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This article studies experimental design in settings where the experimental units are large aggregate entities (e.g., markets), and only one or a small number of units can be exposed to the treatment. In such settings, randomization of the…
The wide-ranging adoption of quantum technologies requires practical, high-performance advances in our ability to maintain quantum coherence while facing the challenge of state collapse under measurement. Here we use techniques from control…
Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression…
Methods that preserve coherence broadly impact all quantum information processing and metrology applications. Dynamical decoupling methods accomplish this by protecting qubits in noisy environments but are typically constrained to the limit…
We consider a system of multiple qubits without any quantum control. We show that one can mediate entanglement between different subsystems in a controlled way by adding a (locally) controlled auxiliary system of the same size that couples…
This paper explores the utility of instantaneous and continuous observations in the optimal control of quantum dynamics. Simulations of the processes are performed on several multilevel quantum systems with the goal of population transfer.…
Synchronization of coupled oscillators is observed in many natural and engineered systems and emerges due to the interactions within the system. It can be both beneficial, e.g., in power grids, and harmful, e.g., in epileptic seizures. In…
In this paper, we study some control problems that derive from time optimal control of coupled spin dynamics in NMR spectroscopy and quantum information and computation. Time optimal control helps to minimize relaxation losses. The ability…
The manipulation of quantum information in large systems requires precise control of quantum systems that are out-of-equilibrium. As the size of the system increases, its fragility in response to external perturbations and intrinsic…
In this study, we address the challenge of controlling quantum systems under environmental influences using the theory of dynamical invariants. We employ a reverse engineering approach to develop control protocols designed to be robust…
Dynamical decoupling protocols are one of the most used tools for efficient quantum error corrections and for reservoir engineering. In this paper we study the effect of dynamical decoupling pulses on the preservation of both quantum and…
We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes,…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which…
The generation and storage of spin squeezing is an attracting topic in quantum metrology and the foundations of quantum mechanics. The major models to realize the spin squeezing are the one- and two-axis twisting models. Here, we consider a…
Unitary control and decoherence appear to be irreconcilable in quantum mechanics. When a quantum system interacts with an environment, control strategies usually fail due to decoherence. In this letter, we propose a time-optimal unitary…
We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in…
Quantum algorithms have demonstrated provable speedups over classical counterparts, yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge. In this work, we decode the quantum…
We have applied a machine learning algorithm to predict the emergence of environment-induced spontaneous synchronization between two qubits in an open system setting. In particular, we have considered three different models, encompassing…
Refocusing, or dynamical decoupling, is a coherent control technique where the internal dynamics of a quantum system is effectively averaged out by an application of specially designed driving fields. The method has originated in nuclear…