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Electronic Colloquium on Computational Complexity

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Reports tagged with postselection:
TR14-091 | 22nd July 2014
Ryan O'Donnell, A. C. Cem Say

One time-travelling bit is as good as logarithmically many

Revisions: 1

We consider computation in the presence of closed timelike curves (CTCs), as proposed by Deutsch. We focus on the case in which the CTCs carry classical bits (as opposed to qubits). Previously, Aaronson and Watrous showed that computation with polynomially many CTC bits is equivalent in power to PSPACE. On ... 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 >>>

TR16-146 | 18th September 2016
Scott Aaronson, Mohammad Bavarian, Giulio Gueltrini

Computability Theory of Closed Timelike Curves

We ask, and answer, the question of what's computable by Turing machines equipped with time travel into the past: that is, closed timelike curves or CTCs (with no bound on their size). We focus on a model for CTCs due to Deutsch, which imposes a probabilistic consistency condition to avoid ... more >>>

TR17-164 | 3rd November 2017
Scott Aaronson

Shadow Tomography of Quantum States

We introduce the problem of *shadow tomography*: given an unknown $D$-dimensional quantum mixed state $\rho$, as well as known two-outcome measurements $E_{1},\ldots,E_{M}$, estimate the probability that $E_{i}$ accepts $\rho$, to within additive error $\varepsilon$, for each of the $M$ measurements. How many copies of $\rho$ are needed to achieve this, ... more >>>

TR23-154 | 12th October 2023
Vishnu Iyer, Siddhartha Jain, Matt Kovacs-Deak, Vinayak Kumar, Luke Schaeffer, Daochen Wang, Michael Whitmeyer

On the Rational Degree of Boolean Functions and Applications

We study a natural complexity measure of Boolean functions known as the (exact) rational degree. For total functions $f$, it is conjectured that $\mathrm{rdeg}(f)$ is polynomially related to $\mathrm{deg}(f)$, where $\mathrm{deg}(f)$ is the Fourier degree. Towards this conjecture, we show that symmetric functions have rational degree at least $\mathrm{deg}(f)/2$ and ... more >>>

TR23-169 | 14th November 2023
Marshall Ball, Dana Dachman-Soled, Eli Goldin, Saachi Mutreja

Extracting Randomness from Samplable Distributions, Revisited

Randomness extractors provide a generic way of converting sources of randomness that are
merely unpredictable into almost uniformly random bits. While in general, deterministic randomness
extraction is impossible, it is possible if the source has some structural constraints.
While much of the literature on deterministic extraction has focused on sources ... more >>>

ISSN 1433-8092 | Imprint