The computational complexity of linear optics

Aaronson, Scott; Архипов, A. A.

doi:10.1145/1993636.1993682

Cited by 886 publications

(1,624 citation statements)

References 43 publications

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“…The boson sampling problem 1 . Given U ∈ SU (m), let A be the column-orthonormal, m × n matrix formed by taking the first n columns of U .…”

Section: Letters Nature Physics Doi: 101038/nphys4270 Methodsmentioning

confidence: 99%

“…Doing this exactly would require summing all probabilities in the CFS for the specific instance of the problem being considered. To approximate the normalization of q x efficiently, here we instead average the probability of the output being collision-free over the Haar measure 1,30 :…”

Section: Events With Collisionsmentioning

confidence: 99%

“…Because approximating the permanent of a random matrix is conjectured to be computationally hard 1 , calculating any transition probability is intractable; the collection of all of the possible collision-free transition probabilities (m choose n) constitutes an exponentially large probability distribution, where each element is exponentially hard to calculate. Running an ideal boson sampler would solve the problem of producing samples from this distribution.Importantly, a strong case for the classical hardness of boson sampling can be made even when the distribution being sampled from is only approximately correct 1 : assuming certain conjectures from computational complexity theory, there can be no efficient classical algorithm to sample from any distribution within a small distance from the boson sampling distribution.Current estimates for the regime in which photonic experiments could achieve quantum supremacy have been between 20 and 30 photons 1,21,22 and, recently, as low as 7 (ref. 7).…”

mentioning

confidence: 99%

“…Current estimates for the regime in which photonic experiments could achieve quantum supremacy have been between 20 and 30 photons 1,21,22 and, recently, as low as 7 (ref. 7).…”

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confidence: 99%

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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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“…The boson sampling problem 1 . Given U ∈ SU (m), let A be the column-orthonormal, m × n matrix formed by taking the first n columns of U .…”

Section: Letters Nature Physics Doi: 101038/nphys4270 Methodsmentioning

confidence: 99%

Section: Events With Collisionsmentioning

confidence: 99%

mentioning

confidence: 99%

“…Current estimates for the regime in which photonic experiments could achieve quantum supremacy have been between 20 and 30 photons 1,21,22 and, recently, as low as 7 (ref. 7).…”

mentioning

confidence: 99%

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

et al. 2017

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“…As a second application (which was actually the original motivation for this work), we extend a recent result of Aaronson and Arkhipov [1]. These authors gave a sampling problem that is solvable using a simple linear-optics experiment (so in particular, in SampBQP), but is not solvable efficiently by a classical computer, unless the permanent of a Gaussian random matrix can be approximated in BPP NP .…”

Section: Our Resultsmentioning

confidence: 76%

The Equivalence of Sampling and Searching

Aaronson

2011

Computer Science – Theory and Applications

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In a sampling problem, we are given an input x ∈ {0, 1} n , and asked to sample approximately from a probability distribution D x over poly (n)-bit strings. In a search problem, we are given an input x ∈ {0, 1} n , and asked to find a member of a nonempty set A x with high probability. (An example is finding a Nash equilibrium.) In this paper, we use tools from Kolmogorov complexity to show that sampling and search problems are "essentially equivalent." More precisely, for any sampling problem S, there exists a search problem R S such that, if C is any "reasonable" complexity class, then R S is in the search version of C if and only if S is in the sampling version. What makes this nontrivial is that the same R S works for every C.As an application, we prove the surprising result that SampP = SampBQP if and only if FBPP = FBQP. In other words, classical computers can efficiently sample the output distribution of every quantum circuit, if and only if they can efficiently solve every search problem that quantum computers can solve.

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Physical Reservoir Computing Based on Nanoscale Materials and Devices

Qi,

Mi,

Qian

et al. 2023

Adv Funct Materials

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Bioinspired computation systems can achieve artificial intelligence, bypassing fundamental bottlenecks and cost constraints. Computational frameworks suited for temporal/sequential data processing such as recurrent neural networks (RNNs) suffer from problems of high complexity and low efficiency. Physical systems assembled with nanoscale materials and devices represent as an alternative route to serve as the core component for physically implanted reservoir computing. In this review, an overview of the development of the paradigm of physical reservoir computing (PRC) is provided and the typical physical reservoirs constructed with nanomaterials and nanodevices are described. The physical reservoirs based on multiple nanomaterials overcome the problems of RNN, show strong robustness, and effectively deal with tasks with improved reliability and availability. Finally, the challenges and perspectives of nanomaterial and nanodevice‐based PRC as a component of next‐generation machine learning systems are discussed.

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The computational complexity of linear optics

Cited by 886 publications

References 43 publications

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

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

The Equivalence of Sampling and Searching

Physical Reservoir Computing Based on Nanoscale Materials and Devices

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