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Quantum simulations are becoming an essential tool for studying complex phenomena, e.g. quantum topology, quantum information transfer, and relativistic wave equations, beyond the limitations of analytical computations and experimental observations. To date, the primary resources used in proof-of-principle experiments are collections of qubits, coherent states or multiple single-particle Fock states. Here we show the first quantum simulation performed using genuine higher-order Fock states, with two or more indistinguishable particles occupying the same bosonic mode. This was implemented by interfering pairs of Fock states with up to five photons on an interferometer, and measuring the output states with photon-number-resolving detectors. Already this resource-efficient demonstration reveals new topological matter, simulates non-linear systems and elucidates a perfect quantum transfer mechanism which can be used to transport Majorana fermions., Comment: New text and results. 19 pages, 13 figures, supplementary material

The tantalizing promise of quantum computational speedup in solving certain problems has been strongly supported by recent experimental evidence from a high-fidelity 53-qubit superconducting processor1 and Gaussian boson sampling (GBS) with up to 76 detected photons. Analogous to the increasingly sophisticated Bell tests that continued to refute local hidden variable theories, quantum computational advantage tests are expected to provide increasingly compelling experimental evidence against the Extended Church-Turing thesis. In this direction, continued competition between upgraded quantum hardware and improved classical simulations is required. Here, we report a new GBS experiment that produces up to 113 detection events out of a 144-mode photonic circuit. We develop a new high-brightness and scalable quantum light source, exploring the idea of stimulated squeezed photons, which has simultaneously near-unity purity and efficiency. This GBS is programmable by tuning the phase of the input squeezed states. We demonstrate a new method to efficiently validate the samples by inferring from computationally friendly subsystems, which rules out hypotheses including distinguishable photons and thermal states. We show that our noisy GBS experiment passes the nonclassicality test using an inequality, and we reveal non-trivial genuine high-order correlation in the GBS samples, which are evidence of robustness against possible classical simulation schemes. The photonic quantum computer, Jiuzhang 2.0, yields a Hilbert space dimension up to $10^{43}$, and a sampling rate $10^{24}$ faster than using brute-force simulation on supercomputers., 23 pages, 6 figures. Comments are welcome

The development of large-scale optical quantum information processing circuits ground on the stability and reconfigurability enabled by integrated photonics. We demonstrate a reconfigurable 8x8 integrated linear optical network based on silicon nitride waveguides for quantum information processing. Our processor implements a novel optical architecture enabling any arbitrary linear transformation and constitutes the largest programmable circuit reported so far on this platform. We validate a variety of photonic quantum information processing primitives, in the form of Hong-Ou-Mandel interference, bosonic coalescence/anticoalescence and high-dimensional single-photon quantum gates. We achieve fidelities that clearly demonstrate the promising future for large-scale photonic quantum information processing using low-loss silicon nitride., Comment: Added supplementary materials, extended introduction, new figures, results unchanged

Recently, quantum advantage over classical computation has been claimed using photons [1] . To control photonic quantum computations such as Boson sampling, a non-universal approach on quantum computation, large-scale quantum processors are needed [2] , [3] . To realize scalable and robust photonic quantum processors integrated photonics is a key technology. In our approach we use the integrated waveguide platform based on silicon nitride [4] , due to its low intrinsic losses and technological maturity. The low losses result in a high fidelity of the quantum photonics processor which is mandatory for reliable quantum computation while maturity of the platform allows for scaling up of the dimensions of the processor. Here, we present a universal 12-mode quantum photonics processor which is the largest of its kind to date.

Photonic processors are pivotal for both quantum and classical information processing tasks using light. In particular, linear optical quantum information processing requires both large-scale and low-loss programmable photonic processors. In this paper, we report the demonstration of the largest universal quantum photonic processor to date: a low-loss 12-mode fully tunable linear interferometer with all-to-all mode coupling based on stoichiometric silicon nitride waveguides.

Photonics integration is a key technology for realizing large-scale photonic quantum information processing. We demonstrate state-of-art reconfigurable photonic processors based on low-loss silicon nitride waveguide networks. We present the science behind such a processor, which consists of a large mesh of integrated reconfigurable Mach Zehnder interferometers. In this talk, we will present the newest results of the current generation of our programmable quantum photonic processors obtained by classical as well as quantum optical characterization. Furthermore, we show the challenges of scaling up quantum photonic processors and the range of potential applications of large-scale quantum information processing those will enable.

