Related papers: Shor's algorithm on a nearest-neighbor machine

Ordinal Embedding places n objects into R^d based on comparisons such as "a is closer to b than c." Current optimization-based approaches suffer from scalability problems and an abundance of low quality local optima. We instead consider a…

In this work, we propose an adder for the 2D NTC architecture, designed to match the architectural constraints of many quantum computing technologies. The chosen architecture allows the layout of logical qubits in two dimensions and the…

The problem of nearest-neighbor (NN) condensation aims to reduce the size of a training set of a nearest-neighbor classifier while maintaining its classification accuracy. Although many condensation techniques have been proposed, few bounds…

Approximate circuit design has gained significance in recent years targeting error tolerant applications. In this paper, we first demonstrate that the commonly used assumption that the inputs to the adder are uniformly distributed results…

We present improved quantum circuit for modular exponentiation of a constant, which is the most expensive operation in Shor's algorithm for integer factorization. While previous work mostly focuses on minimizing the number of qubits or the…

Reversible circuits have applications in digital signal processing, computer graphics, quantum computation and cryptography. In this paper, a generalized k*k reversible gate family is proposed and a 3*3 gate of the family is discussed.…

In the recent years, reversible logic has emerged as a promising technology having its applications in low power CMOS, quantum computing, nanotechnology, and optical computing. The classical set of gates such as AND, OR, and EXOR are not…

Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider…

We study the fundamental problem of approximate nearest neighbor search in $d$-dimensional Hamming space $\{0,1\}^d$. We study the complexity of the problem in the famous cell-probe model, a classic model for data structures. We consider…

We heuristically show that Shor's algorithm for computing general discrete logarithms achieves an expected success probability of approximately 60% to 82% in a single run when modified to enable efficient implementation with the…

In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Eker{\aa} so as to allow for various tradeoffs between the number of times that the algorithm need be executed on the one…

We challenge the idea that edge insertions are local improvement operations and show that the edge-insertion algorithm must sometimes insert an edge between vertices that are at the farthest combinatorial distance apart, and that this edge…

Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…

It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…

There is a folkloric belief that a depth-$\Theta(m)$ quantum circuit is needed to estimate the trace of the product of $m$ density matrices (i.e., a multivariate trace), a subroutine crucial to applications in condensed matter and quantum…

Nearest neighbor (NN) algorithms have been extensively used for missing data problems in recommender systems and sequential decision-making systems. Prior theoretical analysis has established favorable guarantees for NN when the underlying…

This work studies Nash equilibrium seeking for a class of stochastic aggregative games, where each player has an expectation-valued objective function depending on its local strategy and the aggregate of all players' strategies. We propose…

This paper proposes a new algorithm for reducing Approximate Nearest Neighbor problem to Approximate Near Neighbor problem. The advantage of this algorithm is that it achieves O(log n) query time. As a reduction problem, the uery time…

We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…

We propose a semiclassical version of Shor's quantum algorithm to factorize integer numbers, based on spin-1/2 SU(2) generalized coherent states. Surprisingly, we find evidences that the algorithm's success probability is not too severely…