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Electronic Colloquium on Computational Complexity

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All reports by Author Shir Peleg:

TR22-125 | 9th September 2022
Shir Peleg, Amir Shpilka, Ben Lee Volk

Tensor Reconstruction Beyond Constant Rank

We give reconstruction algorithms for subclasses of depth-$3$ arithmetic circuits. In particular, we obtain the first efficient algorithm for finding tensor rank, and an optimal tensor decomposition as a sum of rank-one tensors, when given black-box access to a tensor of super-constant rank. Specifically, we obtain the following results:

1. ... more >>>

TR21-091 | 29th June 2021
Gil Cohen, Dor Minzer, Shir Peleg, Aaron Potechin, Amnon Ta-Shma

Expander Random Walks: The General Case and Limitations

Cohen, Peri and Ta-Shma (STOC'21) considered the following question: Assume the vertices of an expander graph are labelled by $\pm 1$. What "test" functions $f : \{\pm 1\}^t \to \{\pm1 \}$ can or cannot distinguish $t$ independent samples from those obtained by a random walk? [CPTS'21] considered only balanced labelling, ... more >>>

TR21-077 | 6th June 2021
Shir Peleg, Amir Shpilka, Ben Lee Volk

Lower Bounds on Stabilizer Rank

The stabilizer rank of a quantum state $\psi$ is the minimal $r$ such that $\left| \psi \right \rangle = \sum_{j=1}^r c_j \left|\varphi_j \right\rangle$ for $c_j \in \mathbb{C}$ and stabilizer states $\varphi_j$. The running time of several classical simulation methods for quantum circuits is determined by the stabilizer rank of the ... more >>>

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