相关论文: Cancellation-Free Circuits in Unbounded and Bounde…
We consider the problem of computing the second elementary symmetric polynomial S^2_n(X) using depth-three arithmetic circuits of the form "sum of products of linear forms". We consider this problem over several fields and determine EXACTLY…
Proving super-polynomial size lower bounds for $\textsf{TC}^0$, the class of constant-depth, polynomial-size circuits of Majority gates, is a notorious open problem in complexity theory. A major frontier is to prove that $\textsf{NEXP}$…
Gottesman-Knill theorem states that computations on stabilizer circuits can be simulated on a classical computer, conventional simulation algorithms extensively use linear algebra over bit strings. For instance, given a non-adaptive…
We introduce a systematic study of "symmetric quantum circuits", a new restricted model of quantum computation that preserves the symmetries of the problems it solves. This model is well-adapted for studying the role of symmetry in quantum…
We consider one-sided error property testing of $\mathcal{F}$-minor freeness in bounded-degree graphs for any finite family of graphs $\mathcal{F}$ that contains a minor of $K_{2,k}$, the $k$-circus graph, or the $(k\times 2)$-grid for any…
We define and construct efficient depth-universal and almost-size-universal quantum circuits. Such circuits can be viewed as general-purpose simulators for central classes of quantum circuits and can be used to capture the computational…
The recently-discovered polar codes are widely seen as a major breakthrough in coding theory. These codes achieve the capacity of many important channels under successive cancellation decoding. Motivated by the rapid progress in the theory…
Proving that there are problems in $\mathsf{P}^\mathsf{NP}$ that require boolean circuits of super-linear size is a major frontier in complexity theory. While such lower bounds are known for larger complexity classes, existing results only…
One of the most important quantum algorithms ever discovered is Grover's algorithm for searching an unordered set. We give a new lower bound in the query model which proves that Grover's algorithm is exactly optimal. Similar to existing…
We introduce the polynomial coefficient matrix and identify maximum rank of this matrix under variable substitution as a complexity measure for multivariate polynomials. We use our techniques to prove super-polynomial lower bounds against…
With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted…
We study a discrete model of repelling particles, and we show using linear programming bounds that many familiar families of error-correcting codes minimize a broad class of potential energies when compared with all other codes of the same…
We revisit known constructions of efficient learning algorithms from various notions of constructive circuit lower bounds such as distinguishers breaking pseudorandom generators or efficient witnessing algorithms which find errors of small…
In this paper, we introduce a family of graphs which is a generalization of zero-divisor graphs and compute an upper-bound for the diameter of such graphs. We also investigate their cycles and cores.
Let $G$ be an $n$-node simple directed planar graph with nonnegative edge weights. We study the fundamental problems of computing (1) a global cut of $G$ with minimum weight and (2) a~cycle of $G$ with minimum weight. The best previously…
A monotone Boolean (OR,AND) circuit computing a monotone Boolean function f is a read-k circuit if the polynomial produced (purely syntactically) by the arithmetic (+,x) version of the circuit has the property that for every prime implicant…
We first show how to construct an O(n)-depth O(n)-size quantum circuit for addition of two n-bit binary numbers with no ancillary qubits. The exact size is 7n-6, which is smaller than that of any other quantum circuit ever constructed for…
We consider the zero-error capacity of deletion channels. Specifically, we consider the setting where we choose a codebook ${\cal C}$ consisting of strings of $n$ bits, and our model of the channel corresponds to an adversary who may delete…
It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless mid-circuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as…
We present efficient circuits for the addition of binary numbers. We assume that we are given arrival times for all input bits and optimize the delay of the circuits, i.e.\ the time when the last output bit is computed. This contains the…