Related papers: Variational Quantum Linear Solver
Variational quantum algorithms (VQAs) constitute a prominent framework for exploring the capabilities of near-term quantum computers. As the effectiveness of VQAs depends heavily on the design of variational quantum circuits, Quantum…
Quantum linear system algorithms (QLSAs) can provide exponential speedups for the solution of linear systems, but the growth of the condition number for finite element problems can eliminate the exponential speedup. QLSAs are also incapable…
Many problems of industrial interest are NP-complete, and quickly exhaust resources of computational devices with increasing input sizes. Quantum annealers (QA) are physical devices that aim at this class of problems by exploiting quantum…
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…
Quantum computing has the potential to speed up some optimization methods. One can use quantum computers to solve linear systems via Quantum Linear System Algorithms (QLSAs). QLSAs can be used as a subroutine for algorithms that require…
Trotterization-based, iterative approaches to quantum simulation are restricted to simulation times less than the coherence time of the quantum computer, which limits their utility in the near term. Here, we present a hybrid…
Implementing time-evolution operators in shallow quantum circuits is important for quantum simulations. The standard method of Trotterization requires a large number of gates to achieve practical accuracy. Variational Quantum Simulation…
Variational Hybrid Quantum Classical Algorithms (VHQCAs) are a class of quantum algorithms intended to run on noisy intermediate-scale quantum (NISQ) devices. These algorithms employ a parameterized quantum circuit (ansatz) and a…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
Quantum variational optimization has been posed as an alternative to solve optimization problems faster and at a larger scale than what classical methods allow. In this paper we study systematically the role of entanglement, the structure…
Variational quantum algorithms (VQAs) are leading strategies for using near-term quantum devices, with a well-studied bottleneck being their trainability. Standard expectation-value objectives with expressive circuits frequently encounter…
The Variational Quantum Eigensolver (VQE) is a key algorithm for near-term quantum computers, yet its performance is often limited by the classical optimization of circuit parameters. We propose using the velocity Verlet algorithm, inspired…
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…
A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an…
Current universal quantum computers have a limited number of noisy qubits. Because of this, it is difficult to use them to solve large-scale complex optimization problems. In this paper we tackle this issue by proposing a quantum…
Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although…
The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…
Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through…
Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for…
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…