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Electronic Colloquium on Computational Complexity

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Reports tagged with sampling problems:
TR10-128 | 15th August 2010
Scott Aaronson

The Equivalence of Sampling and Searching

Revisions: 1

In a sampling problem, we are given an input $x\in\left\{0,1\right\} ^{n}$, 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
$x\in\left\{ 0,1\right\} ^{n}$, and asked to find a member of a nonempty set
$A_{x}$ with high probability. ... more >>>

TR13-135 | 27th September 2013
Scott Aaronson

BosonSampling Is Far From Uniform

Revisions: 2

BosonSampling, which we proposed three years ago, is a scheme for using linear-optical networks to solve sampling problems that appear to be intractable for a classical computer. In a recent manuscript, Gogolin et al. claimed that even an ideal BosonSampling device's output would be "operationally indistinguishable" from a uniform random ... more >>>

TR16-039 | 15th March 2016
Adam Bouland, Laura Mancinska, Xue Zhang

Complexity Classification of Two-Qubit Commuting Hamiltonians

We classify two-qubit commuting Hamiltonians in terms of their computational complexity. Suppose one has a two-qubit commuting Hamiltonian $H$ which one can apply to any pair of qubits, starting in a computational basis state. We prove a dichotomy theorem: either this model is efficiently classically simulable or it allows one ... more >>>

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