Related papers: A Lower Bound for the Sturm-Liouville Eigenvalue P…
We study the inverse Sturm-Liouville problem on a finite interval from partial knowledge of spectral data. Specifically, we show that the potential can be uniquely reconstructed from the knowledge of a fraction of Dirichlet eigenvalues…
The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here,…
The Quantum Approximate Optimization Algorithm (QAOA) was originally developed to solve combinatorial optimization problems, but has become a standard for assessing the performance of quantum computers. Fully descriptive benchmarking…
Power system fault diagnosis is crucial for identifying the location and causes of faults and providing decision-making support for power dispatchers. However, most classical methods suffer from significant time-consuming, memory overhead,…
We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines Quantum Phase Estimation and Quantum Amplitude Estimation to achieve a quadratic speedup with respect to the best classical…
We develop a spectrally accurate numerical method to compute solutions of a model partial differential equation used in plasma physics to describe diffusion in velocity space due to Fokker-Planck collisions. The solution is represented as a…
Variational quantum eigensolver (VQE) is a promising algorithm suitable for near-term quantum machines. VQE aims to approximate the lowest eigenvalue of an exponentially sized matrix in polynomial time. It minimizes quantum resource…
We build a new estimate for the normalized eigenfunctions of the operator $-\partial_{xx}+\mathcal V(x)$ based on the oscillatory integrals and Langer's turning point method, where $\mathcal V(x)\sim |x|^{2\ell}$ at infinity with $\ell>1$.…
Shenvi, Kempe and Whaley's quantum random-walk search (SKW) algorithm [Phys. Rev. A 67, 052307 (2003)] is known to require $O(\sqrt N)$ number of oracle queries to find the marked element, where $N$ is the size of the search space. The…
Hybrid quantum-classical algorithms have been proposed as a potentially viable application of quantum computers. A particular example - the variational quantum eigensolver, or VQE - is designed to determine a global minimum in an energy…
We propose several algorithms for learning unitary operators from quantum statistical queries with respect to their Choi-Jamiolkowski state. Quantum statistical queries capture the capabilities of a learner with limited quantum resources,…
We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity $O(\sqrt{T}\log n)$ where…
This study investigates quantum computing approaches for solving the windfarm layout optimization (WFLO) problems formulated as a quadratic unconstrained binary optimization (QUBO) problem. We investigate two encoding methods that require…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schr\"odinger equation to obtain molecular energies has been demonstrated to scale polynomially with system…
The study of real-time evolution of lattice quantum field theories using classical computers is known to scale exponentially with the number of lattice sites. Due to a fundamentally different computational strategy, quantum computers hold…
Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…
We analyze the low-lying states for a one-dimensional potential consisting of $N$ identical wells, assuming that the wells are parabolic around the minima. Matching the exact wave functions around the minima and the WKB wave functions in…
In the realm of statistical physics, the number of states in which a system can be realized with a given energy is a key concept that bridges the microscopic and macroscopic descriptions of physical systems. For quantum systems, many…
For the variational quantum eigensolver we propose to generate trial wavefunctions from a small amount of selected Pauli terms of the problem Hamiltonian. Two different approaches, one inspired by the quantum approximate optimization…