Related papers: Quantum Jacobi-Davidson Method
The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for quantum simulation that can be run on near-term quantum hardware. A challenge in VQE -- as well as any other heuristic algorithm for finding ground states…
Variational quantum algorithms, optimized using gradient-based methods, often exhibit sub-optimal convergence performance due to their dependence on Euclidean geometry. Quantum natural gradient descent (QNGD) is a more efficient method that…
Simulating the Hubbard model is of great interest to a wide range of applications within condensed matter physics, however its solution on classical computers remains challenging in dimensions larger than one. The relative simplicity of…
In the Hamiltonian formulation, Quantum Field Theory calculations scale exponentially with spatial volume, making real-time simulations intractable on classical computers and motivating quantum computation approaches. In Hamiltonian…
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum…
An approximate diagonalization method is proposed that combines exact diagonalization and perturbation expansion to calculate low energy eigenvalues and eigenfunctions of a Hamiltonian. The method involves deriving an effective Hamiltonian…
We develop a computationally and numerically efficient method to calculate binding energies and corresponding wave functions of quantum mechanical three-body problems in low dimensions. Our approach exploits the tensor structure of the…
Digital quantum computers provide a computational framework for solving the Schr\"{o}dinger equation for a variety of many-particle systems. Quantum computing algorithms for the quantum simulation of these systems have recently witnessed…
This paper explores the potential contribution of quantum computing, specifically the Variational Quantum Eigensolver (VQE), into atmospheric physics research and application problems using as an example the Lorenz system, a paradigm of…
A method is presented in which the ground-state subspace is projected out of a Hamiltonian representation. As a result of this projection, an effective Hamiltonian is constructed where its ground-state coincides with an excited-state of the…
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,…
For any local Hamiltonian H, I construct a local CPT map and stopping condition which converges to the ground state subspace of H. Like any ground state preparation algorithm, this algorithm necessarily has exponential run-time in general…
The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will…
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…
The simulation of the dynamics of a system coupled to a low-temperature environment is a promising application of quantum computers to determine ground-state properties of physical systems. However, this approach requires not only the…
Sample-based quantum diagonalization (SQD) offers a powerful route to accurate quantum chemistry on noisy intermediate-scale quantum (NISQ) devices by combining quantum sampling with classical diagonalization. Here we introduce HSQD, a…
Understanding the entanglement structure of local Hamiltonian ground spaces is a physically motivated problem, with applications ranging from tensor network design to quantum error-correcting codes. To this end, we study the complexity of…
Quantum state tomography (QST) via local measurements on reduced density matrices (LQST) is a promising approach but becomes impractical for large systems. To tackle this challenge, we developed an efficient quantum state tomography method…
Semidefinite programs (SDPs) are a particular class of convex optimization problems with applications in combinatorial optimization, operational research, and quantum information science. Seminal work by Brand\~{a}o and Svore shows that a…
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…