East University Boulevard, Tucson, AZ Remote quantum entanglement can enable numerous applications including distributed quantum computation, secure communication, and precision sensing. In this paper, we consider how a quantum network-nodes equipped with limited quantum processing capabilities connected via lossy optical links-can distribute high-rate entanglement simultaneously between multiple pairs of users (multiple flows). We develop protocols for such quantum "repeater" nodes, which enable a pair of users to achieve large gains in entanglement rates over using a linear chain of quantum repeaters, by exploiting the diversity of multiple paths in the network. Additionally, we develop repeater protocols that enable multiple user pairs to generate entanglement simultaneously at rates that can far exceed what is possible with repeaters time sharing among assisting individual entanglement flows. Our results suggest that the early-stage development of quantum memories with short coherence times and implementations of probabilistic Bell-state measurements can have a much more profound impact on quantum networks than may be apparent from analyzing linear repeater chains. This framework should spur the development of a general quantum network theory, bringing together quantum memory physics, quantum information theory, and computer network theory.A quantum network can generate, distribute and process quantum information in addition to classical data [1]. The most important function of a quantum network is to generate long distance quantum entanglement, which serves a number of tasks including the generation of multiparty shared secrets whose security relies only on the laws of physics [2,3], distributed quantum computing [4], improved sensing [5,6], blind quantum computing (quantum computing on encrypted data) [7], and secure private-bid auctions [8].Recent experiments have demonstrated entanglement links, viz., long-range entanglement established between quantum memories separated by a few kilometers using a point-to-point optical link [9]. As illustrated in Fig. 1, measurements performed at nodes in a quantum network can be used to glue together small entanglement links into longer-distance clusters. The nodes contain quantum memories that store qubits up to their coherence time, sources that generate photons entangled with the quantum memory to be sent to neighboring nodes, and local quantum processors that can perform multiqubit joint measurements. Entanglement attempts between neighboring nodes are synchronized on a global clock. The quantum routing protocol dictates the measurements to be performed locally at each node in order to obtain the desired entanglement topology. Possible goals of a routing protocol could be to enable high rate entanglement among multiple user-pairs simultaneously, * mpant@mit.edu or to generate multi-partite entanglement (entanglement between three or more parties).The development of network algorithms and protocols for routing and scheduling information flows was critical for the cr...

We present a resource-performance tradeoff of an all-optical quantum repeater that uses photon sources, linear optics, photon detectors and classical feedforward at each repeater node, but no quantum memories. We show that the quantum-secure key rate has the form R(η) = Dη s bits per mode, where η is the end-to-end channel's transmissivity, and the constants D and s are functions of various device inefficiencies and the resource constraint, such as the number of available photon sources at each repeater node. Even with lossy devices, we show that it is possible to attain s < 1, and in turn outperform the maximum key rate attainable without quantum repeaters, R direct (η) = − log 2 (1 − η) ≈ (1/ ln 2)η bits per mode for η 1, beyond a certain total range L, where η ∼ e −αL in optical fiber. We also propose a suite of modifications to a recently-proposed alloptical repeater protocol that ours builds upon, which lower the number of photon sources required to create photonic clusters at the repeaters so as to outperform R direct (η), from ∼ 10 11 to ∼ 10 6 photon sources per repeater node. We show that the optimum separation between repeater nodes is independent of the total range L, and is around 1.5 km for assumptions we make on various device losses.

We demonstrate the generation of quantum-correlated photon pairs combined with the spectral filtering of the pump field by more than 95 dB on a single silicon chip using electrically tunable ring resonators and passive Bragg reflectors. Moreover, we perform the demultiplexing and routing of signal and idler photons after transferring them via an optical fiber to a second identical chip. Nonclassical two-photon temporal correlations with a coincidence-to-accidental ratio of 50 are measured without further off-chip filtering. Our system, fabricated with high yield and reproducibility in a CMOS-compatible process, paves the way toward large-scale quantum photonic circuits by allowing sources and detectors of single photons to be integrated on the same chip.

We introduce fusion-based quantum computing (FBQC) -a model of universal quantum computation in which entangling measurements, called fusions, are performed on the qubits of small constant-sized entangled resource states. We introduce a stabilizer formalism for analyzing fault tolerance and computation in these schemes. This framework naturally captures the error structure that arises in certain physical systems for quantum computing, such as photonics. FBQC can offer significant architectural simplifications, enabling hardware made up of many identical modules, requiring an extremely low depth of operations on each physical qubit and reducing classical processing requirements. We present two pedagogical examples of fault-tolerant schemes constructed in this framework and numerically evaluate their threshold under a hardware agnostic fusion error model including both erasure and Pauli error. We also study an error model of linear optical quantum computing with probabilistic fusion and photon loss. In FBQC the non-determinism of fusion is directly dealt with by the quantum error correction protocol, along with other errors. We find that tailoring the fault-tolerance framework to the physical system allows the scheme to have a higher threshold than schemes reported in literature. We present a ballistic scheme which can tolerate a 10.4% probability of suffering photon loss in each fusion.

