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Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
Solving eigenvalue problems is crucially important for both classical and quantum applications. Many well-known numerical eigensolvers have been developed, including the QR and the power methods for classical computers, as well as the…
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…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
Quantum chemical calculations on quantum computers have been focused mostly on simulating molecules in gas-phase. Molecules in liquid solution are however most relevant for Chemistry. Continuum solvation models represent a good compromise…
Computing the excited states of a given Hamiltonian is computationally hard for large systems, but methods that do so using quantum computers scale tractably. This problem is equivalent to the PCA problem where we are interested in…
In recent years, quantum computing has drawn significant interest within the field of high-energy physics. We explore the potential of quantum algorithms to resolve the combinatorial problems in particle physics experiments. As a concrete…
We address the problem of solving a system of linear equations via the Quantum Singular Value Transformation (QSVT). One drawback of the QSVT algorithm is that it requires huge quantum resources if we want to achieve an acceptable accuracy.…
A universal quantum simulator would enable efficient simulation of quantum dynamics by implementing quantum-simulation algorithms on a quantum computer. Specifically the quantum simulator would efficiently generate qubit-string states that…
We address the question of how a quantum computer can be used to simulate experiments on quantum systems in thermal equilibrium. We present two approaches for the preparation of the equilibrium state on a quantum computer. For both…
Quantum computing presents a promising path toward precise quantum chemical simulations, particularly for systems that challenge classical methods. This work investigates the performance of the Variational Quantum Eigensolver (VQE) in…
We present a hybrid classical-quantum algorithm to solve optimization problems in current quantum computers, whose basic idea is to assist variational quantum eigensolvers (VQE) with adiabatic change of the Hamiltonian. The rational for…
This paper presents a hybrid quantum-classical approach to prime factorization. The proposed algorithm is based on the Variational Quantum Eigensolver (VQE), which employs a classical optimizer to find the ground state of a given…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…
In the last years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised. On one side, "direct" quantum algorithms that aim at encoding the solution of the PDE by executing one…
Variational quantum algorithms exploit the features of superposition and entanglement to optimize a cost function efficiently by manipulating the quantum states. They are suitable for noisy intermediate-scale quantum (NISQ) computers that…
The recent developments of quantum computing present potential novel pathways for quantum chemistry, as the increased computational power of quantum computers could be harnessed to naturally encode and solve electronic structure problems.…
We propose a qubit efficient scheme to study ground state properties of quantum many-body systems on near-term noisy intermediate scale quantum computers. One can obtain a tensor network representation of the ground state using a number of…
Quantum computing brings a promise of new approaches into computational quantum chemistry. While universal, fault-tolerant quantum computers are still not available, we want to utilize today's noisy quantum processors. One of their flagship…