On the complexity and verification of quantum random circuit sampling

Bouland, Adam; Fefferman, Bill; Nirkhe, Chinmay; Vazirani, Umesh

doi:10.1038/s41567-018-0318-2

Cited by 257 publications

(305 citation statements)

References 26 publications

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“…Second, we connect this result to the output distributions of "quantum supremacy" schemes. In all schemes that rely on the Stockmeyer argument, the problem instances are defined in terms of a unitary that is randomly chosen from some restricted family, e.g., linear optical circuits in the case of boson sampling [14] or random universal circuits [15,17] in a qubit architecture . Specifically, we prove that with high probability over the choice of the random unitary, the distribution over outputs associated with this unitary is exponentially flat.…”

Section: Hardness Of Exact Samplingmentioning

confidence: 99%

“…In this work, we rigorously prove for a broad range of sampling problems, specifically for boson sampling [14], universal random circuit sampling [15,17], IQP circuit sampling [16,24], and sampling from post-selected-universal 2-designs [20-22, 28, 29] that they cannot be efficiently certified from classical samples and a description of the target probability distribution. Ironically, it turns out that the same property of a distribution that allows to prove the known approximatehardness results also forbids their non-interactive sampleefficient device independent certification, to the effect that with the known proof methods both properties cannot be achieved simultaneously in such schemes.…”

Section: Introductionmentioning

confidence: 99%

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Sample Complexity of Device-Independently Certified “Quantum Supremacy”

et al. 2019

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Results on the hardness of approximate sampling are seen as important stepping stones towards a convincing demonstration of the superior computational power of quantum devices. The most prominent suggestions for such experiments include boson sampling, IQP circuit sampling, and universal random circuit sampling. A key challenge for any such demonstration is to certify the correct implementation. For all these examples, and in fact for all sufficiently flat distributions, we show that any non-interactive certification from classical samples and a description of the target distribution requires exponentially many uses of the device. Our proofs rely on the same property that is a central ingredient for the approximate hardness results: namely, that the sampling distributions, as random variables depending on the random unitaries defining the problem instances, have small second moments.

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Section: Hardness Of Exact Samplingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sample Complexity of Device-Independently Certified “Quantum Supremacy”

et al. 2019

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“…In analogy to the family of circuits with random gates drawn from an elementary set for qubits, we refer to this architecture as to CV random circuit sampling [26]. Finite resolution in the homodyne detection ensures that we can associate well-defined probabilities to the continuous measurement outcomes through binning.…”

Section: Random Circuit Samplingmentioning

confidence: 99%

Probabilistic fault-tolerant universal quantum computation and sampling problems in continuous variables

et al. 2019

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Continuous-variable (CV) devices are a promising platform for demonstrating large-scale quantum information protocols. In this framework we define a general quantum computational model based on a CV hardware. It consists of vacuum input states, a finite set of gates-including non-Gaussian elements-and homodyne detection. We show that this model incorporates encodings sufficient for probabilistic fault-tolerant universal quantum computing. Furthermore, we show that this model can be adapted to yield sampling problems that cannot be simulated efficiently with a classical computer, unless the polynomial hierarchy collapses. This allows us to provide a simple paradigm for experiments to probe quantum advantage relying on Gaussian states, homodyne detection, and some form of non-Gaussian evolution. We finally address the recently introduced model of instantaneous quantum computing in CV, and prove that the hardness statement is robust with respect to some experimentally relevant simplifications in the definition of that model.

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“…While error-corrected scalable quantum computation is not yet available, recent advances towards small-scale quantum computers [1,2] have spurred interests in seeking noisy intermediate-scale quantum (NISQ) [3] devices that offer unmatched performance beyond the capability of classical devices. The theoretical proof of a quantum advantage over classical computation [4,5] further inspires the search for quantum-assisted schemes tailored for practical tasks. In this regard, quantum variational schemes, in conjunction with classical optimization, are widely applicable to tasks including quantum state preparation [6], variational eigensolvers [7,8], state diagonalization [9], and machine learning [10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Physical-Layer Supervised Learning Assisted by an Entangled Sensor Network

Zhuang

Zhang

2019

Phys. Rev. X

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Many existing quantum supervised learning (SL) schemes consider data given a priori in a classical description. With only noisy intermediate-scale quantum (NISQ) devices available in the near future, their quantum speedup awaits the development of quantum random access memories (qRAMs) and faulttolerant quantum computing. However, there also exist a multitude of SL tasks whose data are acquired by sensors, e.g., pattern classification based on data produced by imaging sensors. Solving such SL tasks naturally requires an integrated approach harnessing tools from both quantum sensing and quantum computing. We introduce supervised learning assisted by an entangled sensor network (SLAEN) as a means to carry out SL tasks at the physical layer. The entanglement shared by the sensors in SLAEN boosts the performance of extracting global features of the object under investigation. We leverage SLAEN to construct an entanglement-assisted support-vector machine for data classification and entanglementassisted principal component analyzer for data compression. In both schemes, variational circuits are employed to seek the optimum entangled probe states and measurement settings to maximize the entanglement-enabled enhancement. We observe that SLAEN enjoys an appreciable entanglement-enabled performance gain, even in the presence of loss, over conventional strategies in which classical data are acquired by separable sensors and subsequently processed by classical SL algorithms. SLAEN is realizable with available technology, opening a viable route toward building NISQ devices that offer unmatched performance beyond what the optimum classical device is able to afford.

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On the complexity and verification of quantum random circuit sampling

Cited by 257 publications

References 26 publications

Sample Complexity of Device-Independently Certified “Quantum Supremacy”

Sample Complexity of Device-Independently Certified “Quantum Supremacy”

Probabilistic fault-tolerant universal quantum computation and sampling problems in continuous variables

Physical-Layer Supervised Learning Assisted by an Entangled Sensor Network

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