Related papers: Finding eigenvectors with a quantum variational al…
Variational quantum algorithms and, in particular, variants of the varational quantum eigensolver have been proposed to address combinatorial optimization (CO) problems. Using only shallow ansatz circuits, these approaches are deemed…
Necessary and sufficient conditions are given for the construction of a hybrid quantum computer that operates on both continuous and discrete quantum variables. Such hybrid computers are shown to be more efficient than conventional quantum…
The Variational Quantum Algorithms (VQAs) are hybrid quantum-classical algorithms and they can be used in the Nosiy Intermadiate Scale Quantum (NISQ) devises. The Variational Quantum Eigensolver (VQE) was suggested as a first VQA. VQE is…
Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments…
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…
Parameterized quantum circuits are a promising technology for achieving a quantum advantage. An important application is the variational simulation of time evolution of quantum systems. To make the most of quantum hardware, variational…
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.
Variational quantum algorithms (VQAs) are hybrid quantum-classical approaches used for tackling a wide range of problems on noisy intermediate-scale quantum (NISQ) devices. Testing these algorithms on relevant hardware is crucial to…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
We introduce a family of variational quantum algorithms called quantum iterative power algorithms (QIPA) that outperform existing hybrid near-term quantum algorithms of the same kind. We demonstrate the capabilities of QIPA as applied to…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
The characterization of observables, expressed via Hermitian operators, is a crucial task in quantum mechanics. For this reason, an eigensolver is a fundamental algorithm for any quantum technology. In this work, we implement a…
This paper proposes a hybrid quantum-classical algorithm that learns a suitable quantum feature map that separates unlabelled data that is originally non linearly separable in the classical space using a Variational quantum feature map and…
Current gate-based quantum computers have the potential to provide a computational advantage if algorithms use quantum hardware efficiently. To make combinatorial optimization more efficient, we introduce the Filtering Variational Quantum…
An important application for near-term quantum computing lies in optimization tasks, with applications ranging from quantum chemistry and drug discovery to machine learning. In many settings --- most prominently in so-called parametrized or…
Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum…
Given a parameterized quantum circuit such that a certain setting of these real-valued parameters corresponds to Grover's celebrated search algorithm, can a variational algorithm recover these settings and hence learn Grover's algorithm? We…
Variational quantum eigensolvers are touted as a near-term algorithm capable of impacting many applications. However, the potential has not yet been realized, with few claims of quantum advantage and high resource estimates, especially due…
In electronic structure theory, variational methods offer a valuable paradigm for approximating electronic ground states. However, for historical reasons, this principle is mostly restricted to model chemistries in pre-defined fixed basis…
Quantum variational algorithms (QVAs) are increasingly potent tools for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. This work examines the application of the Variational Quantum Eigensolver (VQE)…