Related papers: New Developments in Quantum Algorithms
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
Given an item and a list of values of size $N$. It is required to decide if such item exists in the list. Classical computer can search for the item in O(N). The best known quantum algorithm can do the job in $O(\sqrt{N})$. In this paper, a…
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…
With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…
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…
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the…
We create a variety of new quantum algorithms that use Grover's algorithm and similar techniques to give polynomial speedups over their classical counterparts. We begin by introducing a set of tools that carefully minimize the impact of…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor to the complexity. In order to make full…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Quantum computing is gaining popularity across a wide range of scientific disciplines due to its potential to solve long-standing computational problems that are considered intractable with classical computers. One promising area where…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
We present two new quantum algorithms. Our first algorithm is a generalization of amplitude amplification to the case when parts of the quantum algorithm that is being amplified stop at different times. Our second algorithm uses the first…
Only a few classes of quantum algorithms are known which provide a speed-up over classical algorithms. However, these and any new quantum algorithms provide important motivation for the development of quantum computers. In this article new…