Related papers: Algorithms and Lower Bounds for Comparator Circuit…
The notion of vertex sparsification is introduced in \cite{M}, where it was shown that for any graph $G = (V, E)$ and a subset of $k$ terminals $K \subset V$, there is a polynomial time algorithm to construct a graph $H = (K, E_H)$ on just…
An $n$-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of $n$. We describe a classical algorithm with quasipolynomial runtime $n^{O(\log{n})}$ that…
In this paper, we study the problem of computing the majority function by low-depth monotone circuits and a related problem of constructing low-depth sorting networks. We consider both the classical setting with elementary operations of…
We consider the hardness of computing additive approximations to output probabilities of random quantum circuits. We consider three random circuit families, namely, Haar random, $p=1$ QAOA, and random IQP circuits. Our results are as…
The problem of distinguishing between a random function and a random permutation on a domain of size $N$ is important in theoretical cryptography, where the security of many primitives depend on the problem's hardness. We study the quantum…
The All-Pairs Min-Cut problem (aka All-Pairs Max-Flow) asks to compute a minimum $s$-$t$ cut (or just its value) for all pairs of vertices $s,t$. We study this problem in directed graphs with unit edge/vertex capacities (corresponding to…
In this paper we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of…
MergeInsertion, also known as the Ford-Johnson algorithm, is a sorting algorithm which, up to today, for many input sizes achieves the best known upper bound on the number of comparisons. Indeed, it gets extremely close to the…
Asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity of a class of dynamic programming algorithms including matrix chain multiplication, optimal polygon triangulation, and the construction of optimal binary…
The partial coloring method is one of the most powerful and widely used method in combinatorial discrepancy problems. However, in many cases it leads to sub-optimal bounds as the partial coloring step must be iterated a logarithmic number…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
Optimization of circuits is an essential task for both quantum and classical computers to improve their efficiency. In contrast, classical logic optimization is known to be difficult, and a lot of heuristic approaches have been developed so…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
We consider the fundamental Matroid Theory problem of finding a circuit in a matroid spanning a set T of given terminal elements. For graphic matroids this corresponds to the problem of finding a simple cycle passing through a set of given…
We consider submodular function minimization in the oracle model: given black-box access to a submodular set function $f:2^{[n]}\rightarrow \mathbb{R}$, find an element of $\arg\min_S \{f(S)\}$ using as few queries to $f(\cdot)$ as…
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…
Compared to general quantum states, the sparse states arise more frequently in the field of quantum computation. In this work, we consider the preparation for $n$-qubit sparse quantum states with $s$ non-zero amplitudes and propose two…
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…
Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to…
A clear protocol for synthesis of sequential reversible circuits from any particular gate library has been provided. Using that protocol, reversible circuits for SR latch, D latch, JK latch and T latch are designed from NCT gate library.…