Related papers: Quantum Computation of Eigenvalues within Target I…
We consider the problem of learning the Hamiltonian of a quantum system from estimates of Gibbs-state expectation values. Various methods for achieving this task were proposed recently, both from a practical and theoretical point of view.…
We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…
The use of quantum computing to solve a problem in quantum mechanics is illustrated, step by step, by calculating energies and transition amplitudes in a nonrelativistic quark model. The quantum computations feature the use of variational…
Quasi-degenerate eigenvalue problems are central to quantum chemistry and condensed-matter physics, where low-energy spectra often form manifolds of nearly degenerate states that determine physical properties. Standard quantum algorithms,…
We describe a new polynomial time quantum algorithm that uses the quantum fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and…
The computational cost of quantum algorithms for physics and chemistry is closely linked to the spectrum of the Hamiltonian, a property that manifests in the necessary rescaling of its eigenvalues. The typical approach of using the 1-norm…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…
We adapt the robust phase estimation algorithm to the evaluation of energy differences between two eigenstates using a quantum computer. This approach does not require controlled unitaries between auxiliary and system registers or even a…
Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can estimate the ground state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block…
We study the efficiency of quantum tomographic reconstruction where the system under investigation (quantum target) is indirectly monitored by looking at the state of a quantum probe that has been scattered off the target. In particular we…
Approximating ground and a fixed number of excited state energies, or equivalently low order Hamiltonian eigenvalues, is an important but computationally hard problem. Typically, the cost of classical deterministic algorithms grows…
While quantum illumination (QI) can offer a quantum-enhancement in target detection, its potential for performing target ranging remains unclear. With its capabilities hinging on a joint-measurement between a returning signal and its…
In this thesis, we focus on the energetic analysis within autonomous quantum systems. To this aim, we propose a novel and general formalism for a dynamic description of the energy exchanges between interacting subsystems. From the Schmidt…
Eigenvalue estimation is a central problem for demonstrating quantum advantage, yet its implementation on digital quantum computers remains limited by circuit depth and operational overhead. We present an analog quantum phase estimation…
We present a quantum algorithm for the calculation of scattering amplitudes of massive charged scalar particles in scalar quantum electrodynamics. Our algorithm is based on continuous-variable quantum computing architecture resulting in…
Non-Hermitian Hamiltonians possessing a discrete real spectrum motivated a remarkable research activity in quantum physics and new insights have emerged. In this paper we formulate concepts of statistical thermodynamics for systems…
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical…
We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an…
We consider time periodic Hamiltonian on periodic graphs and estimate the number of its quasi-energy eigenvalues on the finite interval.