D. P. Nadlinger

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.

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.

Quantum harmonic oscillators model a wide variety of phenomena ranging from electromagnetic fields to vibrations of atoms in molecules. Their excitations can be represented by bosons such as photons, single particles of light, or phonons, the quanta of vibrational energy. Linear interactions that only create and annihilate single bosons can generate coherent states of light or motion. Introducing nth-order nonlinear interactions, that instead involve n bosons, leads to increasingly complex quantum behaviour. For example, second-order interactions enable squeezing, used to enhance the precision of measurements beyond classical limits, while higher-order interactions create non-Gaussian states essential for continuous-variable quantum computation. However, generating nonlinear interactions is challenging, typically requiring higher-order derivatives of the driving field or specialized hardware. Hybrid systems, where linear interactions couple an oscillator to an additional spin, offer a solution and are readily available across many platforms. Here, using the spin of a single trapped ion coupled to its motion, we employ two linear interactions to demonstrate up to fourth-order bosonic interactions; we focus on generalised squeezing interactions and demonstrate squeezing, trisqueezing, and quadsqueezing. We characterise these interactions, including their spin dependence, and reconstruct the Wigner function of the resulting states. We also discuss the scaling of the interaction strength, where we drive the quadsqueezing interaction more than 100 times faster than using conventional techniques. Our method presents no fundamental limit in the interaction order n and applies to any platform supporting spin-dependent linear interactions. Strong higher-order nonlinear interactions unlock the study of fundamental quantum optics, quantum simulation, and computation in a hitherto unexplored regime.

Microwave-driven logic is a promising alternative to laser control in scaling trapped-ion based quantum processors. However, such electronic gates have yet to match the speed offered by their laser-driven counterparts. Here, we implement Mølmer-Sørensen two-qubit gates on $^{43}\text{Ca}^+$ hyperfine clock qubits in a cryogenic ($\approx25~\text{K}$) surface trap, driven by near-field microwaves. We achieve gate durations of $154~μ\text{s}$ (with $1.0(2)\%$ error) and $331~μ\text{s}$ ($0.5(1)\%$ error), which approaches the performance of typical laser-driven gates. In the $331~μ\text{s}$ gate, we demonstrate a new Walsh-modulated dynamical decoupling scheme which suppresses errors due to fluctuations in the qubit frequency as well as imperfections in the decoupling drive itself.

Individual optical addressing in chains of trapped atomic ions requires generation of many small, closely spaced beams with low cross-talk. Furthermore, implementing parallel operations necessitates phase, frequency, and amplitude control of each individual beam. Here we present a scalable method for achieving all of these capabilities using a novel integrated photonic chip coupled to a network of optical fibre components. The chip design results in very low cross-talk between neighbouring channels even at the micrometre-scale spacing by implementing a very high refractive index contrast between the channel core and cladding. Furthermore, the photonic chip manufacturing procedure is highly flexible, allowing for the creation of devices with an arbitrary number of channels as well as non-uniform channel spacing at the chip output. We present the system used to integrate the chip within our ion trap apparatus and characterise the performance of the full individual addressing setup using a single trapped ion as a light-field sensor. Our measurements showed intensity cross-talk below $10^{-3}$ across the chip, with minimum observed cross-talk as low as $O\left(10^{-5}\right)$.

We use electronic microwave control methods to implement addressed single-qubit gates with high speed and fidelity, for $^{43}\text{Ca}^{+}$ hyperfine "atomic clock" qubits in a cryogenic (100K) surface trap. For a single qubit, we benchmark an error of $1.5$ $\times$ $10^{-6}$ per Clifford gate (implemented using $600~\text{ns}$ $π/2$-pulses). For two qubits in the same trap zone (ion separation $5~μ\text{m}$), we use a spatial microwave field gradient, combined with an efficient 4-pulse scheme, to implement independent addressed gates. Parallel randomized benchmarking on both qubits yields an average error $3.4$ $\times$ $10^{-5}$ per addressed $π/2$-gate. The scheme scales theoretically to larger numbers of qubits in a single register.

