Related papers: Analytic Approach for Controlling Realistic Quantu…
Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on…
The density-matrix renormalization-group (DMRG) algorithm is extended to treat time-dependent problems. The method provides a systematic and robust tool to explore out-of-equilibrium phenomena in quantum many-body systems. We illustrate the…
We review the Random Batch Methods (RBM) for interacting particle systems consisting of $N$-particles, with $N$ being large. The computational cost of such systems is of $O(N^2)$, which is prohibitively expensive. The RBM methods use small…
Simple, precise, and robust control is demanded for operating a large quantum information processor. However, existing routes to high-fidelity quantum control rely heavily on arbitrary waveform generators that are difficult to scale up.…
Analog quantum simulators with global control fields have emerged as powerful platforms for exploring complex quantum phenomena. Despite these advances, a fundamental theoretical question remains unresolved: to what extent can such systems…
Quantum state estimation is a fundamental task in quantum information theory, where one estimates real parameters continuously embedded in a family of quantum states. In the theory of quantum state estimation, the widely used Cram\'er Rao…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…
Restricted Boltzmann Machines (RBM) are simple statistical models defined on a bipartite graph which have been successfully used in studying more complicated many-body systems, both classical and quantum. In this work, we exploit the…
A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of `magic' quantum states. In this context, we develop a general…
In the literature the performance of quantum data transmission systems is usually evaluated in the absence of thermal noise. A more realistic approach taking into account the thermal noise is intrinsically more difficult because it requires…
Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain q-generalizations of the…
Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum…
We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be…
Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of quantum mechanical problems, such as the single particle Schr\"odinger equation with an…
We survey recent mathematical results about the spectrum of random band matrices. We start by exposing the Erd{\H o}s-Schlein-Yau dynamic approach, its application to Wigner matrices, and extension to other mean-field models. We then…
Quantum optimal control has numerous important applications ranging from pulse shaping in magnetic-resonance imagining to laser control of chemical reactions and quantum computing. Our objective is to address two major challenges that have…
Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the…
We describe algorithms, and experimental strategies, for the Pareto optimal control problem of simultaneously driving an arbitrary number of quantum observable expectation values to their respective extrema. Conventional quantum optimal…
Most quantum metrology protocols harness highly entangled probe states and globally accessible measurements to surpass the standard quantum limit. However, it is challenging to satisfy these requirements in realistic many-body sensors. We…
Fifty years of developments in nuclear magnetic resonance (NMR) have resulted in an unrivaled degree of control of the dynamics of coupled two-level quantum systems. This coherent control of nuclear spin dynamics has recently been taken to…