Related papers: Quantum and Classical Strong Direct Product Theore…
Classical data can be copied and re-used for computation, with adverse consequences economically and in terms of data privacy. Motivated by this, we formulate problems in one-way communication complexity where Alice holds some data $x$ and…
We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…
We consider the product of infinitely many copies of a spin-$1\over 2$ system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of $\sigma^x$…
We ask whether there are fundamental limits on storing quantum information reliably in a bounded volume of space. To investigate this question, we study quantum error correcting codes specified by geometrically local commuting constraints…
For many practical applications of quantum computing, the most costly steps involve coherently accessing classical data. We help address this challenge by applying mass production techniques, which can reduce the cost of applying an…
The classic knapsack and related problems have natural generalizations to arbitrary (non-commutative) groups, collectively called knapsack-type problems in groups. We study the effect of free and direct products on their time complexity. We…
Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical advantage by quantum computations, and later…
Matrix product state has become the algorithm of choice when studying one-dimensional interacting quantum many-body systems, which demonstrates to be able to explore the most relevant portion of the exponentially large quantum Hilbert space…
An important part of the information theory folklore had been about the output statistics of codes that achieve the capacity and how the empirical distributions compare to the output distributions induced by the optimal input in the channel…
This article will prove a theorem for the existence of k-factor for k>1 ,and present an efficient algorithm for computing k-factor for all values of k based on this theorem.
Quantum computing promises substantial speedups by exploiting quantum mechanical phenomena such as superposition and entanglement. Corresponding design methods require efficient means of representation and manipulation of quantum…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
We investigate the optimal estimation of a quantum process that can possibly consist of multiple time steps. The estimation is implemented by a quantum network that interacts with the process by sending an input and processing the output at…
In the kSUM problem we are given an array of numbers $a_1,a_2,...,a_n$ and we are required to determine if there are $k$ different elements in this array such that their sum is 0. This problem is a parameterized version of the well-studied…
We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…
The main result of this paper is an optimal strong direct product result for the two-party public-coin randomized communication complexity of the Tribes function. This is proved by providing an alternate proof of the optimal lower bound of…
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…
In this paper we provide proofs of two new theorems that provide a broad class of partition inequalities and that illustrate a na\"ive version of Andrews' anti-telescoping technique quite well. These new theorems also put to rest any notion…
Let f subset of X x Y x Z be a relation. Let the public coin one-way communication complexity of f, with worst case error 1/3, be denoted R^{1,pub}_{1/3}(f). We show that if for computing f^k (k independent copies of f), o(k…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…