Related papers: Lower Bounds for Parallel Quantum Counting
In this work, we study the phase estimation problem. We show an alternative, simpler and self-contained proof of query lower bounds. Technically, compared to the previous proofs [NW99, Bes05], our proof is considerably elementary.…
In this work, we show that parallel repetition of public-coin interactive arguments reduces the soundness error at an exponential rate even in the post-quantum setting. Moreover, we generalize this result to hold for threshold verifiers,…
We present several quantum algorithms for performing nearest-neighbor learning. At the core of our algorithms are fast and coherent quantum methods for computing distance metrics such as the inner product and Euclidean distance. We prove…
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
In this work I present a generalization of Amdahl's law on the limits of a parallel implementation with many processors. In particular I establish some mathematical relations involving the number of processors and the dimension of the…
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…
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…
We present a novel parallelisation scheme that simplifies the adaptation of learning algorithms to growing amounts of data as well as growing needs for accurate and confident predictions in critical applications. In contrast to other…
Motivated by the result that an `approximate' evaluation of the Jones polynomial of a braid at a $5^{th}$ root of unity can be used to simulate the quantum part of any algorithm in the quantum complexity class BQP, and results relating BQP…
Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a…
We report an alternative scheme for implementing generalized quantum measurements that does not require the usage of auxiliary system. Our method utilizes solely: (a) classical randomness and post-processing, (b) projective measurements on…
Parallel algorithms designed for simulation and performance evaluation of single-server tandem queueing systems with both infinite and finite buffers are presented. The algorithms exploit a simple computational procedure based on recursive…
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 present a multipartite nonlocal game in which each player must guess the input received by his neighbour. We show that quantum correlations do not perform better than classical ones at this game, for any prior distribution of the inputs.…
The main reason for query model's prominence in complexity theory and quantum computing is the presence of concrete lower bounding techniques: polynomial and adversary method. There have been considerable efforts to give lower bounds using…
We investigate Quantum Target Ranging in the context of multi-hypothesis testing and its applicability to real-world LiDAR systems. First, we demonstrate that ranging is generally an easier task compared to the well-studied problem of…
Parallel black box optimization consists in estimating the optimum of a function using $\lambda$ parallel evaluations of $f$. Averaging the $\mu$ best individuals among the $\lambda$ evaluations is known to provide better estimates of the…
A simple proof of quantum adiabatic theorem is provided. Quantum adiabatic approximation is divided into two kinds. For Hamiltonian H(t/T), a relation between the size of the error caused by quantum adiabatic approximation and the parameter…
Quantum corrections to Legendre transformations are shown to cancel to all orders in supersymmetric theories in path integral formalism. Using this result, lagrangians for auxiliary fields are generalized to non-quadratic forms. In…
We investigate query-to-communication lifting theorems for models related to the quantum adversary bounds. Our results are as follows: 1. We show that the classical adversary bound lifts to a lower bound on randomized communication…