Related papers: Explicit relation between all lower bound techniqu…
We study the concurrence of arbitrary dimensional bipartite quantum systems. An explicit analytical lower bound of concurrence is obtained, which detects entanglement for some quantum states better than some well-known separability…
In this paper, we introduce a new quantum query lower bound framework. It is inspired by Zhandry's compressed oracle technique, but it also subsumes the polynomial method as a special case. Compared to Zhandry's technique, our approach has…
In this tutorial, we will survey known results on the complexity of conjunctive query evaluation in different settings, ranging from Boolean queries over counting to more complex models like enumeration and direct access. A particular focus…
Let X = (x_0,...,x_{n-1})$ be a sequence of n numbers. For \epsilon > 0, we say that x_i is an \epsilon-approximate median if the number of elements strictly less than x_i, and the number of elements strictly greater than x_i are each less…
Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…
We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the…
We study the concurrence of arbitrary dimensional multipartite quantum systems. An explicit analytical lower bound of concurrence for four-partite mixed states is obtained in terms of the concurrences of tripartite mixed states. Detailed…
Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct…
We study the concurrence of arbitrary-dimensional multipartite quantum states. Analytical lower bounds of concurrence for tripartite quantum states are derived by projecting high-dimensional states to $2\otimes 2\otimes 2$ substates. The…
The standard model of quantum circuits assumes operations are applied in a fixed sequential "causal" order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant…
We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to…
We introduce new combinatorial quantities for concept classes, and prove lower and upper bounds for learning complexity in several models of query learning in terms of various combinatorial quantities. Our approach is flexible and powerful…
We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions…
As a natural extension of the SAT problem, an array of proof systems for quantified Boolean formulas (QBF) have been proposed, many of which extend a propositional proof system to handle universal quantification. By formalising the…
Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our…
Neural networks are getting deeper and more computation-intensive nowadays. Quantization is a useful technique in deploying neural networks on hardware platforms and saving computation costs with negligible performance loss. However, recent…
Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only…
We prove a tight quantum query lower bound $\Omega(n^{k/(k+1)})$ for the problem of deciding whether there exist $k$ numbers among $n$ that sum up to a prescribed number, provided that the alphabet size is sufficiently large. This is an…
We study quantum algorithms that are given access to trusted and untrusted quantum witnesses. We establish strong limitations of such algorithms, via new techniques based on Laurent polynomials (i.e., polynomials with positive and negative…
Inspired by the Elitzur-Vaidman bomb testing problem [arXiv:hep-th/9305002], we introduce a new query complexity model, which we call bomb query complexity $B(f)$. We investigate its relationship with the usual quantum query complexity…