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Boson sampling represents a promising approach to obtain evidence of the supremacy of quantum systems as a resource for the solution of computational problems. The classical hardness of Boson Sampling has been related to the so called Permanent-of-Gaussians Conjecture and has been extended to some generalizations such as Scattershot Boson Sampling, approximate and lossy sampling under some reasonable constraints. However, it is still unclear how demanding these techniques are for a quantum experimental sampler. Starting from a state of the art analysis and taking account of the foreseeable practical limitations, we evaluate and discuss the bound for quantum supremacy for different recently proposed approaches, accordingly to today's best known classical simulators.

Boson sampling (BS) is viewed to be an accessible quantum computing paradigm to demonstrate computational advantage compared to classical computers. In this context, the evolution of permanent calculation algorithms attracts a significant attention as the simulation of BS experiments involves the evaluation of vast number of permanents. For this reason, we generalize the Balasubramanian–Bax–Franklin–Glynn permanent formula, aiming to efficiently integrate it into the BS strategy of Clifford and Clifford (2020 Faster classical boson sampling). A reduction in simulation complexity originating from multiplicities in photon occupation was achieved through the incorporation of a n-ary Gray code ordering of the addends during the permanent evaluation. Implementing the devised algorithm on FPGA-based data-flow engines, we leverage the resulting tool to accelerate boson sampling simulations for up to 40 photons. Drawing samples from a 60-mode interferometer, the achieved rate averages around 80 s per sample, employing 4 FPGA chips. The developed design facilitates the simulation of both ideal and lossy boson sampling experiments.

Boson sampling is a computational problem that has recently been proposed as a candidate to obtain an unequivocal quantum computational advantage. The problem consists in sampling from the output distribution of indistinguishable bosons in a linear interferometer. There is strong evidence that such an experiment is hard to classically simulate, but it is naturally solved by dedicated photonic quantum hardware, comprising single photons, linear evolution, and photodetection. This prospect has stimulated much effort resulting in the experimental implementation of progressively larger devices. We review recent advances in photonic boson sampling, describing both the technological improvements achieved and the future challenges. We also discuss recent proposals and implementations of variants of the original problem, theoretical issues occurring when imperfections are considered, and advances in the development of suitable techniques for validation of boson sampling experiments. We conclude by discussing the future application of photonic boson sampling devices beyond the original theoretical scope.

We explore the possibility of efficient classical simulation of linear optics experiments under the effect of particle losses. Specifically, we investigate the canonical boson sampling scenario in which an n-particle Fock input state propagates through a linear-optical network and is subsequently measured by particle-number detectors in the m output modes. We examine two models of losses. In the first model a fixed number of particles is lost. We prove that in this scenario the output statistics can be well approximated by an efficient classical simulation, provided that the number of photons that is left grows slower than n . In the second loss model, every time a photon passes through a beamsplitter in the network, it has some probability of being lost. For this model the relevant parameter is s, the smallest number of beamsplitters that any photon traverses as it propagates through the network. We prove that it is possible to approximately simulate the output statistics already if s grows logarithmically with m, regardless of the geometry of the network. The latter result is obtained by proving that it is always possible to commute s layers of uniform losses to the input of the network regardless of its geometry, which could be a result of independent interest. We believe that our findings put strong limitations on future experimental realizations of quantum computational supremacy proposals based on boson sampling.

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute—given a many-body state|ψ⟩,Ox(t)Oy|ψ⟩≈OyOx(t)|ψ⟩with arbitrarily small errors—so long as|x−y|≳vt, wherevis finite. Yet, most nonrelativistic physical systems realized in nature have long-range interactions: Two degrees of freedom separated by a distancerinteract with potential energyV(r)∝1/rα. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: At the sameα, some quantum information processing tasks are constrained by a linear light cone, while others are not. In one spatial dimension, this linear light cone exists for every many-body state|ψ⟩whenα>3(Lieb-Robinson light cone); for a typical state|ψ⟩chosen uniformly at random from the Hilbert space whenα>52(Frobenius light cone); and for every state of a noninteracting system whenα>2(free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones—and their tightness—also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, is bounded by the Frobenius light cone and, therefore, is poorly constrained by all Lieb-Robinson bounds.

Random unitary matrices find a number of applications in quantum information science, and are central to the recently defined boson sampling algorithm for photons in linear optics. We describe an operationally simple method to directly implement Haar random unitary matrices in optical circuits, with no requirement for prior or explicit matrix calculations. Our physically motivated and compact representation directly maps independent probability density functions for parameters in Haar random unitary matrices, to optical circuit components. We go on to extend the results to the case of random unitaries for qubits.

Transmon qubits have traditionally been regarded as limited to random circuit sampling, incapable of performing Fock state boson sampling—a problem known to be classically intractable. This work challenges that assumption by introducing q-boson Fock state sampling, a variant in which transmon qubits can operate effectively. Through direct mapping to the q-boson formalism, we demonstrate that transmons possess the capability to achieve quantum supremacy in q-boson sampling tasks. This finding expands the potential applications of transmon-based quantum processors and paves the way for new avenues in quantum computation.

The superconducting nanowire single-photon detector (SNSPD) is a quantum-limit superconducting optical detector based on the Cooper-pair breaking effect by a single photon, which exhibits a higher detection efficiency, lower dark count rate, higher counting rate, and lower timing jitter when compared with those exhibited by its counterparts. SNSPDs have been extensively applied in quantum information processing, including quantum key distribution and optical quantum computation. In this review, we present the requirements of single-photon detectors from quantum information, as well as the principle, key metrics, latest performance issues, and other issues associated with SNSPD. The representative applications of SNSPDs with respect to quantum information will also be covered.

We study the sampling complexity of a probability distribution associated with an ensemble of identical noninteracting bosons undergoing a quantum random walk on a one-dimensional lattice. With uniform nearest-neighbor hopping we show that one can efficiently sample the distribution for times logarithmic in the size of the system, while for longer times there is no known efficient sampling algorithm. With time-dependent hopping and optimal control, we design the time evolution to approximate an arbitrary Haar-random unitary map analogous to that designed for photons in a linear optical network. This approach highlights a route to generating quantum complexity by optimal control only of a single-body unitary matrix. We study this in the context of two potential experimental realizations: a spinor optical lattice of ultracold atoms and a quantum gas microscope.

Photon indistinguishability plays a fundamental role in information processing, with applications such as linear-optical quantum computation and metrology. It is then necessary to develop appropriate tools to quantify the amount of this resource in a multiparticle scenario. Here we report a four-photon experiment in a linear-optical interferometer designed to simultaneously estimate the degree of indistinguishability between three pairs of photons. The interferometer design dispenses with the need of heralding for parametric down-conversion sources, resulting in an efficient and reliable optical scheme. We then use a recently proposed theoretical framework to quantify four-photon indistinguishability, as well as to obtain bounds on three unmeasured two-photon overlaps. Our findings are in high agreement with the theory, and represent a new resource-effective technique for the characterization of multiphoton interference.