Verification of a quantum advantage in the presence of noise is a key open problem in the study of near-term quantum devices. In this work, we show how to assess the quality of photonic interference in a linear optical quantum device (boson sampler) by using a maximum likelihood method to measure the strength at which various noise sources are present in the experiment. This allows us to use a sparse set of samples to test whether a given boson-sampling experiment meets known upper bounds on the level of noise permissible to demonstrate a quantum advantage. Furthermore, this method allows us to monitor the evolution of noise in real time, creating a valuable diagnostic tool. Finally, we observe that sources of noise in the experiment compound, meaning that the observed value of the mutual photon indistinguishability, which is the main imperfection in our study, is an effective value taking into account all sources of error in the experiment.

We study the hardness of classically simulating boson sampling with superposition and Gaussian input states at nonzero photon indistinguishability. We find that, similar to regular boson sampling, distinguishability causes exponential attenuation of the many-photon interference terms in both these boson sampling variants. For superposition sampling, we find that it is not simulable with out method at zero indistinguishability, which is evidence for the computational hardness of this problem, and we find that it is simulable at any level of particle distinguishability, similar to regular boson sampling. If an efficient classical algorithm to approximate a given sum over permanents is found, this approach also leads to an efficient classical algorithm to simulate Gaussian boson sampling in the presence of distinguishability.

We show a method for assessing the quality of photonic quantum interference (boson sampling) in the regime of fewer samples than outcomes. We present an error budget for a state of the art boson sampler.

Boson Sampling is the problem of sampling from the same distribution as indistinguishable single photons at the output of a linear optical interferometer. It is an example of a non-universal quantum computation which is believed to be feasible in the near term and cannot be simulated on a classical machine. Like all purported demonstrations of "quantum supremacy", this motivates optimizing classical simulation schemes for a realistic model of the problem, in this case Boson Sampling when the implementations experience lost or distinguishable photons. Although current simulation schemes for sufficiently imperfect boson sampling are classically efficient, in principle the polynomial runtime can be infeasibly large. In this work, we develop a scheme for classical simulation of Boson Sampling under uniform distinguishability and loss, based on the idea of sampling from distributions where at most k photons are indistinguishable. We show that asymptotically this scheme can provide a polynomial improvement in the runtime compared to classically simulating idealised Boson Sampling. More significantly, we show that in the regime considered experimentally relevant, our approach gives an substantial improvement in runtime over other classical simulation approaches., Comment: 15 pages, 5 figures, comments welcome

Universal linear optical networks made of on-chip tunable beam splitters and phase shifters form a very promising platform for quantum information processing (QIP). Thanks to their phase stability and reconfigurability, they are robust and enable a variety of quantum information and communication protocols such as quantum teleportation [1], quantum key distribution [2], photonic qubit gate protocols [3] and boson sampling [4]. Two known materials for on-chip platforms are silicon-on-insulator (SOI) and doped silica, where SOI allows for a high component density due to its high index contrast and silica has a low loss.

Gaussian boson sampling is a promising scheme for demonstrating a quantum computational advantage using photonic states that are accessible in a laboratory and, thus, offer scalable sources of quantum light. In this contribution, we study two-point photon-number correlation functions to gain insight into the interference of Gaussian states in optical networks. We investigate the characteristic features of statistical signatures which enable us to distinguish classical from quantum interference. In contrast to the typical implementation of boson sampling, we find additional contributions to the correlators under study which stem from the phase dependence of Gaussian states and which are not observable when Fock states interfere. Using the first three moments, we formulate the tools required to experimentally observe signatures of quantum interference of Gaussian states using two outputs only. By considering the current architectural limitations in realistic experiments, we further show that a statistically significant discrimination between quantum and classical interference is possible even in the presence of loss, noise, and a finite photon-number resolution. Therefore, we formulate and apply a theoretical framework to benchmark the quantum features of Gaussian boson sampling under realistic conditions.

