a variety of systems, this technique has applications extending beyond trapped-ion quantum computers, providing a viable pathway towards large-scale quantum computing for a range of physical platforms.

We integrate a long-lived memory qubit into a mixed-species trapped-ion quantum network node. Ion-photon entanglement first generated with a network qubit in Sr-88 is transferred to Ca-43 with 0.977(7) fidelity, and mapped to a robust memory qubit. We then entangle the network qubit with a second photon, without affecting the memory qubit. We perform quantum state tomography to show that the fidelity of ion-photon entanglement decays ~70 times slower on the memory qubit. Dynamical decoupling further extends the storage duration; we measure an ion-photon entanglement fidelity of 0.81(4) after 10s.