Quantum Subspace Expansion
1. Introduction As quantum computing enters the noisy intermediate-scale quantum (NISQ) era, one of the key challenges is managing errors and limited coherence times. Quantum Subspace Expansion (QSE) is a….
Category: Quantum Computing
Quantum Algorithms for Sparse Problems
1. Introduction In many real-world applications—from data science and machine learning to physics and engineering—problems are sparse. This means most of the data or matrix elements involved are zero or….
Quantum Gibbs Sampling
1. Introduction In statistical mechanics, economics, and machine learning, we often want to understand how a system behaves under uncertainty — especially when it’s influenced by randomness, temperature, or energy…..
Quantum Amplitude Estimation
1. Introduction Quantum Amplitude Estimation (QAE) is a cornerstone algorithm in quantum computing, playing a key role in a variety of applications such as finance, machine learning, physics simulations, and….
Quantum Sampling Algorithms
1. Introduction Quantum sampling algorithms are a class of quantum algorithms designed to sample from probability distributions that are either hard or impossible to sample using classical computers. Unlike traditional….
Quantum Algorithms for Optimization Problems
1. Introduction Optimization problems are central to many fields including operations research, logistics, finance, engineering, and artificial intelligence. These problems typically involve finding the best solution from a set of….
Quantum Walks on Graphs
1. Introduction In classical computation, random walks on graphs are a powerful tool used in algorithms, search, and probability theory. They form the backbone of important applications in web page….
Quantum Algorithms for Solving PDEs
1. Introduction to PDEs Partial Differential Equations (PDEs) are foundational in modeling dynamic systems that evolve over time and space. They are used extensively across fields such as physics (wave….
Quantum Matrix Inversion Techniques
1. Introduction Matrix inversion is a fundamental operation in science and engineering. Whether in data science, computer graphics, or physical simulations, inverting a matrix is often a crucial step to….
Quantum Algorithms for Linear Systems (HHL Algorithm)
1. Introduction Solving linear systems of equations is at the heart of many scientific, engineering, and business problems. Whether it’s modeling traffic flow, performing financial risk assessments, or simulating physical….