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We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to…
In previous research, quantum resources were concretely estimated for solving Elliptic Curve Discrete Logarithm Problem(ECDLP). In [1], the quantum algorithm was optimized for the binary elliptic curves and the main optimization target was…
The widespread adoption of blockchain technology has amplified the spectrum of potential threats to its integrity and security. The ongoing quest to exploit vulnerabilities emphasizes how critical it is to expand on current research…
This paper considers a sensor attack and fault detection problem for linear cyber-physical systems, which are subject to system noise that can obey an unknown light-tailed distribution. We propose a new threshold-based detection mechanism…
In this paper, we improve Bruschweiler's algorithm such that only one query is needed for searching the single object z from N=2^n unsorted elements. Our algorithm construct the new oracle query function g(.) satisfying g(x)=0 for all input…
We provide a robust defence to adversarial attacks on discriminative algorithms. Neural networks are naturally vulnerable to small, tailored perturbations in the input data that lead to wrong predictions. On the contrary, generative models…
We describe an efficient quantum algorithm for solving the linear matrix equation AX+XB=C, where A, B, and C are given complex matrices and X is unknown. This is known as the Sylvester equation, a fundamental equation with applications in…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
Differential equations (DEs) serve as the cornerstone for a wide range of scientific endeavors, their solutions weaving through the core of diverse fields such as structural engineering, fluid dynamics, and financial modeling. DEs are…
Random linear network coding can be used in peer-to-peer networks to increase the efficiency of content distribution and distributed storage. However, these systems are particularly susceptible to Byzantine attacks. We quantify the impact…
The Feistel construction is a fundamental technique for building pseudorandom permutations and block ciphers. This paper shows that a simple adaptation of the construction is resistant, even to algorithm substitution attacks -- that is,…
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
Variational hybrid quantum-classical algorithms are promising candidates for near-term implementation on quantum computers. In these algorithms, a quantum computer evaluates the cost of a gate sequence (with speedup over classical cost…
Significant efforts are being spent on building a quantum computer. At the same time, developments in quantum software are rapidly progressing. Insufficient quantum resources often are the problem when running quantum algorithms. New…
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to…
We present a reduced-dimension, ballistic deposition, Monte Carlo particle packing algorithm and discuss its application to the analysis of the microstructure of hard-sphere systems with broad particle size distributions. We extend our…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…