Related papers: Quantum algorithm for non-homogeneous linear parti…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…
Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum…
In this paper we presents an algorithm for finding a solution of the linear nonhomogeneous quaternionic-valued differential equations. Moveover, several examples shows the feasibility of our algorithm.
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
Quantum computers are a highly promising tool for efficiently simulating quantum many-body systems. The preparation of their eigenstates is of particular interest and can be addressed, e.g., by quantum phase estimation algorithms. The…
Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex. Here, based on energy variance, we propose a variational method for solving the…
A quantum algorithm for computing the determinant of a unitary matrix $U\in U(N)$ is given. The algorithm requires no preparation of eigenstates of $U$ and estimates the phase of the determinant to $t$ binary digits accuracy with…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown…
In this work we present an algorithm to perform algorithmic differentiation in the context of quantum computing. We present two versions of the algorithm, one which is fully quantum and one which employees a classical step (hybrid…
The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient…
Linear dissipative differential equation is a fundamental model for a large number of physical systems, such as quantum dynamics with non-Hermitian Hamiltonian, open quantum system dynamics, diffusion process and damped system. In this…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum…