Related papers: An exact quantum order finding algorithm and its a…
Deutsch-Jozsa (DJ) problem is one of the most important problems demonstrating the power of quantum algorithm. DJ problem can be described as a Boolean function $f$: $\{0,1\}^n\rightarrow \{0,1\}$ with promising it is either constant or…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
We report the realization, using nuclear magnetic resonance techniques, of the first quantum computer that reliably executes an algorithm in the presence of strong decoherence. The computer is based on a quantum error avoidance code that…
We propose a probabilistic quantum algorithm that decides whether a monochrome picture matches a given template (or one out of a set of templates). As a major advantage to classical pattern recognition, the algorithm just requires a few…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
Linear combination of unitaries (LCU for short) is one of the most important techniques in designing quantum algorithms. In this paper, we propose a new quantum algorithm in three different forms to achieve LCU. Different from previous…
Grover's algorithm, orginally conceived as a means of searching an unordered database, can also be used to extract solutions from the result sets generated by quantum computations. The Grover algorithm exploits the concept of an oracle…
In this note we study the number of quantum queries required to identify an unknown multilinear polynomial of degree d in n variables over a finite field F_q. Any bounded-error classical algorithm for this task requires Omega(n^d) queries…
Principal component analysis has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the…
Quantum computing has gained a lot of attention recently, and scientists have seen potential applications in this field using quantum computing for Cryptography and Communication to Machine Learning and Healthcare. Protein folding has been…
We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
We present a quantum algorithm for simulating complex many-body systems and finding their ground states, combining the use of tensor networks and density matrix renormalization group (DMRG) techniques. The algorithm is based on von…
Consider the unstructured search of an unknown number l of items in a large unsorted database of size N. The multi-object quantum search algorithm consists of two parts. The first part of the algorithm is to generalize Grover's…
We present a fast algorithm for modular exponentiation when the factorization of the modulus is known. Let $a,n,m$ be positive integers and suppose $m$ factors canonically as $\prod_{i=1}^k p_i^{e_i}$. Choose integer parameters $t_i\in [1,…
Generic quantum search algorithm searches for target entity in an unsorted database by repeatedly applying canonical Grover's quantum rotation transform to reach near the vicinity of the target entity represented by a basis state in the…
Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor's algorithm is well beyond the…
Shor's algorithm for the prime factorization of numbers provides an exponential speedup over the best known classical algorithms. However, nontrivial practical applications have remained out of reach due to experimental limitations. The…
Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high…
Quantum algorithms are typically understood in terms of the evolution of a multi-qubit quantum system under a prescribed sequence of unitary transformations. The input to the algorithm prescribes some of the unitary transformations in the…