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Quantum Recommendation Systems
TLDR
This work presents the first algorithm for recommendation systems that runs in time polylogarithmic in the dimensions of the matrix and provides an example of a quantum machine learning algorithm for a real world application. Expand
Exponential separation of quantum and classical one-way communication complexity
TLDR
The Hidden Matching Problem HMn is defined and it is proved that any randomized linear one-way protocol with bounded error for this problem requires Ω(√[3] n log n) bits of communication. Expand
Competitive recommendation systems
TLDR
This paper presents a notion of competitive recommendation systems, and presents a matrix reconstruction scheme that is competitive: it requires a small overhead in the number of users and products to be sampled, delivering in the process a net utility that closely approximates the best possible with full knowledge of all user-product preferences. Expand
Exponential lower bound for 2-query locally decodable codes via a quantum argument
TLDR
This work uses a quantum argument to prove that LDCs with 2 classical queries require exponential length: m = 2Ω(n), and extends the lower bounds to non-binary alphabets and somewhat improves the polynomial lower bounds by Katz and Trevisan for L DCs with more than 2 queries. Expand
Exponential lower bound for 2-query locally decodable codes via a quantum argument
TLDR
This work proves that LDCs with 2 classical queries need exponential length, and shows that a 2-query LDC can be decoded with only 1 quantum query, and proves an exponential lower bound for such 1-query locally quantum-decodable codes. Expand
Exponential separations for one-way quantum communication complexity, with applications to cryptography
We give an exponential separation between one-way quantum and classical communication protocols for twopartial Boolean functions, both of which are variants of the Boolean Hidden Matching Problem ofExpand
Optimal Quantum Strong Coin Flipping
TLDR
The construction of a quantum strong coin flipping protocol with cheating probability arbitrarily close to 1/sqrt{2}+O(epsilon) is presented, which follows from the construction and the optimal quantum weak coin flips protocol described by Mochon. Expand
Quantum gradient descent for linear systems and least squares
Quantum machine learning and optimization are exciting new areas that have been brought forward by the breakthrough quantum algorithm of Harrow, Hassidim, and Lloyd for solving systems of linearExpand
Lower Bounds on Information Complexity via Zero-Communication Protocols and Applications
TLDR
A relaxed version of the partition bound of Jain and Klauck is defined and it is proved that it lower bounds the information complexity of any function. Expand
Communication Complexity of Conditional Disclosure of Secrets and Attribute-Based Encryption
TLDR
A general upper bound and the first non-trivial lower bounds for conditional disclosure of secrets are presented, which explain the trade-off between ciphertext and secret key sizes of several existing attribute-based encryption schemes based on the dual system methodology. Expand
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