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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > QUANTUM COMPLEXITY THEORY:
Reports tagged with quantum complexity theory:
TR12-130 | 3rd October 2012
Abuzer Yakaryilmaz

Public-qubits versus private-coins

We introduce a new public quantum interactive proof system, namely qAM, by augmenting the verifier with a fixed-size quantum register in Arthur-Merlin game. We focus on space-bounded verifiers, and compare our new public system with private-coin interactive proof (IP) system in the same space bounds. We show that qAM systems ... more >>>


TR19-131 | 11th September 2019
Lieuwe Vinkhuijzen, André Deutz

A Simple Proof of Vyalyi's Theorem and some Generalizations

In quantum computational complexity theory, the class QMA models the set of problems efficiently verifiable by a quantum computer the same way that NP models this for classical computation. Vyalyi proved that if $\text{QMA}=\text{PP}$ then $\text{PH}\subseteq \text{QMA}$. In this note, we give a simple, self-contained proof of the theorem, using ... more >>>


TR20-185 | 1st December 2020
Srinivasan Arunachalam, Alex Grilo, Tom Gur, Igor Oliveira, Aarthi Sundaram

Quantum learning algorithms imply circuit lower bounds

We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathrm{C}$ be a class of polynomial-size concepts, and suppose that $\mathrm{C}$ can be PAC-learned with membership queries under the uniform distribution with error $1/2 - \gamma$ by a time $T$ quantum algorithm. ... more >>>




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