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We experimentally demonstrate a testing strategy for boson samplers that is based on efficiently computable expressions for the output photon counting distributions binned over multiple optical modes. We apply this method to validate boson sampling experiments with three photons on a reconfigurable photonic chip, which implements a four-mode interferometer, analyzing 50 Haar-random unitary transformations while tuning photon distinguishability via controlled delays. We show that for high values of indistinguishability, the experiment accurately reproduces the ideal boson sampling binned-mode distributions, which exhibit variations that depend both on the specific interferometer implemented as well as the choice of bin, confirming the usefulness of the method to diagnose imperfections such as partial distinguishability or imperfect chip control. Finally, we analyze the behavior of Haar-averaged binned-mode distributions with partial distinguishability and demonstrate analytically that its variance is proportional to the average of the square of the photons' indistinguishability parameter. These findings highlight the central role of binning in boson sampling validation, offering a scalable and efficient framework for assessing multiphoton interference and experimental performance., Comment: 21 pages, 14 figures

In the quest to build general-purpose photonic quantum computers, fusion-based quantum computation has risen to prominence as a promising strategy. This model allows a ballistic construction of large cluster states which are universal for quantum computation, in a scalable and loss-tolerant way without feed-forward, by fusing many small n-photon entangled resource states. However, a key obstacle to this architecture lies in efficiently generating the required essential resource states on photonic chips. One such critical seed state that has not yet been achieved is the heralded three-photon Greenberger-Horne-Zeilinger (3-GHZ) state. Here, we address this elementary resource gap, by reporting the first experimental realization of a heralded dual-rail encoded 3-GHZ state. Our implementation employs a low-loss and fully programmable photonic chip that manipulates six indistinguishable single photons of wavelengths in the telecommunication regime. Conditional on the heralding detection, we obtain the desired 3-GHZ state with a fidelity 0.573+-0.024. Our work marks an important step for the future fault-tolerant photonic quantum computing, leading to the acceleration of building a large-scale optical quantum computer., Comment: Submitted. Comments are welcome!

We report new Gaussian boson sampling experiments with pseudo-photon-number-resolving detection, which register up to 255 photon-click events. We consider partial photon distinguishability and develop a more complete model for the characterization of the noisy Gaussian boson sampling. In the quantum computational advantage regime, we use Bayesian tests and correlation function analysis to validate the samples against all current classical mockups. Estimating with the best classical algorithms to date, generating a single ideal sample from the same distribution on the supercomputer Frontier would take ~ 600 years using exact methods, whereas our quantum computer, Jiuzhang 3.0, takes only 1.27 us to produce a sample. Generating the hardest sample from the experiment using an exact algorithm would take Frontier ~ 3.1*10^10 years., Comment: PRL 2023 to appear

The unification of general relativity and quantum theory is one of the fascinating problems of modern physics. One leading solution is Loop Quantum Gravity (LQG). Simulating LQG may be important for providing predictions which can then be tested experimentally. However, such complex quantum simulations cannot run efficiently on classical computers, and quantum computers or simulators are needed. Here, we experimentally demonstrate quantum simulations of spinfoam amplitudes of LQG on an integrated photonics quantum processor. We simulate a basic transition of LQG and show that the derived spinfoam vertex amplitude falls within 4% error with respect to the theoretical prediction, despite experimental imperfections. We also discuss how to generalize the simulation for more complex transitions, in realistic experimental conditions, which will eventually lead to a quantum advantage demonstration as well as expand the toolbox to investigate LQG., Comment: 5 pages, 4 figures. comments are welcome

Reconfigurable quantum photonic processors are an essential technology for photonic quantum computing. Although most large-scale reconfigurable quantum photonic processors were demonstrated at the telecommunications C band around 1550 nm, high-performance single photon light sources utilizing quantum dots that are well-suited for photonic quantum computing operate at a variety of wavelengths. Thus, a demand exists for the compatibility of quantum photonic processors with a larger wavelength range. Silicon nitride (SiN) has a high confinement and wide transparency window, enabling compact, low-loss quantum photonic processors at wavelengths outside the C band. Here, we report a SiN universal 12-mode quantum photonic processor with optimal operation at a wavelength of 940 nm, which is compatible with InGaAs quantum dot light sources that emit light in the 900 nm to 970 nm wavelength range. The processor can implement arbitrary unitary transformations on its 12 input modes with a fidelity of 98.6 %, with a mean optical loss of 3.4 dB/mode.

Integrated photonics is an essential technology for optical quantum computing. Universal, phase-stable, reconfigurable multimode interferometers (quantum photonic processors) enable manipulation of photonic quantum states and are one of the main components of photonic quantum computers in various architectures. In this paper, we report the realization of the largest quantum photonic processor to date. The processor enables arbitrary unitary transformations on its 20 input modes with an amplitude fidelity of $F_{\text{Haar}} = 97.4\%$ and $F_{\text{Perm}} = 99.5\%$ for Haar-random and permutation matrices, respectively, an optical loss of 2.9 dB averaged over all modes, and high-visibility quantum interference with $V_{\text{HOM}}=98\%$. The processor is realized in $\mathrm{Si_3N_4}$ waveguides and is actively cooled by a Peltier element., Comment: Added authors Narasimhan Kannan and Ward L. Vleeshouwers that were missing. Added references and further technical information. Corrected the name of the funding agency (NWO). Made changes after acceptance for publication in Quantum

Efficient and reliable measurements of photonic indistinguishability are crucial to solidify claims of a quantum advantage in photonics. Existing indistinguishability witnesses may be vulnerable to implementation loopholes, showing the need for a measurement which depends on as few assumptions as possible. Here, we introduce a semi-device-independent witness of photonic indistinguishability and measure it on an integrated photonic processor, certifying three-photon indistinguishability in a way that is insensitive to implementation errors in our processor.

