Related papers: Parallel Spooky Pebbling Makes Regev Factoring Mor…
Quantum memory management is becoming a pressing problem, especially given the recent research effort to develop new and more complex quantum algorithms. The only existing automatic method for quantum states clean-up relies on the…
We show how to support efficient back traversal in a unidirectional list, using small memory and with essentially no slowdown in forward steps. Using $O(\log n)$ memory for a list of size $n$, the $i$'th back-step from the farthest point…
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…
Search pattern experienced by the processor to search an element in secondary storage devices follows a random sequence. Formally, it is a random walk and its modeling is crucial in studying performance metrics like memory access time. In…
We consider the problem of selecting the best variable-value strategy for solving a given problem in constraint programming. We show that the recent Embarrassingly Parallel Search method (EPS) can be used for this purpose. EPS proposes to…
Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A key challenge lies in the search for parsimonious and…
Measures of quantum nonlocality traditionally assume perfect local computation. In real experiments, however, each computational primitive is imperfect. Fault-tolerant techniques enable arbitrarily accurate quantum computation but do not…
Quantum computing is a hotspot technology for its potential to accelerate specific applications by exploiting quantum parallelism. However, current physical quantum computers are limited to a relatively small scale, simulators based on…
Cumulative memory -- the sum of space used per step over the duration of a computation -- is a fine-grained measure of time-space complexity that was introduced to analyze cryptographic applications like password hashing. It is a more…
Consider a distribution of pebbles on a graph. A pebbling move removes two pebbles from a vertex and place one at an adjacent vertex. A vertex is reachable under a pebble distribution if it has a pebble after the application of a sequence…
Pebbling is a game played on a graph. The single player is given a graph and a configuration of pebbles and may make pebbling moves by removing 2 pebbles from one vertex and placing one at an adjacent vertex to eventually have one pebble…
The growth in the use of computationally intensive statistical procedures, especially with Big Data, has necessitated the usage of parallel computation on diverse platforms such as multicore, GPU, clusters and clouds. However, slowdown due…
A pebbling move on a graph G consists of the removal of two pebbles from one vertex and the placement of one pebble on an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed, which is also called the…
Regev recently introduced a quantum factoring algorithm that may be perceived as a $d$-dimensional variation of Shor's factoring algorithm. In this work, we extend Regev's factoring algorithm to an algorithm for computing discrete…
We study the question of whether parallelization in the exploration of the feasible set can be used to speed up convex optimization, in the local oracle model of computation. We show that the answer is negative for both deterministic and…
In this paper, we describe efficient MapReduce simulations of parallel algorithms specified in the BSP and PRAM models. We also provide some applications of these simulation results to problems in parallel computational geometry for the…
Pipeline parallelism is one of the key components for large-scale distributed training, yet its efficiency suffers from pipeline bubbles which were deemed inevitable. In this work, we introduce a scheduling strategy that, to our knowledge,…
Given a distribution of pebbles to the vertices of a graph, a pebbling move removes two pebbles from a single vertex and places a single pebble on an adjacent vertex. The pebbling number $\pi(G)$ is the smallest number such that, for any…
Pebble games are single-player games on DAGs involving placing and moving pebbles on nodes of the graph according to a certain set of rules. The goal is to pebble a set of target nodes using a minimum number of pebbles. In this paper, we…
We provide a high-level cost comparison between Regev's quantum algorithm with Eker{\aa}-G\"artner's extensions on the one hand, and existing state-of-the-art quantum algorithms for factoring and computing discrete logarithms on the other.…