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In slowly driven classical systems, work is a stochastic quantity and its probability distribution is known to satisfy the work fluctuation-dissipation relation, which states that the mean and variance of the dissipated work are linearly…
The universal quantum work relation connects a functional of an arbitrary observable averaged over the forward process to the free energy difference and another functional averaged over the time-reversed process. Here, we ask the question…
Achieving fast, excitation-free quantum control is a vital challenge in modern quantum technologies. In many cases, shortcuts to adiabaticity enable fast adiabatic-like protocols, yet determining control parameters that satisfy practical…
Unitary processes allow for the transfer of work to and from Hamiltonian systems. However, to achieve nonzero power for the practical extraction of work, these processes must be performed within a finite time, which inevitably induces…
In this thesis, it is presented a set of results in adiabatic dynamics (closed and open system) and transitionless quantum driving that promote some advances in our understanding on quantum control and Hamiltonian inverse engineering. In…
Quantum phase estimation requires simulating the evolution of the Hamiltonian, for which product formulas are attractive due to their smaller qubit cost and ease of implementation. However, the estimation of the error incurred by product…
Nonequilibrium work-Hamiltonian connection for a microstate plays a central role in diverse branches of statistical thermodynamics (fluctuation theorems, quantum thermodynamics, stochastic thermodynamics, etc.). We show that the change in…
We show that the quantum Fisher information attained in an adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision and therefore regular quantum metrology under optimal settings is always superior.…
Quantum coherence profoundly alters classical thermodynamic expectations by modifying the structure and accessibility of probability distributions. Classically, transitions to lower-entropy states (local second-law violations) are…
Quantum fluctuations driven by non-stoquastic Hamiltonians have been conjectured to be an important and perhaps essential missing ingredient for achieving a quantum advantage with adiabatic optimization. We introduce a transformation that…
In this paper we consider the problem of tracking the state of a quantum system via a continuous measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation.…
The operation of near-term quantum technologies requires the development of feasible, implementable, and robust strategies of controlling complex many body systems. To this end, a variety of techniques, so-called "shortcuts to adiabaticty",…
We investigate the statistics of the work performed during a quench across a quantum phase transition using the adiabatic perturbation theory. It is shown that all the cumulants of work exhibit universal scaling behavior analogous to the…
Adiabatic quantum state evolution can be accelerated through a variety of shortcuts to adiabaticity. In one approach, a counterdiabatic quantum Hamiltonian $\hat H_{CD}$ is constructed to suppress nonadiabatic excitations. In the analogous…
The existence of singularities in the spectrum of non-Hermitian Hamiltonians leads to a non-trivial spectral topology which can be exploited to generate topological operations. However, their implementation has remained elusive due to the…
Counterdiabatic driving (CD) exploits auxiliary control fields to tailor the nonequilibrium dynamics of a quantum system, making possible the suppression of dissipated work in finite-time thermodynamics and the engineering of optimal…
Quantum phase estimation (QPE) is a central algorithmic primitive that estimates eigenvalues of a Hamiltonian up to precision $\epsilon$ in Heisenberg-limited time $T=\Theta(1/\epsilon)$. Standard gate-based implementations of QPE require…
Time-continuous quantum error correction, necessary to protect quantum information under time-dependent Hamiltonians, relies on weak continuous syndrome measurements. Implementing these measurements requires a continuous coupling among at…
The standard definition of quantum fluctuating work is based on the two-projective energy measurement, which however does not apply to systems with initial quantum coherence because the first projective energy measurement destroys the…
An open question of fundamental importance in quantum thermodynamics is how to describe the statistics of work for initial state with quantum coherence. In this paper, work statistics is considered from a fully new perspective of…