We show that boson sampling is classically simulable in the presence of linear loss (constant per-photon transmission). We discuss the impact that this has on experimental efforts to demonstrate a quantum advantage.

Integrated universal linear optical networks are essential for the development of quantum information processing (QIP). We demonstrate a universal, reconfigurable, 8×8 photonic processor based on Si3N4 waveguides showing a variety of QIP primitives.

Integrated universal linear optical networks are essential for the development of quantum information processing (QIP). We demonstrate a universal, reconfigurable, 8×8 photonic processor based on Si3N4 waveguides showing a variety of QIP primitives.

The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode many-body quantum correlations and go beyond the usual phase-space formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.

We demonstrate how boson sampling with photons of partial distinguishability can be expressed in terms of interference of fewer photons. We use this observation to propose a classical algorithm to simulate the output of a boson sampler fed with photons of partial distinguishability. We find conditions for which this algorithm is efficient, which gives a lower limit on the required indistinguishability to demonstrate a quantum advantage. Under these conditions, adding more photons only polynomially increases the computational cost to simulate a boson sampling experiment.

Superconducting nanowire single photon detectors (SNSPD) made from amorphous superconductors have showed great promise for achieving high fabrication yields, due to the highly uniform nature of the films. We present progress on the development of SNSPD based on amorphous MoSi with a critical temperature of around 5 K, which is ideal for detector operation at temperatures of 1 – 2.5 K, accessible with widely available cryogenic systems. First generation devices have achieved a saturated internal efficiency from visible to near-infrared wavelengths, which is the first requirement for high overall system efficiency. The broadband response has allowed us to make a robust study the energy-current relation in these devices, which defines the current required for a saturated internal detection efficiency for a given incident photon energy. Contrary to previous studies with other material systems, we find a nonlinear energy-current relation, which is an important insight into the detection mechanism in SNSPDs. The latest generation devices have been embedded into an micro-cavity structure in order to increase the system detection efficiency, which has increased to over 65% at 1550 nm. The efficiency is believed to be limited by fabrication imperfections and we present ongoing progress towards improving this characteristic as well as the yield of the devices. Efforts are also being made towards increasing the maximum operating temperature of the devices.

Quantum optics experiments are increasingly taking an integrated format for the benefits of phase stability and scalability. Silica has proved an advantageous material for this work due to its low propagation loss and high-efficiency coupling to optical fibre, and a number of key on-chip experiments have already been carried out with up to four photons using this material [1]. Fabrication imperfections create a number of difficulties in moving to more complex setups since the classical performance of the network must be characterised before an analysis of its quantum properties can be carried out, and this process becomes greatly more challenging as the circuit complexity grows.

We propose an optimized design for nanowire superconducting single photon detectors, using the recently discovered position dependent detection efficiency in these devices. This knowledge allows an optimized the design of meandering wire NbN detectors by altering the field distribution across the wire. In order to calculate the response of the detectors with different geometries, we use a monotonic local detection efficiency from a nanowire and optical absorption distribution via finite-different-time-domain simulations. The calculations predict a trade-off between average absorption and the edge effect leading to a predicted optimal wire width close to 100 nm for 1550 nm wavelength, which drops to 50 nm wire width for 600 nm wavelength. The absorption at the edges can be enhanced by depositing a silicon nanowire on top of the superconducting nanowire, which improves both the total absorption efficiency as well as the internal detection efficiency of meandering wire structures., 10 pages, 5 figures

We introduce a method for the verification of nonclassical light which is independent of the complex interaction between the generated light and the material of the detectors. This is accomplished by means of a multiplexing arrangement. Its theoretical description yields that the coincidence statistics of this measurement layout is a mixture of multinomial distributions for any classical light field and any type of detector. This allows us to formulate bounds on the statistical properties of classical states. We apply our directly accessible method to heralded multiphoton states which are detected with a single multiplexing step only and two detectors, which are in our work superconducting transition-edge sensors. The nonclassicality of the generated light is verified and characterized through the violation of the classical bounds without the need for characterizing the used detectors., Comment: close to published version