Quantum information science offers inherently more powerful methods for communication, computation, and precision measurement that take advantage of quantum superposition and entanglement. In recent years, theoretical and experimental advances in quantum computing and simulation with photons have spurred great interest in developing large photonic entangled states that challenge today's classical computers. As experiments have increased in complexity, there has been an increasing need to transition bulk optics experiments to integrated photonics platforms to control more spatial modes with higher fidelity and phase stability. The silicon-on-insulator (SOI) nanophotonics platform offers new possibilities for quantum optics, including the integration of bright, nonclassical light sources, based on the large third-order nonlinearity (χ (3) ) of silicon, alongside quantum state manipulation circuits with thousands of optical elements, all on a single phase-stable chip. How large do these photonic systems need to be? Recent theoretical work on Boson Sampling suggests that even the problem of sampling from ~30 identical photons, having passed through an interferometer of hundreds of modes, becomes challenging for classical computers. While experiments of this size are still challenging, the SOI platform has the required component density to enable low-loss and programmable interferometers for manipulating hundreds of spatial modes.Here, we discuss the SOI nanophotonics platform for quantum photonic circuits with hundreds-to-thousands of optical elements and the associated challenges. We compare SOI to competing technologies in terms of requirements for quantum optical systems. We review recent results on large-scale quantum state evolution circuits and strategies for realizing high-fidelity heralded gates with imperfect, practical systems. Next, we review recent results on silicon photonics-based photonpair sources and device architectures, and we discuss a path towards large-scale source integration. Finally, we review monolithic integration strategies for single-photon detectors and their essential role in on-chip feed forward operations.

Based on a time-dependent quantum model, a relation between the onset of the optical tunneling regime and the metal work function is determined. In the multiphoton regime, the number of photons required for absorption is reduced from n = 3 (at pulse length τ > 20 fs) to n = 2 (at τ < 8 fs) due to the energy uncertainty principle. The phase of the laser is important for optical tunneling, but is only manifest in the multiphoton regime when the number of laser cycles is close to or less than 1. The effect of the field gradient at the tip can be important when the radius of the tip is 40 nm or smaller. The extension of the model to include nonequilibrium electron distribution due to ultrafast laser excitation is discussed. Comparisons with other models and experimental findings are presented.

Useful fault-tolerant quantum computers require very large numbers of physical qubits. Quantum computers are often designed as arrays of static qubits executing gates and measurements. Photonic qubits require a different approach. In photonic fusion-based quantum computing (FBQC), the main hardware components are resource-state generators (RSGs) and fusion devices connected via waveguides and switches. RSGs produce small entangled states of a few photonic qubits, whereas fusion devices perform entangling measurements between different resource states, thereby executing computations. In addition to these components, low-loss photonic delays such as optical fiber can be used as fixed-time quantum memories simultaneously storing thousands of photonic qubits. Here, we present a modular architecture for FBQC in which these components are combined to form interleaving modules consisting of one RSG with its associated fusion devices and a few fiber delays. Exploiting the multiplicative power of delay components, each interleaving module can add thousands of physical qubits to the computational Hilbert space. Networks of interleaving modules are universal fault-tolerant quantum computers, which we demonstrate using surface codes and lattice surgery as a guiding example. Our numerical analysis shows that in a network of modules containing 1-km-long fiber delays, a single RSG can generate four logical surface-code qubits with a code distance of 35 while tolerating photon loss rates above 2% in addition to the fiber-delay loss. We illustrate how the combination of interleaving with further uses of non-local fiber connections can reduce the cost of various logical operations and facilitate the implementation of unconventional geometries such as periodic boundaries or stellated surface codes. Interleaving applies beyond purely optical architectures, and can also turn many small disconnected matter-qubit devices with transduction to photons into a large-scale quantum computer.

Despite linear-optical fusion (Bell measurement) being probabilistic, photonic cluster states for universal quantum computation can be prepared without feed-forward by fusing small n -photon entangled clusters, if the success probability of each fusion attempt is above a threshold, . We prove a general bound , and develop a conceptual method to construct long-range-connected clusters where becomes the bond percolation threshold of a logical graph. This mapping lets us find constructions that require lower fusion success probabilities than currently known, and settle a heretofore open question by showing that a universal cluster state can be created by fusing 3-photon clusters over a 2D lattice with a fusion success probability that is achievable with linear optics and single photons, making this attractive for integrated-photonic realizations.