Related papers: Block-encoding based quantum algorithm for linear …
With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
We present a fast block direct solver for the unified dynamic simulations of power systems. This solver uses a novel Q-learning based method for task scheduling. Unified dynamic simulations of power systems represent a method in which the…
Distributed-memory matrix multiplication (MM) is a key element of algorithms in many domains (machine learning, quantum physics). Conventional algorithms for dense MM rely on regular/uniform data decomposition to ensure load balance. These…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
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…
The Kaczmarz algorithm is a simple iterative scheme for solving consistent linear systems. At each step, the method projects the current iterate onto the solution space of a single constraint. Hence, it requires very low cost per iteration…
The recent emergence of novel computational devices, such as quantum computers, coherent Ising machines, and digital annealers presents new opportunities for hardware-accelerated hybrid optimization algorithms. Unfortunately, demonstrations…
Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we…
Solving the Toeplitz systems, which is to find the vector $x$ such that $T_nx = b$ given an $n\times n$ Toeplitz matrix $T_n$ and a vector $b$, has a variety of applications in mathematics and engineering. In this paper, we present a…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling…
Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount…
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…
We present a quantum algorithm for solving algebraic Riccati equations, with applications to quantum-chemical random-phase approximation (RPA) and higher-order RPA theories. Our method block-encodes stabilizing Riccati solutions via Riesz…
The rapid pace of recent advancements in numerical computation, notably the rise of GPU and TPU hardware accelerators, have allowed tensor network (TN) algorithms to scale to even larger quantum simulation problems, and to be employed more…
Charged particle reconstruction or track reconstruction is one of the most crucial components of pattern recognition in high-energy collider physics. It is known to entail enormous consumption of computing resources, especially when the…
In this paper, we propose a new of coding/decoding algorithm using Padovan Q-matrices. This method is based on blocked message matrices. an advantage of this method is that the encryption of each message matrix will use a different key and…
Solving differential equations is one of the most computationally expensive problems in classical computing, occupying the vast majority of high-performance computing resources devoted towards practical applications in various fields of…
Quantum computing has the potential to speed up some optimization methods. One can use quantum computers to solve linear systems via Quantum Linear System Algorithms (QLSAs). QLSAs can be used as a subroutine for algorithms that require…