In a recent contribution, we introduced and applied a detector-independent method to uncover nonclassicality. Here, we extend those techniques and give more details on the performed analysis. We derive a general theory of the positive-operator-valued measure that describes multiplexing layouts with arbitrary detectors. From the resulting quantum version of a multinomial statistics, we infer nonclassicality probes based on a matrix of normally ordered moments. We discuss these criteria and apply the theory to our data which are measured with superconducting transition-edge sensors. Our experiment produces heralded multi-photon states from a parametric down-conversion light source. We show that the known notions of sub-Poisson and sub-binomial light can be deduced from our general approach, and we establish the concept of sub-multinomial light, which is shown to outperform the former two concepts of nonclassicality for our data., close to published version

It has recently been shown that optical parametric oscillator (OPO) Ising machines, consisting of coupled optical pulses circulating in a cavity with parametric gain, can be used to probabilistically find low-energy states of Ising spin systems. In this work, we study optical Ising machines that operate under simplified Gaussian dynamics. We show that these dynamics are sufficient for reaching probabilities of success comparable to previous work. Based on this result, we propose modified optical Ising machines with simpler designs that do not use parametric gain yet achieve similar performance, thus suggesting a route to building much larger systems., 6 pages

Photon losses are among the strongest imperfections affecting multi-photon interference. Despite their importance, little is known about their effect on boson sampling experiments. In this work we show that using classical computers, one can efficiently simulate multi-photon interference in all architectures that suffer from an exponential decay of the transmission with the depth of the circuit, such as integrated photonic circuits or optical fibers. We prove that either the depth of the circuit is large enough that it can be simulated by thermal noise with an algorithm running in polynomial time, or it is shallow enough that a tensor network simulation runs in quasi-polynomial time. This result suggests that in order to implement a quantum advantage experiment with single-photons and linear optics new experimental platforms may be needed., info:eu-repo/semantics/published

We experimentally investigate the detection mechanism in a meandered molybdenum silicide (MoSi) superconducting nanowire single-photon detector by characterising the detection probability as a function of bias current in the wavelength range of 750 to 2050 nm. Contrary to some previous observations on niobium nitride (NbN) or tungsten silicide (WSi) detectors, we find that the energy-current relation is nonlinear in this range. Furthermore, thanks to the presence of a saturated detection efficiency over the whole range of wavelengths, we precisely quantify the shape of the curves. This allows a detailed study of their features, which are indicative of both Fano fluctuations and position-dependent effects.

We perform quantum state reconstruction of coherent and thermal states with a detector which has an enhanced multiphoton response. The detector is based on superconducting nanowires, where the bias current sets the dependence of the click probability on the photon number; this bias current is used as tuning parameter in the state reconstruction. The nonlinear response makes our nanowire-based detector superior to the linear detectors that are conventionally used for quantum state reconstruction., Comment: revision of intro compared to V1

Hybrid light-matter networks offer the promise for delivering robust quantum information processing technologies, from sensor arrays to quantum simulators. New sources, detectors and memories illustrate progress towards build a resilient, scalable photonic quantum network.

We use quantum detector tomography to investigate the detection mechanism in WSi nanowire superconducting single photon detectors (SSPDs). To this purpose, we fabricated a 250nm wide and 250nm long WSi nanowire and measured its response to impinging photons with wavelengths ranging from $\lambda$ = 900 nm to $\lambda$ = 1650 nm. Tomographic measurements show that the detector response depends on the total excitation energy only. Moreover, for energies Et > 0.8eV the current energy relation is linear, similar to what was observed in NbN nanowires, whereas the current-energy relation deviates from linear behaviour for total energies below 0.8eV.

We probe the local detection efficiency in a nanowire superconducting single-photon detector along the cross-section of the wire with a far subwavelength resolution. We experimentally find a strong variation in the local detection efficiency of the device. We demonstrate that this effect explains previously observed variations in NbN detector efficiency as a function of device geometry.

We determine the full photon number response of a NbN superconducting nanowire single photon detector via quantum detector tomography, and the results show the separation of linear, effective absorption efficiency from the internal detection efficiencies. In addition, we demonstrate an error budget for the complete quantum characterization of the detector. We find that for short times, the dominant noise source is shot noise, while laser power fluctuations limit the accuracy for longer timescales. The combined standard uncertainty of the internal detection efficiency derived from our measurements is about 2%. (C) 2015 AIP Publishing LLC.

