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Quantum computing promises the possibility of studying the real-time dynamics of nonperturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices…
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…
We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium…
We propose a quantum-classical hybrid algorithm to encode a given arbitrarily quantum state $\vert \Psi \rangle$ onto an optimal quantum circuit $\hat{\mathcal{C}}$ with a finite number of single- and two-qubit quantum gates. The proposed…
In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
Due to recent technological advances, actual quantum devices are being constructed and used to perform computations. As a result, many classical problems are being restated so as to be solved on quantum computers. Some examples include…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is…
We show how to perform universal quantum computation with atoms confined in optical lattices which works both in the presence of defects and without individual addressing. The method is based on using the defects in the lattice, wherever…
Quantum algorithms for factoring and discrete logarithm have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden…
The quantum hybrid algorithm has become a very promising and speedily method today for solving the larger-scale optimization in the noisy intermediate-scale quantum (NISQ) era. The unit commitment (UC) problem is a fundamental problem in…
In this paper we show that certain special cases of the hidden subgroup problem can be solved in polynomial time by a quantum algorithm. These special cases involve finding hidden normal subgroups of solvable groups and permutation groups,…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that…
Unit group computations are a cryptographic primitive for which one has a fast quantum algorithm, but the required number of qubits is $\tilde O(m^5)$. In this work we propose a modification of the algorithm for which the number of qubits…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…