Related papers: High-Entanglement Capabilities for Variational Qua…
This work studies the variational quantum eigensolver algorithm, designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. Methods of reducing the number of required qubit…
The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues and eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
Quantum computers offer a promising route to tackling problems that are classically intractable such as in prime-factorization, solving large-scale linear algebra and simulating complex quantum systems, but potentially require…
The Pauli matrices are 2-by-2 matrices that are very useful in quantum computing. They can be used as elementary gates in quantum circuits but also to decompose any matrix of $\mathbb{C}^{2^n \times 2^n}$ as a linear combination of tensor…
Extracting eigenvalues and eigenvectors of exponentially large matrices will be an important application of near-term quantum computers. The Variational Quantum Eigensolver (VQE) treats the case when the matrix is a Hamiltonian. Here, we…
The optimization of circuit parameters of variational quantum algorithms such as the variational quantum eigensolver (VQE) or the quantum approximate optimization algorithm (QAOA) is a key challenge for the practical deployment of near-term…
Solving differential equations is one of the most computationally expensive problems in classical computing, occupying the vast majority of high-performance computing resources devoted towards practical applications in various fields of…
Quantum computers hold immense potential in the field of chemistry, ushering new frontiers to solve complex many body problems that are beyond the reach of classical computers. However, noise in the current quantum hardware limits their…
We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…
Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
With the current rate of progress in quantum computing technologies, systems with more than 50 qubits will soon become reality. Computing ideal quantum state amplitudes for circuits of such and larger sizes is a fundamental step to assess…
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…
When applying eigenvalue decomposition on the quadratic term matrix in a type of linear equally constrained quadratic programming (EQP), there exists a linear mapping to project optimal solutions between the new EQP formulation where $Q$ is…
The role of entanglement and quantum correlations in complex physical systems and quantum information processing devices has become a topic of intense study in the past two decades. In this work we present new tools for learning about…
Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have…
Exploring the potential application of quantum computers in material design and drug discovery has attracted a lot of interest in the age of quantum computing. However, the quantum resource requirement for solving practical electronic…
The variational quantum eigensolver (VQE) is an attracting possible application of near-term quantum computers. Originally, the aim of the VQE is to find a ground state for a given specific Hamiltonian. It is achieved by minimizing the…
Variational quantum algorithms (VQAs) are increasingly being applied in simulations of strongly-bound (covalently bonded) systems using full molecular orbital basis representations. The application of quantum computers to the weakly-bound…