We use quantum detector tomography to identify photon assisted vortex entry as the photon detection mechanism in superconducting NbN nanowires. We exploit the polarization dependence to resolve the response of the nanowire with subwavelength resolution.

In this paper we intend to give a comprehensive description of the current understanding of the detection mechanism in superconducting nanowire single-photon detectors. We will review key experimental results related to the detection mechanism, e.g. the variations of the detection probability as a function of bias current, temperature or magnetic field. Commonly used detection models will be introduced and we will analyze their predictions in view of the experimental observations. Although none of the proposed detection models is able to describe all experimental data, it is becoming increasingly clear that vortices are essential for the formation of the initial normal-conducting domain that triggers a detection event.

International audience; We experimentally investigate the effect of a magnetic field on photon detection in superconducting single-photon detectors (SSPDs). At low fields, the effect of a magnetic field is through the direct modification of the quasiparticle density of states of the superconductor, and magnetic field and bias current are interchangeable, as is expected for homogeneous dirty-limit superconductors. At the field where a first vortex enters the detector, the effect of the magnetic field is reduced, up until the point where the critical current of the detector starts to be determined by flux flow. From this field on, increasing the magnetic field does not alter the detection of photons anymore, whereas it does still change the rate of dark counts. This result points at an intrinsic difference in dark and photon counts, and also shows that no enhancement of the intrinsic detection efficiency of a straight SSPD wire is achievable in a magnetic field. (C) 2015 AIP Publishing LLC.

Using detector tomography, we investigate the detection mechanism in NbN-based superconducting single photon detectors (SSPDs). We demonstrate that the detection probability uniquely depends on a particular linear combination of bias current and energy, for a large variation of bias currents, input energies and detection probabilities, producing a universal detection curve. We obtain this result by studying multiphoton excitations in a nanodetector with a sparsity-based tomographic method that allows factoring out of the optical absorption. We discuss the implication of our model system for the understanding of meander-type SSPDs., Comment: Revised version

Spatial quantum correlations are an important resource for quantum imaging and future quantum technologies based on high-dimensional entanglement. We experimentally explore spatial correlations in four-photon states generated by a highly efficient parametric down-conversion process in a 2 mm long periodically poled KTP crystal. The four-photon states produced in the crystal contain a contribution due to independent double pairs produced via spontaneous pair emission and a highly correlated four-photon state produced by stimulated emission of a second photon pair. We separate this contribution and introduce a joint spatial density for stimulated pair emission. We observe a maximum visibility $\ensuremath{\chi}=0.25$ of the four-photon state for a 1.5 nm bandpass filter.

We explore four-photon spatial entanglement created by stimulated emission of photon pairs in a 2 mm long periodically poled KTP crystal. We vary the experimental conditions to explore and optimize the visiblity of stimulated pairs.

We demonstrate high fidelity quantum state reconstruction of coherent and thermal states of light using a single NbN superconducting single photon detector (SSPD). SSPDs outperform commonly used avalanche photodiodes for the task of quantum state reconstruction.

We present an experimental method to characterize multi-photon detectors with a small overall detection efficiency. We do this by separating the nonlinear action of the multiphoton detection event from linear losses in the detector. Such a characterization is a necessary step for quantum information protocols with single and multiphoton detectors and can provide quantitative information to understand the underlying physics of a given detector. This characterization is applied to a superconducting multiphoton nanodetector, consisting of an NbN nanowire with a bowtie-shaped subwavelength constriction. Depending on the bias current, this detector has regimes with single and multiphoton sensitivity. We present the first full experimental characterization of such a detector.

Room temperature atomic ensembles in a spin-protected environment are useful systems both for quantum information science and metrology. Here we utilize a setup consisting of two atomic ensembles as a memory for quantum information initially encoded in the polarization state of two entangled light modes. We also use the ensembles as a radio frequency entanglement-assisted magnetometer with projection noise limited sensitivity below femtoTesla/. The performance of the quantum memory as well as the magnetometer was improved by spin-squeezed or entangled atomic states generated by quantum non demolition measurements. Finally, we present preliminary results of long lived entangled atomic states generated by dissipation. With the method presented, one should be able to generate an entangled steady state.