Related papers: Worm Algorithm for Problems of Quantum and Classic…
The worm algorithm is a versatile technique in the Markov chain Monte Carlo method for both classical and quantum systems. The algorithm substantially alleviates critical slowing down and reduces the dynamic critical exponents of various…
These lecture notes aim to provide a clear and comprehensive introduction to using open quantum system theory for quantum algorithms. The main arguments are Variational Quantum Algorithms, Quantum Error Correction, Dynamical Decoupling and…
This is a short introduction to Quantum Computing intended for physicists. The basic idea of a quantum computer is introduced. Then we concentrate on Shor's integer factoring algorithm.
We present a new class of algorithms for performing valence-bond quantum Monte Carlo of quantum spin models. Valence-bond quantum Monte Carlo is a T=0 Monte Carlo method based on sampling of a set of operator-strings that can be viewed as…
Worm algorithms have been very successful with the simulation of sigma models with fixed length spins which result from scalar field theories in the limit of infinite quartic coupling lambda. Here we investigate closer their algorithmic…
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor's algorithm this peculiar problem can be solved in…
This article surveys the state of the art in quantum computer algorithms, including both black-box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so a representative sample is given. This includes a…
This paper surveys the field of quantum computer algorithms. It gives a taste of both the breadth and the depth of the known algorithms for quantum computers, focusing on some of the more recent results. It begins with a brief review of…
Quantum computers, with parallel computing and entanglement effects, excel in cryptography analysis and big data processing. However, they are not fully developed yet, and their performance needs further evaluation. Traditional computer…
We discuss the implementation of a directed geometrical worm algorithm for the study of quantum link-current models. In this algorithm Monte Carlo updates are made through the biased reptation of a worm through the lattice. A directed…
We investigate in this work a recently proposed diagrammatic quantum Monte Carlo method --- the inchworm Monte Carlo method --- for open quantum systems. We establish its validity rigorously based on resummation of Dyson series. Moreover,…
This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase…
This is a set of lecture notes used in a graduate topic class in applied mathematics called ``Quantum Algorithms for Scientific Computation'' at the Department of Mathematics, UC Berkeley during the fall semester of 2021. These lecture…
Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding…
We review the path-integral quantum Monte Carlo method and discuss its implementation by multiworm algorithms. We analyze in details the features of the algorithms, and focus our attention on the computation of the $N$-body density matrix…
Classifying phases of local quantum systems is a general problem that includes special cases such as free fermions, commuting projectors, and others. An important distinction in this classification should be made between classifying…
We discuss an effective theory for QCD at finite chemical potential and non-zero temperature, where QCD is reduced to its center degrees of freedom. The effective action can be mapped to a flux representation, where the complex phase…