Satellite-based quantum repeaters are a promising means of reaching global distances in quantum networking due to the polynomial decrease of optical transmission with distance in free space, in contrast to the exponential decrease in optical fibers. We propose a satellite-based quantum repeater architecture with trapped individual atomic qubits, which can serve both as quantum memories and true single-photon sources. This hardware allows for nearly deterministic Bell measurements and exhibits long coherence times, without the need for costly cryogenic technology in space. We develop a detailed analytical model of the repeater, which includes the main imperfections of the quantum hardware and the optical link, assuming high-altitude ground stations, and consequently working in a regime of weak atmospheric turbulence. Our model allows us to estimate that high-rate and high-fidelity entanglement distribution can be achieved over intercontinental distances. In particular, we find that high-fidelity entanglement distribution over thousands of kilometres at a rate of 100 Hz can be achieved with orders of magnitude fewer memory modes than conventional architectures based on optical Bell state measurements.

Connecting multiple smaller qubit modules by generating high-fidelity entanglement is a promising path for scaling quantum computing hardware. The performance of such a modular quantum computer depends on the quality and rate of entanglement generation. However, identifying optimal architectures and entanglement generation protocols remains an open question. How can modular quantum architectures be designed to achieve fault tolerance while requiring only feasible entanglement rates and hardware? Focusing on solid-state quantum hardware, we investigate the threshold and logical failure rate of a fully distributed surface code. We consider both emission-based and scattering-based entanglement schemes between the modules to link the performance to the physical hardware and identify the regime for fault tolerance. We compare architectures with one or two data qubits per module. For some entanglement schemes, thresholds nearing the thresholds of non-distributed implementations (~ 0.4%) appear feasible with future parameters minimizing the performance gap between modular and monolithic quantum processors.

Reliable quantum communication over hundreds of kilometers is a daunting yet necessary requirement for a quantum internet. To overcome photon loss, the deployment of quantum repeater stations between distant network nodes is necessary. A plethora of different quantum hardware is being developed for this purpose, each platform with its own opportunities and challenges. Here, we propose to combine two promising hardware platforms in a hybrid quantum repeater architecture to lower the cost and boost the performance of long-distance quantum communication. We outline how ensemble-based quantum memories combined with single-spin photon transducers, which can transfer quantum information between a photon and a single spin, can facilitate massive multiplexing, efficient photon generation, and quantum logic for amplifying communication rates. As a specific example, we describe how a single Rubidium (Rb) atom coupled to nanophotonic resonators can function as a high-rate, telecom-visible entangled photon source with the visible photon being compatible with storage in a Thulium-doped crystal memory (Tm-memory) and the telecom photon being compatible with low-loss fiber propagation. We experimentally verify that the Tm and Rb transitions resonate with each other. Our analysis shows that by employing up to nine repeater stations, each equipped with two Tm-memories capable of holding up to 625 storage modes, along with four single Rb atoms, one can reach a quantum communication rate of about 10 secret bits per second across distances of up to 1000 km.

The estimation of many-qubit observables is an essential task of quantum information processing. The generally applicable approach is to decompose the observables into weighted sums of multiqubit Pauli strings, i.e., tensor products of single-qubit Pauli matrices, which can readily be measured with low-depth Clifford circuits. The accumulation of shot noise in this approach, however, severely limits the achievable variance for a finite number of measurements. We introduce a novel method, dubbed coherent Pauli summation (CPS), that circumvents this limitation by exploiting access to a single-qubit quantum memory in which measurement information can be stored and accumulated. CPS offers a reduction in the required number of measurements for a given variance that scales linearly with the number of Pauli strings in the decomposed observable. Our work demonstrates how a single long-coherence qubit memory can assist the operation of many-qubit quantum devices in a cardinal task.

Generating entanglement between distributed network nodes is a prerequisite for the quantum internet. Entanglement distribution protocols based on high-dimensional photonic qudits enable the simultaneous generation of multiple entangled pairs, which can significantly reduce the required coherence time of the qubit registers. However, current schemes require fast optical switching, which is experimentally challenging. In addition, the higher degree of error correlation between the generated entangled pairs in qudit protocols compared to qubit protocols has not been widely studied in detail. We propose a qudit-mediated entangling protocol that completely circumvents the need for optical switches at the expense of a lower success probability of the scheme. Furthermore, we quantify the amount of error correlation between the simultaneously generated entangled pairs and analyze the effect on entanglement purification algorithms and teleportation-based quantum error correction. We find that optimized purification schemes can efficiently correct the correlated errors, while the quantum error correction codes studied here perform worse than for uncorrelated error models.

