Related papers: Quantum Lattice Sieving
Quantum optimal control problems are typically solved by gradient-based algorithms such as GRAPE, which suffer from exponential growth in storage with increasing number of qubits and linear growth in memory requirements with increasing…
Quantum algorithms based on quantum kernel methods have been investigated previously [1]. A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise…
The set of nonnegative integer lattice points in a polytope, also known as the fiber of a linear map, makes an appearance in several applications including optimization and statistics. We address the problem of sampling from this set using…
A fundamental computational problem is to find a shortest non-zero vector in Euclidean lattices, a problem known as the Shortest Vector Problem (SVP). This problem is believed to be hard even on quantum computers and thus plays a pivotal…
The NP-hardness of the closest vector problem (CVP) is an important basis for quantum-secure cryptography, in much the same way that integer factorisation's conjectured hardness is at the foundation of cryptosystems like RSA. Recent work…
A lattice reduction is an algorithm that transforms the given basis of the lattice to another lattice basis such that problems like finding a shortest vector and closest vector become easier to solve. We define a class of bases called…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
Compute-and-Forward is an emerging technique to deal with interference. It allows the receiver to decode a suitably chosen integer linear combination of the transmitted messages. The integer coefficients should be adapted to the channel…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
Quantum computers are expected to break today's public key cryptography within a few decades. New cryptosystems are being designed and standardised for the post-quantum era, and a significant proportion of these rely on the hardness of…
Lattice-based cryptography has emerged as one of the most prominent candidates for post-quantum cryptography, projected to be secure against the imminent threat of large-scale fault-tolerant quantum computers. The Shortest Vector Problem…
Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion…
We present the first explicit connection between quantum computation and lattice problems. Namely, we show a solution to the Unique Shortest Vector Problem (SVP) under the assumption that there exists an algorithm that solves the hidden…
We consider the problem of clustering data that reside on discrete, low dimensional lattices. Canonical examples for this setting are found in image segmentation and key point extraction. Our solution is based on a recent approach to…
Why study Lattice-based Cryptography? There are a few ways to answer this question. 1. It is useful to have cryptosystems that are based on a variety of hard computational problems so the different cryptosystems are not all vulnerable in…
We consider the problem of revealing a small hidden lattice from the knowledge of a low-rank sublattice modulo a given sufficiently large integer -- the {\em Hidden Lattice Problem}. A central motivation of study for this problem is the…
Lattice reduction is a popular preprocessing strategy in multiple-input multiple-output (MIMO) detection. In a quest for developing a low-complexity reduction algorithm for large-scale problems, this paper investigates a new framework…
Machine-learning tasks frequently involve problems of manipulating and classifying large numbers of vectors in high-dimensional spaces. Classical algorithms for solving such problems typically take time polynomial in the number of vectors…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
We show polynomial-time quantum algorithms for the following problems: (*) Short integer solution (SIS) problem under the infinity norm, where the public matrix is very wide, the modulus is a polynomially large prime, and the bound of…