Related papers: Solving the encoding bottleneck: of the HHL algori…
We study the problems of state preparation, ground state preparation and quantum state preparation. We propose an analytic approach to a stochastic quantum algorithm which prepares the ground state for $n$-qubit Hamiltonian that is…
In this perspective, we discuss conditions under which it would be possible for a modest fault-tolerant quantum computer to realize a runtime advantage by executing a quantum algorithm with only a small polynomial speedup over the best…
The role of entanglement is discussed in the Harrow-Hassidim-Lloyd (HHL) algorithm. We compute all tripartite entanglement at every steps of the HHL algorithm. The tripartite entanglement is generated in the first quantum phase estimation…
Preparing quantum states is a fundamental task in various quantum algorithms. In particular, state preparation in quantum harmonic oscillators (HOs) is crucial for the creation of qudits and the implementation of high-dimensional…
Computational Fluid Dynamics simulations are crucial in industrial applications but require extensive computational resources, particularly for extreme turbulent regimes. While classical digital approaches remain the standard, quantum…
Following the celebrated quantum algorithm for solving linear equations (so-called HHL algorithm), Childs, Kothari and Somma [SIAM Journal on Computing, {\bf 46}: 1920, (2017)] provided an approach to solve a linear system of equations with…
We introduce a new quantum optimization algorithm for dense Linear Programming problems, which can be seen as the quantization of the Interior Point Predictor-Corrector algorithm \cite{Predictor-Corrector} using a Quantum Linear System…
Scaling up quantum computers to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation demand excessive space overheads by using many physical qubits…
We devise new quantum algorithms that exponentially speeds up the training and prediction procedures of twin support vector machines (TSVM). To train TSVMs using quantum methods, we demonstrate how to prepare the desired input states…
We reiterate the contribution made by Harrow, Hassidim, and Llyod to the quantum matrix equation solver with the emphasis on the algorithm description and the error analysis derivation details. Moreover, the behavior of the amplitudes of…
Leverage score sampling is crucial to the design of randomized algorithms for large-scale matrix problems, while the computation of leverage scores is a bottleneck of many applications. In this paper, we propose a quantum algorithm to…
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…
The solution of linear systems of equations is a very frequent operation and thus important in many fields. The complexity using classical methods increases linearly with the size of equations. The HHL algorithm proposed by Harrow et al.…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
Quantum algorithms manipulate the amplitudes of quantum states to find solutions to computational problems. In this work, we present a framework for applying a general class of non-linear functions to the amplitudes of quantum states, with…
While the preparation of a general quantum state is challenging, realistic problem instances, such as those encountered in quantum chemistry and quantum machine learning-typically exhibit hierarchical amplitude structures, consisting of a…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize…
Attaining a quantum speedup in solving practically useful optimization problems has been one of the holy grails in the field of quantum computing. While prior approaches have demonstrated speedups for certain structured problem classes,…