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Commercially impactful quantum algorithms such as quantum chemistry and Shor's algorithm require a number of qubits and gates far beyond the capacity of any existing quantum processor. Distributed architectures, which scale horizontally by networking modules, provide a route to commercial utility and will eventually surpass the capability of any single quantum computing module. Such processors consume remote entanglement distributed between modules to realize distributed quantum logic. Networked quantum computers will therefore require the capability to rapidly distribute high fidelity entanglement between modules. Here we present preliminary demonstrations of some key distributed quantum computing protocols on silicon T centres in isotopically-enriched silicon. We demonstrate the distribution of entanglement between modules and consume it to apply a teleported gate sequence, establishing a proof-of-concept for T centres as a distributed quantum computing and networking platform., Comment: 14 pages, 13 figures

We observe that the comment of [1, arXiv:2302.07897] is consistent with [2] on key points: i) the microscopic mechanism of the experimentally observed teleportation is size winding and ii) the system thermalizes and scrambles at the time of teleportation. These properties are consistent with a gravitational interpretation of the teleportation dynamics, as opposed to the late-time dynamics. The objections of [1] concern counterfactual scenarios outside of the experimentally implemented protocol., Comment: 5 pages, 4 figures

We demonstrate a three-node quantum network for C-band photon pairs using 2 pairs of 59 km of deployed fiber between Fermi and Argonne National Laboratories. The C-band pairs are directed to nodes using a standard telecommunication switch and synchronized to picosecond-scale timing resolution using a coexisting O- or L-band optical clock distribution system. We measure a reduction of coincidence-to-accidental ratio (CAR) of the C-band pairs from 51 $\pm$ 2 to 5.3 $\pm$ 0.4 due to Raman scattering of the O-band clock pulses. Despite this reduction, the CAR is nevertheless suitable for quantum networks.

The Illinois Express Quantum Network (IEQNET) is a program to realize metropolitan scale quantum networking over deployed optical fiber using currently available technology. IEQNET consists of multiple sites that are geographically dispersed in the Chicago metropolitan area. Each site has one or more quantum nodes (Q-nodes) representing the communication parties in a quantum network. Q-nodes generate or measure quantum signals such as entangled photons and communicate the measurement results via standard, classical signals and conventional networking processes. The entangled photons in IEQNET nodes are generated at multiple wavelengths, and are selectively distributed to the desired users via transparent optical switches. Here we describe the network architecture of IEQNET, including the Internet-inspired layered hierarchy that leverages software-defined networking (SDN) technology to perform traditional wavelength routing and assignment between the Q-nodes. Specifically, SDN decouples the control and data planes, with the control plane being entirely implemented in the classical domain. We also discuss the IEQNET processes that address issues associated with synchronization, calibration, network monitoring, and scheduling. An important goal of IEQNET is to demonstrate the extent to which the control plane classical signals can co-propagate with the data plane quantum signals in the same fiber lines (quantum-classical signal "coexistence"). This goal is furthered by the use of tunable narrow-band optical filtering at the receivers and, at least in some cases, a wide wavelength separation between the quantum and classical channels. We envision IEQNET to aid in developing robust and practical quantum networks by demonstrating metro-scale quantum communication tasks such as entanglement distribution and quantum-state teleportation., Comment: 20 pages, 11 figures. arXiv admin note: text overlap with arXiv:2111.10256

The operation of long-distance quantum networks requires photons to be synchronized and must account for length variations of quantum channels. We demonstrate a 200 MHz clock-rate fiber optic-based quantum network using off-the-shelf components combined with custom-made electronics and telecommunication C-band photons. The network is backed by a scalable and fully automated synchronization system with ps-scale timing resolution. Synchronization of the photons is achieved by distributing O-band-wavelength laser pulses between network nodes. Specifically, we distribute photon pairs between three nodes, and measure a reduction of coincidence-to-accidental ratio from 77 to only 42 when the synchronization system is enabled, which permits high-fidelity qubit transmission. Our demonstration sheds light on the role of noise in quantum communication and represents a key step in realizing deployed co-existing classical-quantum networks., Comment: 7 pages, 7 figures

Deterministic generation of single photons is essential for many quantum information technologies. A bulk optical nonlinearity emitting a photon pair, where the measurement of one of the photons heralds the presence of the other, is commonly used with the caveat that the single-photon emission rate is constrained due to a trade-off between multiphoton events and pair emission rate. Using an efficient and low noise photon-number-resolving superconducting nanowire detector we herald, in real time, a single photon at telecommunication wavelength. We perform a second-order photon correlation $g^{2}(0)$ measurement of the signal mode conditioned on the measured photon number of the idler mode for various pump powers and demonstrate an improvement of a heralded single-photon source. We develop an analytical model using a phase-space formalism that encompasses all multiphoton effects and relevant imperfections, such as loss and multiple Schmidt modes. We perform a maximum-likelihood fit to test the agreement of the model to the data and extract the best-fit mean photon number $\mu$ of the pair source for each pump power. A maximum reduction of $0.118 \pm 0.012$ in the photon $g^{2}(0)$ correlation function at $\mu = 0.327 \pm 0.007$ is obtained, indicating a strong suppression of multiphoton emissions. For a fixed $g^{2}(0) = 7e-3$, we increase the single pair generation probability by 25%. Our experiment, built using fiber-coupled and off-the-shelf components, delineates a path to engineering ideal sources of single photons., Comment: Model and analysis integrated into main text. Corrected equations. 17 pages, 11 figures

