Related papers: Exact and Tunable Quantum Krylov Subspaces via Uni…
Quantum computation and quantum control operate by building unitary transformations out of sequences of elementary quantum logic operations or applications of control fields. This paper puts upper bounds on the minimum time required to…
Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a…
Holonomic quantum computation exploits a quantum state's non-trivial, matrix-valued geometric phase (holonomy) to perform fault-tolerant computation. Holonomies arising from systems where the Hamiltonian traces a continuous path through…
We propose a new variational quantum algorithm, which we refer to as TIMES-ADAPT, that prepares time-evolved states in a low-energy or symmetric subspace of a time-independent Hamiltonian on a quantum computer. Using a specially trained…
In this study, we analyze Krylov Complexity in two-dimensional conformal field theories subjected to deformed SL$(2,\mathbb{R})$ Hamiltonians. In the vacuum state, we find that the K-complexity exhibits a universal phase structure. The…
In this paper, we study time-optimal control problems related to system of two coupled qubits where the time scales involved in performing unitary transformations on each qubit are significantly different. In particular, we address the case…
Understanding the complexity of quantum many-body systems has been attracting much attention recently for its fundamental importance in characterizing complex quantum phases beyond the scope of quantum entanglement. Here, we investigate…
We present a new short-recurrence reaidual-optimal Krylov subspace recycling method for sequences of Hermitian systems of linear equations with a fixed system matrix and changing right-hand sides. Such sequences of linear systems occur…
We analyze the asymptotic behavior of discrete-time, Markovian quantum systems with respect to a subspace of interest. Global asymptotic stability of subspaces is relevant to quantum information processing, in particular for initializing…
We propose a time-exact Krylov-subspace-based method for solving linear ODE (ordinary differential equation) systems of the form $y'=-Ay + g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an…
We discuss efficient solutions to systems of shifted linear systems arising in computations for oscillatory hydraulic tomography (OHT). The reconstruction of hydrogeological parameters such as hydraulic conductivity and specific storage…
In this work we present a detailed analysis of variational quantum phase estimation (VQPE), a method based on real-time evolution for ground and excited state estimation on near-term hardware. We derive the theoretical ground on which the…
In this dissertation I analyze Hamiltonian control of $d$-dimensional quantum systems as realized in alkali atomic spins. Alkali atoms provide an ideal platform for studies of quantum control due to the extreme precision with which the…
We derive an augmented Krylov subspace method with subspace recycling for computing a sequence of matrix function applications on a set of vectors. The matrix is either fixed or changes as the sequence progresses. We assume consecutive…
We show that every finite-dimensional quantum system with Markovian (i.e., GKLS-generated) time evolution has an autonomous unitary dilation which can be dynamically decoupled. Since there is also always an autonomous unitary dilation which…
We investigate the complexity of states and operators evolved with the modular Hamiltonian by using the Krylov basis. In the first part, we formulate the problem for states and analyse different examples, including quantum mechanics,…
We show that the area operator of a quantum extremal surface can be reconstructed directly from boundary dynamics without reference to bulk geometry. Our approach combines the operator-algebra quantum error-correction (OAQEC) structure of…
In this work the determination of low-energy bound states in Quantum Chromodynamics is recast so that it is linked to a weak-coupling problem. This allows one to approach the solution with the same techniques which solve Quantum…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…
A central result in the study of Quantum Hamiltonian Complexity is that the k-Local hamiltonian problem is QMA-complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian is bounded below some value, or above…