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Questions tagged [probabilistic-circuits]

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Is there a universal gate set for classical probabilistic computing?

We know that NAND gates are universal for deterministic classical circuits, Toffoli gates are universal for reversible deterministic classical circuits, and Clifford+T is universal for quantum ...
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0answers
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Solving 0/1 integer programming and solving ACC-of-SYM circuits

I am referring to the proof of Theorem 1.4 in this STOC 2014 paper, https://arxiv.org/abs/1401.2444. In particular my question is about the argument that begins in the 8th line of page 9 where the ...
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0answers
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What is the average sensitivity of a quantum circuit with depth $d$ and size $s$?

We have some quantum circuit $C$ with $k$ ancillae and $n$ input bits of depth $d$ and size $s$, and we can define a function $f$ which, for any $x \in \{0, 1\}^n$, is the random variable which is the ...
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2answers
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Is there any notion of sensitivity for probabilistic Boolean functions?

Sensitivity is defined here. Denoting the neighbors of $x$ in the Boolean cube as $N(x)$, we define the sensitivity to be $s(f, x) = \sum_{y \in N(x)} I(f(x) \neq f(y))$, where $I$ is $1$ if the ...
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11answers
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What is the most efficient way to generate a random permutation from probabilistic pairwise swaps?

The question I am interested in is related to generating random permutations. Given a probabilistic pairwise swap gate as the basic building block, what is the most efficient way to produce a ...
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1answer
286 views

On Defining Probabilistic/Nondeterministic Circuits

Assume that we are interested in deterministic circuits of size $f(n)$. Here, $n$ represents the number of inputs to the circuit. The standard way of defining probabilistic/nondeterministic circuits ...