Gaussian Boson Sampling

We introduce a new family of quantum circuits in continuous variables and we show that, relying on the widely accepted conjecture that the polynomial hierarchy of complexity classes does not collapse, their output probability distribution cannot be efficiently simulated by a classical computer. These circuits are composed of input photon-subtracted (or photon-added) squeezed states, passive linear optics evolution, and eight-port homodyne detection. We address the proof of hardness for the exact probability distribution of these quantum circuits by exploiting mappings onto different architectures of sub-universal quantum computers. We obtain both a worst-case and an average-case hardness result. Hardness of Boson Sampling with eight-port homodyne detection is obtained as the zero squeezing limit of our model. We conclude with a discussion on the relevance and interest of the present model in connection to experimental applications and classical simulations.

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“…For the sake of clarity of the present manuscript, we refer to [13] for the detailed derivation of this expression.…”

Section: Proof Of Hardness For Cvs Circuitsmentioning

confidence: 99%

“…The classical hardness of circuits of the latter kind, corresponding to Gaussian Boson Sampling (GBS), was proven in Ref. [12,13]. These circuits are composed of input squeezed states, passive linear optics evolution, and photon counters.…”

Section: Introductionmentioning

confidence: 99%

Continuous-variable sampling from photon-added or photon-subtracted squeezed states

et al. 2017

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“…Such error correction schemes might then be carried over into other photonic quantum technologies. Finally, we note that our classical sampling methods could be more broadly applicable to other sampling algorithms, not least to the many variants of boson sampling that have arisen 39,40 . …”

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Classical boson sampling algorithms with superior performance to near-term experiments

et al. 2017

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It is predicted that quantum computers will dramatically outperform their conventional counterparts. However, largescale universal quantum computers are yet to be built. Boson sampling 1 is a rudimentary quantum algorithm tailored to the platform of linear optics, which has sparked interest as a rapid way to demonstrate such quantum supremacy 2-6 . Photon statistics are governed by intractable matrix functions, which suggests that sampling from the distribution obtained by injecting photons into a linear optical network could be solved more quickly by a photonic experiment than by a classical computer. The apparently low resource requirements for large boson sampling experiments have raised expectations of a near-term demonstration of quantum supremacy by boson sampling 7,8 . Here we present classical boson sampling algorithms and theoretical analyses of prospects for scaling boson sampling experiments, showing that near-term quantum supremacy via boson sampling is unlikely. Our classical algorithm, based on Metropolised independence sampling, allowed the boson sampling problem to be solved for 30 photons with standard computing hardware. Compared to current experiments, a demonstration of quantum supremacy over a successful implementation of these classical methods on a supercomputer would require the number of photons and experimental components to increase by orders of magnitude, while tackling exponentially scaling photon loss.It is believed that new types of computing machines will be constructed to exploit quantum mechanics for an exponential speed advantage in solving certain problems compared with classical computers 9 . Recent large state and private investments in developing quantum technologies have increased interest in this challenge. However, it is not yet experimentally proven that a large computationally useful quantum system can be assembled, and such a task is highly non-trivial given the challenge of overcoming the effects of errors in these systems.Boson sampling is a simple task which is native to linear optics and has captured the imagination of quantum scientists because it seems possible that the anticipated supremacy of quantum machines could be demonstrated by a near-term experiment. The advent of integrated quantum photonics 10 has enabled large, complex, stable and programmable optical circuitry 11,12 , while recent advances in photon generation [13][14][15] and detection 16,17 have also been impressive. The possibility to generate many photons, evolve them under a large linear optical unitary transformation, then detect them, seems feasible, so the role of a boson sampling machine as a rudimentary but legitimate computing device is particularly appealing. Compared to a universal digital quantum computer, the resources required for experimental boson sampling appear much less demanding. This approach of designing quantum algorithms to demonstrate computational supremacy with nearterm experimental capabilities has inspired a raft of proposals suited to different hardware platforms [18]...

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“…A detailed investigation of links between these experiments and computation complexity classes, in particular the relation to computation complexity with linear optics would be interesting [36][37][38].…”

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confidence: 99%

Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings

Krenn

Zeilinger

2017

Phys. Rev. Lett.

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We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and Graph Theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the complexity class #P-complete, thus cannot be done efficiently. To strengthen the link further, theorems from Graph Theory -such as Hall's marriage problem -are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and potentially simulate properties of Graphs and Networks with quantum experiments (such as critical exponents and phase transitions).When a pair of photons is created, and one cannot -even in principle -determine what its origin is, the resulting quantum state is a coherent superposition of all possibilities [1,2]. This phenomenon has found a manifold of applications such as in spectroscopy [3], in quantum imaging [4], for the investigation of complementarity [5], in superconducting cavities [6] and for investigating quantum correlations [7]. By exploiting these ideas, the creation of a large number of highdimensional multipartite entangled states has been proposed recently [8] (inspired by computer-designed quantum experiments [9]).Here we show that Graph Theory is a very good abstract descriptive tool for such quantum experimental configuration: Every experiment corresponds to an undirected Graph, and every undirected Graph is associated with an experiment. On the one hand, we explicitly show how to translate questions from quantum experiments and answer them with graph theoretical methods. On the other hand, we rephrase theorems in Graph Theory and explain them in terms of quantum experiments.An important example for this link is the number of terms in the resulting quantum state for a given quantum experiment. It is the number of perfect matchings that exists in the corresponding graph -a problem that lies in the complexity class #P-complete [10]. Futhermore, the link can be used as a natural implementation for the experimental investigation of quantum random networks [11].Experiments and Graph -The optical setup for creating a 3-dimensional generalization of a 4-photon Greenberger-Horne-Zeilinger state [12,13] is shown in Fig. 1A [8]. The experiment consists of three layers of two down-conversion crystals each. Each crystal can create a pair of photons in the state |0, 0 , where the mode number could correspond to the orbital angular momentum (OAM) of photons [14][15][16] or some other (high-dimensional) degree-of-freedom. A laser pumps all of the six crystals coherently, such that two pairs of photons...

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Gaussian Boson Sampling

Cited by 69 publications

References 12 publications

Continuous-variable sampling from photon-added or photon-subtracted squeezed states

Continuous-variable sampling from photon-added or photon-subtracted squeezed states

Classical boson sampling algorithms with superior performance to near-term experiments

Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings

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