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arXiv:2007.07872quant-ph

Sampling random quantum circuits: a pedestrian's guide

Sean Mullane

Abstract

Recent experiments completed by collaborating research groups from Google, NASA Ames, UC Santa Barbara, and others provided compelling evidence that quantum supremacy has finally been achieved on a superconducting quantum processor. The theoretical basis for these experiments depends on sampling the output distributions of random quantum circuits; unfortunately, understanding how this theoretical basis can be used to define quantum supremacy is an extremely difficult task. Anyone attempting to understand how this sampling task relates to quantum supremacy must study concepts from random matrix theory, mathematical analysis, quantum chaos, computational complexity, and probability theory. Resources connecting these concepts in the context of quantum supremacy are scattered and often difficult to find. This article is an attempt to alleviate this difficulty in those who wish to understand the theoretical basis of Google's quantum supremacy experiments, by carefully walking through a derivation of their precise mathematical definition of quantum supremacy. It's designed for advanced undergraduate or graduate students who want more information than can be provided in popular science articles, but who might not know where to begin when tackling the many research papers related to quantum supremacy.

arXiv comments
25 pages, 4 figures
Journal reference
DOI
Subjects
quant-phQuantum Physics

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Discussed in comments3 threads

  1. Google claims to have proved its supremacy with new quantum computer 1 comment

    • The cited paper[1] references "random circuit sampling" which is defined in [2] which then gets so heavy into abstract math, and I give up. Can someone explain this in terms an EE or programmer can understand? [1] https://arxiv.org/abs/2304.11119 [2]…

      mikewarotView on HNParent context

  2. China takes quantum supremacy lead.This QC is 60k times faster than supercomp 1 comment

    • If, like me, you are wondering what the calculation was, here is a dummies' guide: https://arxiv.org/pdf/2007.07872.pdf It still makes no sense to me, but might help others.

      robthebrewView on HNParent context

  3. Strong quantum computational advantage using a superconducting quantum processor 1 comment

    • My understanding is that this simulation of random quantum circuits is already known to be hard in a theoretical sense[1], and there is no argument that a classical computer could compete with a quantum computer much bigger than 50-60ish qubits. And that arguments against those…

      throw149102View on HNParent context

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