Related papers: Quantum Speedup for Nonreversible Markov Chains
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum…
The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems. It has been conjectured that quantum analogs of…
These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…
Markov chain methods are remarkably successful in computational physics, machine learning, and combinatorial optimization. The cost of such methods often reduces to the mixing time, i.e., the time required to reach the steady state of the…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
We study from a theoretical viewpoint the fundamental problem of efficiently computing the stationary distribution of general classes of structured Markov processes. In strong contrast with previous work, we consider this fundamental…
Markov chain Monte Carlo algorithms have important applications in counting problems and in machine learning problems, settings that involve estimating quantities that are difficult to compute exactly. How much can quantum computers speed…
Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum…
It is shown that quantum computer can detect the existence of root of a function almost exponentially more efficient than the classical counterpart. It is also shown that a quantum computer can produce quantum state corresponding to the…
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Since quantum systems produce counter-intuitive patterns believed not to be efficiently…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
Sampling from the stationary distribution is one of the fundamental tasks of Markov chain-based algorithms and has important applications in machine learning, combinatorial optimization and network science. For the quantum case, qsampling…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
An enduring challenge in computer science is reducing the runtime required to solve computational problems. Quantum computing has attracted significant attention due to its potential to deliver asymptotically faster solutions to certain…
Quantum computers can in principle solve certain problems exponentially more quickly than their classical counterparts. We have not yet reached the advent of useful quantum computation, but when we do, it will affect nearly all scientific…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
Quantum computers (QCs) are maturing. When QCs are powerful enough, they may be able to handle problems in chemistry, physics, and finance that are not classically solvable. However, the applicability of quantum algorithms to speed up…