Related papers: Quantum and Classical Algorithms for Bounded Dista…
We give a quantum algorithm for solving the Bounded Distance Decoding (BDD) problem with a subexponential approximation factor on a class of integer lattices. The quantum algorithm uses a well-known but challenging-to-use quantum state on…
The current paper investigates the bounded distance decoding (BDD) problem for ensembles of lattices whose generator matrices have sub-Gaussian entries. We first prove that, for these ensembles the BDD problem is NP-hard in the worst case.…
We consider a version of the nearest-codeword problem on finite fields $\mathbb{F}_q$ using the Manhattan distance, an analog of the Hamming metric for non-binary alphabets. Similarly to other lattice related problems, this problem is…
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…
We propose a complete quantum-classical hybrid branch-and-bound algorithm (QCBB) to solve binary linear programs with equality constraints. That includes bound calculation, convergence metrics and optimality guarantee to the quantum…
In this paper, we study quantum Ordered Binary Decision Diagrams($OBDD$) model; it is a restricted version of read-once quantum branching programs, with respect to "width" complexity. It is known that the maximal gap between deterministic…
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…
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…
We present several results on comparative complexity for different variants of OBDD models. - We present some results on comparative complexity of classical and quantum OBDDs. We consider a partial function depending on parameter k such…
The techniques of distance verification known for general linear codes are re-applied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance verification…
We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given $n$ $d$-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…
We survey the existing techniques for calculating code distances of classical codes and apply these techniques to generic quantum codes. For classical and quantum LDPC codes, we also present a new linked-cluster technique. It reduces…
Brand\~ao and Svore very recently gave quantum algorithms for approximately solving semidefinite programs, which in some regimes are faster than the best-possible classical algorithms in terms of the dimension $n$ of the problem and the…
In this paper, we prove a lower bound on the soundness of quantum locally testable codes under the distance balancing construction of Evra et al. arXiv:2004.07935 [quant-ph]. Our technical contribution is that the new soundness of the…
Longest common substring (LCS), longest palindrome substring (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved in near linear time. In this work, we present sublinear time quantum algorithms…
The distance of a classical or quantum code is a key figure of merit which reflects its capacity to detect errors. Quantum LDPC code families have considerable promise in reducing the overhead required for fault-tolerant quantum…
The most important computational problem on lattices is the Shortest Vector Problem (SVP). In this paper, we present new algorithms that improve the state-of-the-art for provable classical/quantum algorithms for SVP. We present the…
This paper studies the limitations of the generic approaches to solving cryptographic problems in classical and quantum settings in various models. - In the classical generic group model (GGM), we find simple alternative proofs for the…