Continuous-Variable Instantaneous Quantum Computing is Hard to Sample

Douce, Tom; Markham, Damian; Kashefi, Elham; Diamanti, Eleni; Coudreau, Thomas; Milman, P.; Loock, Peter van; Ferrini, Giulia

doi:10.1103/physrevlett.118.070503

Cited by 63 publications

(78 citation statements)

References 48 publications

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“…Recently it was also proposed that IQP Sampling could be performed via continuous variable optical systems. 51 However, for all such proposals it should be remarked that the level of experimental precision required to definitively demonstrate quantum supremacy, even given generous constant total variation distance bound (such as required in), 12 is very high. Asymptotically this typically requires the precision of each circuit component must improve by an inverse polynomial in the number of qubits.…”

Section: Experimental Implementations Of Bosonsamplingmentioning

confidence: 99%

Quantum sampling problems, BosonSampling and quantum supremacy

2017

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There is a large body of evidence for the potential of greater computational power using information carriers that are quantum mechanical over those governed by the laws of classical mechanics. But the question of the exact nature of the power contributed by quantum mechanics remains only partially answered. Furthermore, there exists doubt over the practicality of achieving a large enough quantum computation that definitively demonstrates quantum supremacy. Recently the study of computational problems that produce samples from probability distributions has added to both our understanding of the power of quantum algorithms and lowered the requirements for demonstration of fast quantum algorithms. The proposed quantum sampling problems do not require a quantum computer capable of universal operations and also permit physically realistic errors in their operation. This is an encouraging step towards an experimental demonstration of quantum algorithmic supremacy. In this paper, we will review sampling problems and the arguments that have been used to deduce when sampling problems are hard for classical computers to simulate. Two classes of quantum sampling problems that demonstrate the supremacy of quantum algorithms are BosonSampling and Instantaneous Quantum Polynomial-time Sampling. We will present the details of these classes and recent experimental progress towards demonstrating quantum supremacy in BosonSampling.npj Quantum Information (2017) 3:15 ; doi:10.1038/s41534-017-0018-2 INTRODUCTIONThere is a growing sense of excitement that in the near future prototype quantum computers might be able to outperform any classical computer. That is, they might demonstrate supremacy over classical devices.1 This excitement has in part been driven by theoretical research into the complexity of intermediate quantum computing models, which over the last 15 years has seen the physical requirements for a quantum speedup lowered while increasing the level of rigour in the argument for the difficulty of classically simulating such systems.These advances are rooted in the discovery by Terhal and DiVincenzo 2 that sufficiently accurate classical simulations of even quite simple quantum computations could have significant implications for the interrelationships between computational complexity classes.3 Since then the theoretical challenge has been to demonstrate such a result holds for levels of precision commensurate with what is expected from realisable quantum computers. A first step in this direction established that classical computers cannot efficiently mimic the output of ideal quantum circuits to within a reasonable multiplicative (or relative) error in the frequency with which output events occur without similarly disrupting the expected relationships between classical complexity classes.4, 5 In a major breakthrough Aaronson and Arkhipov laid out an argument for establishing that efficient classical simulation of linear optical systems was not possible, even if that simulation was only required to be accurate to within a...

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Section: Experimental Implementations Of Bosonsamplingmentioning

confidence: 99%

Quantum sampling problems, BosonSampling and quantum supremacy

2017

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“…As already considered in Refs. [14,16], in order to give meaning to the obtained probability distribution, that must be defined on discrete values, we assume a finite binning of size η for the output probability density of CVS circuits [23]. This allows for the definition of a set of indicesb = (b…”

Section: Definition Of the Circuit Familymentioning

confidence: 99%

“…These circuits are composed of input squeezed states, passive linear optics evolution, and photon counters. Circuits of the second kind are for instance related to the CV implementation of Instantaneous Quantum Computing -another sub-universal model, where input states and measurements are Gaussian, while the evolution contains nonGaussian gates [14,15]. First definitions of the former class of CV circuits, i.e.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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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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“…Despite this fact, this protocol still retains a conceptual interest in the context of recent proposals for sub-universal models of quantum computation, such as CV Instantaneous Quantum Computing [31]. In the latter protocol, polynomial evolutions diagonal in the quadratureq are required as building blocks, and homodyne detections of thep quadrature are performed.…”

Section: Discussionmentioning

confidence: 99%

Polynomial approximation of non-Gaussian unitaries by counting one photon at a time

2017

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In quantum computation with continous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to realize in the lab. We propose and analyze two methods to apply a polynomial approximation of any unitary operator diagonal in the amplitude quadrature representation, including non-Gaussian operators, to an unknown input state. Our protocols use as a primary non-Gaussian resource a single-photon counter. We use the fidelity of the transformation with the target one on Fock and coherent states to assess the quality of the approximate gate.

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Continuous-Variable Instantaneous Quantum Computing is Hard to Sample

Cited by 63 publications

References 48 publications

Quantum sampling problems, BosonSampling and quantum supremacy

Quantum sampling problems, BosonSampling and quantum supremacy

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

Polynomial approximation of non-Gaussian unitaries by counting one photon at a time

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