The generation of entanglement between distant quantum systems is at the core of quantum networking. In recent years, numerous theoretical protocols for remote-entanglement generation have been proposed, many of which have been experimentally realized. Here, we provide a modular theoretical framework to elucidate the general mechanisms of photon-mediated entanglement generation between single spins in atomic or solid-state systems. Our framework categorizes existing protocols at various levels of abstraction and allows for combining the elements of different schemes in new ways. These abstraction layers make it possible to readily compare protocols for different quantum hardware. To enable the practical evaluation of protocols tailored to specific experimental parameters, we have devised numerical simulations based on the framework with our codes available online.

Color centers integrated with nanophotonic devices have emerged as a compelling platform for quantum science and technology. Here, we integrate tin-vacancy centers in a diamond waveguide and investigate the interaction with light at the single-photon level in both reflection and transmission. We observe single-emitter-induced extinction of the transmitted light up to 25% and measure the nonlinear effect on the photon statistics. Furthermore, we demonstrate fully tunable interference between the reflected single-photon field and laser light backscattered at the fiber end and show the corresponding controlled change between bunched and antibunched photon statistics in the reflected field.

Characterizing the interactions and dynamics of quantum mechanical systems is an essential task in developing quantum technologies. We propose an efficient protocol based on the estimation of the time-derivatives of few qubit observables using polynomial interpolation for characterizing the underlying Hamiltonian dynamics and Markovian noise of a multi-qubit device. For finite range dynamics, our protocol exponentially relaxes the necessary time-resolution of the measurements and quadratically reduces the overall sample complexity compared to previous approaches. Furthermore, we show that our protocol can characterize the dynamics of systems with algebraically decaying interactions. The implementation of the protocol requires only the preparation of product states and single-qubit measurements. Furthermore, we improve a shadow tomography method for quantum channels that is of independent interest and discuss the robustness of the protocol to various errors. This protocol can be used to parallelize the learning of the Hamiltonian, rendering it applicable for the characterization of both current and future quantum devices.

The generation of entanglement between remote matter qubits has developed into a key capability for fundamental investigations as well as for emerging quantum technologies. In the single-photon, protocol entanglement is heralded by generation of qubit-photon entangled states and subsequent detection of a single photon behind a beam splitter. In this work we perform a detailed theoretical and experimental investigation of this protocol and its various sources of infidelity. We develop an extensive theoretical model and subsequently tailor it to our experimental setting, based on nitrogen-vacancy centers in diamond. Experimentally, we verify the model by generating remote states for varying phase and amplitudes of the initial qubit superposition states and varying optical phase difference of the photons arriving at the beam splitter. We show that a static frequency offset between the optical transitions of the qubits leads to an entangled state phase that depends on the photon detection time. We find that the implementation of a Charge-Resonance check on the nitrogen-vacancy center yields transform-limited linewidths. Moreover, we measure the probability of double optical excitation, a significant source of infidelity, as a function of the power of the excitation pulse. Finally, we find that imperfect optical excitation can lead to a detection-arm-dependent entangled state fidelity and rate. The conclusion presented here are not specific to the nitrogen-vacancy centers used to carry out the experiments, and are therefore readily applicable to other qubit platforms.

One-way quantum repeaters where loss and operational errors are counteracted by quantum error-correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such repeaters, for example, the number of qubits per repeater node and the complexity of the quantum error-correcting operations are kept to a minimum to allow for near-future implementations. To this end, we propose a one-way quantum repeater that targets both the loss and operational error rates in a communication channel in a resource-efficient manner using code concatenation. Specifically, we consider a tree-cluster code as an inner loss-tolerant code concatenated with an outer 5-qubit code for protection against Pauli errors. Adopting flag-based stabilizer measurements, we show that intercontinental distances of up to 10,000 km can be bridged with a minimized resource overhead by interspersing repeater nodes that each specialize in suppressing either loss or operational errors. Our work demonstrates how tailored error-correcting codes can significantly lower the experimental requirements for long-distance quantum communication.

We report on the realization of a multi-node quantum network. Using the network, we have demonstrated three protocols; generation of a entangled state shared by all nodes, entanglement swapping and quantum teleportation between non-neighboring nodes.

