Efficient Classical Algorithm for Boson Sampling with Partially Distinguishable Photons

Renema, Jelmer J.; Menssen, Adrian J.; Clements, William R.; Triginer, Gil; Kolthammer, W. Steven

doi:10.1103/physrevlett.120.220502

Cited by 103 publications

(156 citation statements)

References 30 publications

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“…Let U be an m×m Haarrandom matrix, where m n O 2 = ( ), and denote by  the probability distribution over outcomes generated by a boson sampling computer, i.e. with probabilities given by equation (10). Suppose there is a classical algorithm  that takes as input the unitary matrix U and an error bound 0  > and outputs a sample from some distribution ¢ such that    -¢ <   , in time poly n, 1  ( ).…”

Section: Complexity-theoretic Considerationsmentioning

confidence: 99%

“…Shortly after the seminal boson sampling [3] paper was published, several works started investigating the effects of realistic experimental imperfections on the idealized theoretical model. The robustness of boson sampling was analyzed under the effect of partial photon distinguishability [9,10], fabrication imperfections on the linear-optical transformation [11][12][13], losses [14,15], probabilistic sources [16] and so on. On the experimental side, several small-scale implementations of boson sampling have been reported so far [17][18][19][20][21][22][23][24][25][26][27][28], with state-of-the-art implementations with up to four and five photons using near-deterministic quantum dot sources [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

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Classical simulation of photonic linear optics with lost particles

2018

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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 nparticle 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.

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Section: Complexity-theoretic Considerationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Classical simulation of photonic linear optics with lost particles

2018

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“…where * indicates the complex conjugate. In other words, when we know how to represent the wave functions in either the time or frequency domain, we can use it to calculate | ψ | ϕ | 2 in (108) or (109).…”

Section: The Hong-ou-mandel Effectmentioning

confidence: 99%

Signatures of many-particle interference

Walschaers¹

2020

J. Phys. B: At. Mol. Opt. Phys.

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Quantum systems with many constituents give rise to a range of conceptual, analytical and computational challenges, hence, the label "complex systems". In the first place, one can think of interactions, described by a manybody Hamiltonian, as the source of such complexity. However, it has gradually become clear that, even in absence of interactions, many-body systems are more than just the sum of their parts. This feature is due to many-body interference.One of the most well-known interference phenomena is the Hong-Ou-Mandel effect, where total destructive interference is observed for a pair of (noninteracting) identical photons. This two-photon interference effect can be generalised to systems of many particles which can be either fermionic or bosonic. The resulting many-particle interference goes beyond quantum statistical effects that are contained in the Bose-Einstein or Fermi-Dirac distributions, and is dynamical in nature.This Tutorial will introduce the mathematical framework for describing systems of identical particles, and explain the notion of indistinguishability. We will then focus our attention on dynamical systems of free particles and formally introduce the concept of many-particle interference. Its impact on manyparticle transition probabilities is computationally challenging to evaluate, and it becomes rapidly intractable for systems with large numbers of identical particles. Hence, this Tutorial will build up towards alternative, more efficient methods for observing signatures of many-particle interference. A first type of signatures relies on the detection of a highly sensitive -but also highly fragile-processes of total destructive interference that occurs in interferometers with a high degree of symmetry. A second class of signatures is based on the statistical features that arise when we study the typical behaviour of correlations between a small number of the interferometer's output ports. We will ultimately show how these statistical signatures of many-particle interference lead us to a statistical version of the Hong-Ou-Mandel effect.The work presented in this Tutorial was one of the four shortlisted finalists of the 2018 DPG SAMOP dissertation prize.

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“…On the other hand, photonadded coherent states [16] and quantum superpositions of coherent states (cat states) [17] have been claimed to yield hard-to-simulate outputs. Partially distinguishable photons seem to yield an intermediate regime deserving further investigation [18][19][20][21]. The effect of losses on simulation complexity was also considered [22,23].…”

Section: Introductionmentioning

confidence: 99%

Experimental generalized quantum suppression law in Sylvester interferometers

et al. 2018

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Photonic interference is a key quantum resource for optical quantum computation, and in particular for so-called boson sampling devices. In interferometers with certain symmetries, genuine multiphoton quantum interference effectively suppresses certain sets of events, as in the original HongOu-Mandel effect. Recently, it was shown that some classical and semi-classical models could be ruled out by identifying such suppressions in Fourier interferometers. Here we propose a suppression law suitable for random-input experiments in multimode Sylvester interferometers, and verify it experimentally using 4-and 8-mode integrated interferometers. The observed suppression occurs for a much larger fraction of input-output combinations than what is observed in Fourier interferometers of the same size, and could be relevant to certification of boson sampling machines and other experiments relying on bosonic interference, such as quantum simulation and quantum metrology.

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Efficient Classical Algorithm for Boson Sampling with Partially Distinguishable Photons

Cited by 103 publications

References 30 publications

Classical simulation of photonic linear optics with lost particles

Classical simulation of photonic linear optics with lost particles

Signatures of many-particle interference

Experimental generalized quantum suppression law in Sylvester interferometers

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