We describe an implementation of a quantum network over installed fiber in the Chicago area.We present network topology and control architecture of this network and illustrate preliminary results for quantum teleportation and coexistence of quantum and classical data on the same fiber link.

Indistinguishable photons are imperative for advanced quantum communication networks. Indistinguishability is difficult to obtain because of environment-induced photon transformations and loss imparted by communication channels, especially in noisy scenarios. Strategies to mitigate these transformations often require hardware or software overhead that is restrictive (e.g. adding noise), infeasible (e.g. on a satellite), or time-consuming for deployed networks. Here we propose and develop resource-efficient Bayesian optimization techniques to rapidly and adaptively calibrate the indistinguishability of individual photons for quantum networks using only information derived from their measurement. To experimentally validate our approach, we demonstrate the optimization of Hong-Ou-Mandel interference between two photons -- a central task in quantum networking -- finding rapid, efficient, and reliable convergence towards maximal photon indistinguishability in the presence of high loss and shot noise. We expect our resource-optimized and experimentally friendly methodology will allow fast and reliable calibration of indistinguishable quanta, a necessary task in distributed quantum computing, communications, and sensing, as well as for fundamental investigations.

The Illinois Express Quantum Network (IEQNET) is a program to realize metro-scale quantum networking over deployed optical fiber using currently available technology. IEQNET consists of multiple sites that are geographically dispersed in the Chicago metropolitan area. Each site has one or more quantum nodes (Q-nodes) representing the communication parties in a quantum network. Q-nodes generate or measure quantum signals such as entangled photons and communicate the results via standard, classical, means. The entangled photons in IEQNET nodes are generated at multiple wavelengths, and are selectively distributed to the desired users via optical switches. Here we describe the network architecture of IEQNET, including the Internet-inspired layered hierarchy that leverages software-defined-networking (SDN) technology to perform traditional wavelength routing and assignment between the Q-nodes. Specifically, SDN decouples the control and data planes, with the control plane being entirely classical. Issues associated with synchronization, calibration, network monitoring, and scheduling will be discussed. An important goal of IEQNET is demonstrating the extent to which the control plane can coexist with the data plane using the same fiber lines. This goal is furthered by the use of tunable narrow-band optical filtering at the receivers and, at least in some cases, a wide wavelength separation between the quantum and classical channels. We envision IEQNET to aid in developing robust and practical quantum networks by demonstrating metro-scale quantum communication tasks such as entanglement distribution and quantum-state teleportation., Comment: 9 pages, 4 figures

Quantum teleportation is essential for many quantum information technologies including long-distance quantum networks. Using fiber-coupled devices, including state-of-the-art low-noise superconducting nanowire single photon detectors and off-the-shelf optics, we achieve quantum teleportation of time-bin qubits at the telecommunication wavelength of 1536.5 nm. We measure teleportation fidelities of >=90% that are consistent with an analytical model of our system, which includes realistic imperfections. To demonstrate the compatibility of our setup with deployed quantum networks, we teleport qubits over 22 km of single-mode fiber while transmitting qubits over an additional 22 km of fiber. Our systems, which are compatible with emerging solid-state quantum devices, provide a realistic foundation for a high-fidelity quantum internet with practical devices., Comment: 15 pages, 7 Figures ; fixed typos on affiliation of Christoph Simon (Calgary)

Quantum transduction, the process of converting quantum signals from one form of energy to another, is an important area of quantum science and technology. The present perspective article reviews quantum transduction between microwave and optical photons, an area that has recently seen a lot of activity and progress because of its relevance for connecting superconducting quantum processors over long distances, among other applications. Our review covers the leading approaches to achieving such transduction, with an emphasis on those based on atomic ensembles, opto-electromechanics, and electro-optics. We briefly discuss relevant metrics from the point of view of different applications, as well as challenges for the future., Comment: 13 pages, 5 figures

