Classical and quantum shortcuts to adiabaticity in a tilted piston

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 classical problem, a counterdiabatic classical Hamiltonian $H_{CD}$ ensures that the classical action remains constant even under rapid driving. Both the quantum and classical versions of this problem have been solved for the special case of scale-invariant driving, characterized by linear expansions, contractions or translations of the system. Here we investigate an example of a non-scale-invariant system -- a tilted piston. We solve exactly for the classical counterdiabatic Hamiltonian $H_{CD}(q,p,t)$, which we then quantize to obtain a Hermitian operator $\hat H_{CD}(t)$. Using numerical simulations, we find that $\hat H_{CD}$ effectively suppresses non-adiabatic excitations under rapid driving. These results offer a proof of principle -- beyond the special case of scale-invariant driving -- that quantum shortcuts to adiabaticity can successfully be constructed from their classical counterparts.Comment: 13 pages, 7 figure

Bridging quantum, classical and stochastic shortcuts to adiabaticity

Adiabatic invariants -- quantities that are preserved under the slow driving of a system's external parameters -- are important in classical mechanics, quantum mechanics and thermodynamics. Adiabatic processes allow a system to be guided to evolve to a desired final state. However, the slow driving of a quantum system makes it vulnerable to environmental decoherence, and for both quantum and classical systems, it is often desirable and time-efficient to speed up a process. {\it Shortcuts to adiabaticity} are strategies for preserving adiabatic invariants under rapid driving, typically by means of an auxiliary field that suppresses excitations, otherwise generated during rapid driving. Several theoretical approaches have been developed to construct such shortcuts. In this dissertation we focus on two different approaches, namely {\it counterdiabatic} driving and {\it fast-forward} driving, which were originally developed for quantum systems. The counterdiabatic approach introduced independently by Dermirplak and Rice [{\it J. Phys. Chem. A}, 107:9937, 2003], and Berry [{\it J. Phys. A: Math. Theor.}, 42:365303, 2009] formally provides an exact expression for the auxiliary Hamiltonian, which however is abstract and difficult to translate into an experimentally implementable form. By contrast, the fast-forward approach developed by Masuda and Nakamura [{\it Proc. R. Soc. A}, 466(2116):1135, 2010] provides an auxiliary potential that may be experimentally implementable but generally applies only to ground states. The central theme of this dissertation is that classical shortcuts to adiabaticity can provide useful physical insights and lead to experimentally implementable shortcuts for analogous quantum systems. We start by studying a model system of a tilted piston to provide a proof of principle that quantum shortcuts can successfully be constructed from their classical counterparts. In the remainder of the dissertation, we develop a general approach based on {\it flow-fields} which produces simple expressions for auxiliary terms required for both counterdiabatic and fast-forward driving. We demonstrate the applicability of this approach for classical, quantum as well as stochastic systems. We establish strong connections between counterdiabatic and fast-forward approaches, and also between shortcut protocols required for classical, quantum and stochastic systems. In particular, we show how the fast-forward approach can be extended to highly excited states of quantum systems

Quantum Discord in a spin-1/2 transverse XY Chain Following a Quench

We report a study on the zero-temperature quantum discord as a measure of two-spin correlation of a transverse XY spin chain following a quench across a quantum critical point and investigate the behavior of mutual information, classical correlations and hence of discord in the final state as a function of the rate of quenching. We show that though discord vanishes in the limit of very slow as well as very fast quenching, it exhibits a peak for an intermediate value of the quenching rate. We show that though discord and also the mutual information exhibit a similar behavior with respect to the quenching rate to that of concurrence or negativity following an identical quenching, there are quantitative differences. Our studies indicate that like concurrence, discord also exhibits a power law scaling with the rate of quenching in the limit of slow quenching though it may not be expressible in a closed power law form. We also explore the behavior of discord on quenching linearly across a quantum multicritical point (MCP) and observe a scaling similar to that of the defect density.Comment: 6 pages, 5 figure

Path dependent scaling of geometric phase near a quantum multi-critical point

We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in the vicinity of a quantum multi-critical point. We approach the multi-critical point along different paths and estimate the geometric phase by applying a rotation in all spins about z-axis by an angle $\eta$. Although the geometric phase itself vanishes at the multi-critical point, the derivative with respect to the anisotropy parameter of the model shows peaks at different points on the ferromagnetic side close to it where the energy gap is a local minimum; we call these points `quasi-critical'. The value of the derivative at any quasi-critical point scales with the system size in a power-law fashion with the exponent varying continuously with the parameter $\alpha$ that defines a path, upto a critical value $\alpha = \alpha_{c}=2$. For $\alpha > \alpha_{c}$, or on the paramagnetic side no such peak is observed. Numerically obtained results are in perfect agreement with analytical predictions.Comment: 5 pages, 6 figure

Integration of multiple epigenomic marks improves prediction of variant impact in saturation mutagenesis reporter assay

The integrative analysis of highâ throughput reporter assays, machine learning, and profiles of epigenomic chromatin state in a broad array of cells and tissues has the potential to significantly improve our understanding of noncoding regulatory element function and its contribution to human disease. Here, we report results from the CAGI 5 regulation saturation challenge where participants were asked to predict the impact of nucleotide substitution at every base pair within five diseaseâ associated human enhancers and nine diseaseâ associated promoters. A library of mutations covering all bases was generated by saturation mutagenesis and altered activity was assessed in a massively parallel reporter assay (MPRA) in relevant cell lines. Reporter expression was measured relative to plasmid DNA to determine the impact of variants. The challenge was to predict the functional effects of variants on reporter expression. Comparative analysis of the full range of submitted prediction results identifies the most successful models of transcription factor binding sites, machine learning algorithms, and ways to choose among or incorporate diverse datatypes and cellâ types for training computational models. These results have the potential to improve the design of future studies on more diverse sets of regulatory elements and aid the interpretation of diseaseâ associated genetic variation.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151884/1/humu23797_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151884/2/humu23797.pd

Shortcuts to Thermodynamic Computing: The Cost of Fast and Faithful Information Processing.

Landauer's Principle states that the energy cost of information processing must exceed the product of the temperature, Boltzmann's constant, and the change in Shannon entropy of the information-bearing degrees of freedom. However, this lower bound is achievable only for quasistatic, near-equilibrium computations-that is, only over infinite time. In practice, information processing takes place in finite time, resulting in dissipation and potentially unreliable logical outcomes. For overdamped Langevin dynamics, we show that counterdiabatic potentials can be crafted to guide systems rapidly and accurately along desired computational paths, providing shortcuts that allow for the precise design of finite-time computations. Such shortcuts require additional work, beyond Landauer's bound, that is irretrievably dissipated into the environment. We show that this dissipated work is proportional to the computation rate as well as the square of the information-storing system's length scale. As a paradigmatic example, we design shortcuts to create, erase, and transfer a bit of information metastably stored in a double-well potential. Though dissipated work generally increases with operation fidelity, we show that it is possible to compute with perfect fidelity in finite time with finite work. We also show that the robustness of information storage affects an operation's energetic cost-specifically, the dissipated work scales as the information lifetime of the bistable system. Our analysis exposes a rich and nuanced relationship between work, speed, size of the information-bearing degrees of freedom, storage robustness, and the difference between initial and final informational statistics