Recently we became aware of an important reference that was published during the preparations of our manuscript, which we failed to cite in the original paper. In Ref. [1], the authors propose a similar scheme for the generation of multiple entangled pairs between qubit registers using a high-dimensional photonic qudit and cavity-mediated spin-photon gates. Contrary to Ref. [1], we show that such photonic qudit-mediated entanglement generation schemes have similar distribution rates as standard (parallel) qubit approaches but the memory requirements are significantly relaxed for the qudit schemes.

Future quantum internet applications will derive their power from the ability to share quantum information across the network^1,2. Quantum teleportation allows for the reliable transfer of quantum information between distant nodes, even in the presence of highly lossy network connections³. Although many experimental demonstrations have been performed on different quantum network platforms^4–10, moving beyond directly connected nodes has, so far, been hindered by the demanding requirements on the pre-shared remote entanglement, joint qubit readout and coherence times. Here we realize quantum teleportation between remote, non-neighbouring nodes in a quantum network. The network uses three optically connected nodes based on solid-state spin qubits. The teleporter is prepared by establishing remote entanglement on the two links, followed by entanglement swapping on the middle node and storage in a memory qubit. We demonstrate that, once successful preparation of the teleporter is heralded, arbitrary qubit states can be teleported with fidelity above the classical bound, even with unit efficiency. These results are enabled by key innovations in the qubit readout procedure, active memory qubit protection during entanglement generation and tailored heralding that reduces remote entanglement infidelities. Our work demonstrates a prime building block for future quantum networks and opens the door to exploring teleportation-based multi-node protocols and applications^2,11–13.

The generation of multiple entangled qubit pairs between distributed nodes is a prerequisite for a future quantum Internet. To achieve a practicable generation rate, standard protocols based on photonic qubits require multiple long-term quantum memories, which remains a significant experimental challenge. In this paper, we propose a novel protocol based on 2m-dimensional time-bin photonic qudits that allows for the simultaneous generation of multiple (m) entangled pairs between two distributed qubit registers and we outline a specific implementation of the protocol based on cavity-mediated spin-photon interactions. By adopting the qudit protocol, the required qubit memory time is independent of the transmission loss between the nodes, in contrast to standard qubit approaches. As such, our protocol can significantly boost the performance of near-term quantum networks.

We propose neutral atoms coupled to telecom nanophotonic cavities as quantum network nodes. Our novel protocol for generating atom-telecom photon entanglement enables a scalable network architecture featuring identical qubits and direct telecom operation.

We propose neutral atoms coupled to telecom nanophotonic cavities as quantum network nodes. Our novel protocol for generating atom-telecom photon entanglement enables a scalable network architecture featuring identical qubits and direct telecom operation.

As progress is made towards the first generation of error-corrected quantum computers, robust characterization and validation protocols are required to assess the noise environments of physical quantum processors. While standard coherence metrics and characterization protocols such as T1 and T2, process tomography, and randomized benchmarking are now ubiquitous, these techniques provide only partial information about the dynamic multiqubit loss channels responsible for processor errors, which can be described more fully by a Lindblad operator in the master equation formalism. Here, we introduce and experimentally demonstrate Lindblad tomography, a hardware-agnostic characterization protocol for tomographically reconstructing the Hamiltonian and Lindblad operators of a quantum noise environment from an ensemble of time-domain measurements. Performing Lindblad tomography on a small superconducting quantum processor, we show that this technique naturally builds on standard process tomography and T1/T2 measurement protocols, characterizes and accounts for state-preparation and measurement errors, and allows one to place bounds on the fit to a Markovian model. Comparing the results of single- and two-qubit measurements on a superconducting quantum processor, we demonstrate that Lindblad tomography can also be used to identify and quantify sources of crosstalk on quantum processors, such as the presence of always-on qubit-qubit interactions.

We describe a resource-efficient approach to studying many-body quantum states on noisy, intermediate-scale quantum devices. We employ a sequential generation model that allows us to bound the range of correlations in the resulting many-body quantum states. From this, we characterize situations where the estimation of local observables does not require the preparation of the entire state. Instead smaller patches of the state can be generated from which the observables can be estimated. This can potentially reduce circuit size and number of qubits for the computation of physical properties of the states. Moreover, we show that the effect of noise decreases along the computation. Our results apply to a broad class of widely studied tensor network states and can be directly applied to near-term implementations of variational quantum algorithms.