We report the first hybrid matter-photon implementation of verifiable blind quantum computing. We use a trapped-ion quantum server and a client-side photonic detection system networked via a fibre-optic quantum link. The availability of memory qubits and deterministic entangling gates enables interactive protocols without post-selection - key requirements for any scalable blind server, which previous realisations could not provide. We quantify the privacy at <~0.03 leaked classical bits per qubit. This experiment demonstrates a path to fully verified quantum computing in the cloud.

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.

Cryptographic key exchange protocols traditionally rely on computational conjectures such as the hardness of prime factorisation to provide security against eavesdropping attacks. Remarkably, quantum key distribution protocols like the one proposed by Bennett and Brassard provide information-theoretic security against such attacks, a much stronger form of security unreachable by classical means. However, quantum protocols realised so far are subject to a new class of attacks exploiting implementation defects in the physical devices involved, as demonstrated in numerous ingenious experiments. Following the pioneering work of Ekert proposing the use of entanglement to bound an adversary's information from Bell's theorem, we present here the experimental realisation of a complete quantum key distribution protocol immune to these vulnerabilities. We achieve this by combining theoretical developments on finite-statistics analysis, error correction, and privacy amplification, with an event-ready scheme enabling the rapid generation of high-fidelity entanglement between two trapped-ion qubits connected by an optical fibre link. The secrecy of our key is guaranteed device-independently: it is based on the validity of quantum theory, and certified by measurement statistics observed during the experiment. Our result shows that provably secure cryptography with real-world devices is possible, and paves the way for further quantum information applications based on the device-independence principle.

Precise control of charged particles in radio-frequency (Paul) traps requires minimising excess micromotion induced by stray electric fields. We present a method to detect and compensate such fields through amplitude modulation of the radio-frequency trapping field. Modulation at frequencies close to the motional modes of the trapped particle excites coherent motion whose amplitude linearly depends on the stray field. In trapped-ion experiments, this motion can be detected by recording the arrival times of photons scattered during laser cooling. Only a single laser beam is required to resolve fields in multiple directions. In a demonstration using a $^{88}\mathrm{Sr}^{+}$ ion in a surface electrode trap, we achieve a sensitivity of $0.1\, \mathrm{V}\, \mathrm{m}^{-1}\, /\, \sqrt{\mathrm{Hz}}$ and a minimal uncertainty of $0.015\, \mathrm{V}\, \mathrm{m}^{-1}$.

We demonstrate remote entanglement of trapped-ion qubits via a quantum-optical fiber link with fidelity and rate approaching those of local operations. Two ${}^{88}$Sr${}^{+}$ qubits are entangled via the polarization degree of freedom of two photons which are coupled by high-numerical-aperture lenses into single-mode optical fibers and interfere on a beamsplitter. A novel geometry allows high-efficiency photon collection while maintaining unit fidelity for ion-photon entanglement. We generate remote Bell pairs with fidelity $F=0.940(5)$ at an average rate $182\,\mathrm{s}^{-1}$ (success probability $2.18\times10^{-4}$).

Robust qubit memory is essential for quantum computing, both for near-term devices operating without error correction, and for the long-term goal of a fault-tolerant processor. We directly measure the memory error $ε_m$ for a $^{43}$Ca$^+$ trapped-ion qubit in the small-error regime and find $ε_m<10^{-4}$ for storage times $t\lesssim50\,\mbox{ms}$. This exceeds gate or measurement times by three orders of magnitude. Using randomized benchmarking, at $t=1\,\mbox{ms}$ we measure $ε_m=1.2(7)\times10^{-6}$, around ten times smaller than that extrapolated from the $T_{2}^{\ast}$ time, and limited by instability of the atomic clock reference used to benchmark the qubit.