Related papers: Quantum Lattice Sieving
The closest vector problem (CVP) is a fundamental optimization problem in lattice-based cryptography and its conjectured hardness underpins the security of lattice-based cryptosystems. Furthermore, Schnorr's lattice-based factoring…
We prove that any algorithm for learning parities requires either a memory of quadratic size or an exponential number of samples. This proves a recent conjecture of Steinhardt, Valiant and Wager and shows that for some learning problems a…
The Systematic Normal Form (SysNF) is a canonical form of lattices introduced in [Eldar,Shor '16], in which the basis entries satisfy a certain co-primality condition. Using a "smooth" analysis of lattices by SysNF lattices we design a…
Lattices are a popular field of study in mathematical research, but also in more practical areas like cryptology or multiple-input/multiple-output (MIMO) transmission. In mathematical theory, most often lattices over real numbers are…
Efficiently serving large language models (LLMs) requires batching of many requests to reduce the cost per request. Yet, with larger batch sizes and longer context lengths, the key-value (KV) cache, which stores attention keys and values to…
Nonlinear polynomial selection algorithms for the number field sieve address the problem of constructing polynomials with small coefficients by reducing to instances of the well-studied problem of finding short vectors in lattices. The…
Compute-and-Forward (C&F) has been proposed as an efficient strategy to reduce the backhaul load for the distributed antenna systems. Finding the optimal coefficients in C&F has commonly been treated as a shortest vector problem (SVP),…
We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…
Quantum annealing is a promising approach for obtaining good approximate solutions to difficult optimization problems. Folding a protein sequence into its minimum-energy structure represents such a problem. For testing new algorithms and…
In 1994, P. Shor discovered quantum algorithms which can break both the RSA cryptosystem and the ElGamal cryptosystem. In 2007, D-Wave demonstrated the first quantum computer. These events and further developments have brought a crisis to…
Quantum computing poses a threat to contemporary cryptosystems, with advances to a state in which it will cause problems predicted for the next few decades. Many of the proposed cryptosystems designed to be quantum-secure are based on the…
We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the $L_1$ norm of the feature weights vector and relies on a quantum linear programming solver instead…
A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a…
Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern…
We give a deterministic algorithm for solving the (1+eps)-approximate Closest Vector Problem (CVP) on any n dimensional lattice and any norm in 2^{O(n)}(1+1/eps)^n time and 2^n poly(n) space. Our algorithm builds on the lattice point…
Key Encapsulation Mechanisms (KEMs) are a set of cryptographic techniques that are designed to provide symmetric encryption key using asymmetric mechanism (public key). In the current study, we concentrate on design and analysis of key…
Quantum memory is a central component for quantum information processing devices, and will be required to provide high-fidelity storage of arbitrary states, long storage times and small access latencies. Despite growing interest in applying…
Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer,…
Prime generation is a fundamental task in cryptography, number theory, and randomized algorithms. While the classical Sieve of Eratosthenes is simple and efficient in theory, its practical performance on modern central processing units is…
Spike sorting is a class of algorithms used in neuroscience to attribute the time occurences of particular electric signals, called action potential or spike, to neurons. We rephrase this problem as a particular optimization problem : Lasso…