The existence of fully transmissive eigenchannels ("open channels") in a random scattering medium is a counterintuitive and unresolved prediction of random matrix theory. The smoking gun of such open channels, namely a bimodal distribution of the transmission efficiencies of the scattering channels, has so far eluded experimental observation. We observe an experimental distribution of transmission efficiencies that obeys the predicted bimodal Dorokhov-Mello-Pereyra-Kumar distribution. Thereby we show the existence of open channels in a linear optical scattering system. The characterization of the scattering system is carried out by a quantum-optical readout method. We find that missing a single channel in the measurement already prevents detection of the open channels, illustrating why their observation has proven so elusive until now. Our work confirms a long-standing prediction of random matrix theory underlying wave transport through disordered systems., Comment: 9 pages including methods and supplementary materials. 3 figures

With the recent claim of a quantum advantage demonstration in photonics by Zhong et al, the question of the computation of lower-order approximations of boson sampling with arbitrary quantum states at arbitrary distinguishability has come to the fore. In this work, we present results in this direction, building on the results of Clifford and Clifford. In particular, we show: 1) How to compute marginal detection probabilities (i.e. probabilities of the detection of some but not all photons) for arbitrary quantum states. 2) Using the first result, how to generalize the sampling algorithm of Clifford and Clifford to arbitrary photon distinguishabilities and arbitrary input quantum states. 3) How to incorporate truncations of the quantum interference into a sampling algorithm. 4) A remark considering maximum likelihood verification of the recent photonic quantum advantage experiment.

Photonic processors are pivotal for both quantum and classical information processing tasks using light. In particular, linear optical quantum information processing requires both largescale 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 coupling based on stoichiometric silicon nitride waveguides.

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 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 Gaussian boson sampling at nonzero photon distinguishability. We find that similar to regular boson sampling, distinguishability causes exponential attenuation of the many-photon interference terms in Gaussian boson sampling. Barring an open problem in the theory of matrix permanents, this leads to an efficient classical algorithm to simulate Gaussian boson sampling in the presence of distinguishability. We also study a new form of boson sampling based on photon number superposition states, for which we also show noise sensivity. The fact that such superposition boson sampling is not simulable with out method at zero distinguishability is the first evidence for the computational hardness of this problem.

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

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

We propose and demonstrate a modular architecture for reconfigurable on-chip linear-optical circuits. Each module contains 10 independent phase-controlled Mach-Zehnder interferometers; several such modules can be connected to each other to build large reconfigurable interferometers. With this architecture, large interferometers are easier to build and characterize than with traditional, bespoke, monolithic designs. We demonstrate our approach by fabricating three modules in the form of UV-written silica-on-silicon chips. We characterize these chips, connect them to each other, and implement a wide range of linear optical transformations. We envisage that this architecture will enable many future experiments in quantum optics., Comment: 5 pages, 3 figures

The current shift in the quantum optics community towards large-size experiments -- with many modes and photons -- necessitates new classical simulation techniques that go beyond the usual phase space formulation of quantum mechanics. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. As a toy model, 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.

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.

We study the impact of experimental imperfections on a recently proposed protocol for performing quantum simulations of vibronic spectroscopy. Specifically, we propose a method for quantifying the impact of these imperfections, optimizing an experiment to account for them, and benchmarking the results against a classical simulation method. We illustrate our findings using a proof of principle experimental simulation of part of the vibronic spectrum of tropolone. Our findings will inform the design of future experiments aiming to simulate the spectra of large molecules beyond the reach of current classical computers., Comment: 11 pages

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.

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., Comment: 6 pages

We numerically investigate the implementation of Haar-random unitarity transformations and Fourier transformations in photonic devices consisting of beam splitters and phase shifters, which are used for integrated photonics implementations of boson sampling. The distribution of reflectivities required to implement an arbitrary unitary transformation is skewed towards low values, and this skew becomes stronger the larger the number of modes. A realistic implementation using Mach-Zehnder interferometers is incapable of doing this perfectly and thus has limited fidelity. We show that numerical optimisation and adding extra beam splitters to the network can help to restore fidelity.

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., Comment: 10 pages, 5 figures

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 spatial resolution of 10 nm. 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 function of device geometry.

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

We use a quantum non-demolition measurement to generate a spin squeezed state and to create entanglement in a cloud of 10^5 cold cesium atoms, and for the first time operate an atomic clock improved by spin squeezing beyond the projection noise limit in a proof-of-principle experiment. For a clock-interrogation time of 10 \mu\s the experiments show an improvement of 1.1 dB in the signal-to-noise ratio, compared to the atomic projection noise limit.