We design a quantum repeater architecture, necessary for long distance quantum networks, using the recently proposed microwave cat state qubits, formed and manipulated via interaction between a superconducting nonlinear element and a microwave cavity. These qubits are especially attractive for repeaters because in addition to serving as excellent computational units with deterministic gate operations, they also have coherence times long enough to deal with the unavoidable propagation delays. Since microwave photons are too low in energy to be able to carry quantum information over long distances, as an intermediate step, we expand on a recently proposed microwave to optical transduction protocol using excited states of a rare-earth ion ($\mathrm{Er^{3+}}$) doped crystal. To enhance the entanglement distribution rate, we propose to use spectral multiplexing by employing an array of cavities at each node. We compare our achievable rates with direct transmission and with two other promising repeater approaches, and show that ours could be higher in appropriate regimes, even in the presence of realistic imperfections and noise, while maintaining reasonably high fidelities of the final state. Thus, in the short term, our work could be directly useful for secure quantum communication, whereas in the long term, we can envision a large scale distributed quantum computing network built on our architecture., Comment: 16+7 pages, 8+5 figures and tables

Efficient and reversible optical to microwave coherent transducers are required to enable entanglement transfer between superconducting qubits and light for quantum networks. Rare-earth-doped crystals that possess narrow optical and spin transitions are a promising way to implement these devices. Current approaches use ground-state electron spin transitions that have coherence lifetimes ($T_2$) often limited by spin flip-flop processes and/or spectral diffusion, even at very low temperatures. Here, we investigate spin coherence in an optically excited state of an Er$^{3+}$:Y$_2$SiO$_5$ crystal at temperatures from 1.6 to 3.5 K and under a weak 8.7 mT magnetic field. Spin coherence and population lifetimes of up to 1.6 $\mu$s and 1.2 ms, respectively, are measured by 2- and 3-pulse optically-detected spin echo experiments. Analysis of the dephasing processes suggest that ms $T_2$ can be reached at lower temperatures for the excited-state spins, whereas ground-state spin states could be limited to a few $\mu$s due to resonant interactions with the other Er$^{3+}$ spins in the lattice (spin diffusion). We propose a quantum transducer scheme with the potential for close to unit efficiency that exploits the specific advantages offered by the spin states of optically excited electronic energy levels.

Highly efficient sources of indistinguishable single photons that can operate at room temperature would be very beneficial for many applications in quantum technology. We show that the implementation of such sources is a realistic goal using solid-state emitters and ultrasmall mode volume cavities. We derive and analyze an expression for photon indistinguishability that accounts for relevant detrimental effects, such as plasmon-induced quenching and pure-dephasing. We then provide the general cavity and emitter conditions required to achieve efficient indistinguishable photon emission, and also discuss constraints due to phonon sideband emission. Using these conditions, we propose that a nanodiamond negatively charged silicon-vacancy center combined with a plasmonic-Fabry-Perot hybrid cavity is an excellent candidate system., Comment: 10 pages, 4 figures

We present a detailed theoretical analysis of a Fock-state filter based on the photon-number dependent group delay in cavity induced transparency proposed in Phys. Rev. Lett. 105, 013601 (2010). We derive a general expression for the propagation velocity of different photon-number components of a light pulse interacting with an optically dense ensemble of three-level atoms coupled to a resonator mode under conditions of cavity induced transparency. These predictions are compared to numerical simulations of the propagation of few photon wave packets, and an estimation for experimental realization is made., Comment: 7 pages, 9 figures

A protocol is discussed which allows one to realize a transducer for single photons between the optical and the microwave frequency range. The transducer is a spin ensemble, where the individual emitters possess both an optical and a magnetic-dipole transition. Reversible frequency conversion is realized by combining optical photon storage, by means of EIT, with the controlled switching of the coupling between the magnetic-dipole transition and a superconducting qubit, which is realized by means of a microwave cavity. The efficiency is quantified by the global fidelity for transferring coherently a qubit excitation between a single optical photon and the superconducting qubit. We test various strategies and show that the total efficiency is essentially limited by the optical quantum memory: It can exceed 80% for ensembles of NV centers and approaches 99% for cold atomic ensembles, assuming state-of-the-art experimental parameters. This protocol allows one to bridge the gap between the optical and the microwave regime so to efficiently combine superconducting and optical components in quantum networks.

We propose a scheme to couple short single photon pulses to superconducting qubits. An optical photon is first absorbed into an inhomogeneously broadened rare-earth doped crystal using controlled reversible inhomogeneous broadening. The optical excitation is then mapped into a spin state using a series of $\pi$-pulses and subsequently transferred to a superconducting qubit via a microwave cavity. To overcome the intrinsic and engineered inhomogeneous broadening of the optical and spin transitions in rare earth doped crystals, we make use of a special transfer protocol using staggered $\pi$-pulses. We predict total transfer efficiencies on the order of 90%., Comment: 5 pages, 3 figures

We study the effects of the four-wave mixing (4WM) in a quantum memory scheme based on electromagnetically induced transparency (EIT). We treat the problem of field propagation on the quantum mechanical level, which allows us to calculate the fidelity for propagation for a quantum light pulse such as a single photon. While 4WM can be beneficial for classical, all-optical information storage, the quantum noise associated with the signal amplification and idler generation is in general detrimental for a quantum memory. We identify a range of parameters where 4WM makes a single photon quantum memory impossible.