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We consider the problem of controlling in minimum time a two-level quantum system which can be subject to a drift. The control is assumed to be bounded in magnitude, and to affect two or three independent generators of the dynamics. We…
We derive a Geometric quantum speed limit (QSL) for imaginary-time evolution, where the dynamics is governed by a non-unitary Schr\"{o}dinger equation. By introducing a cost function based on the angular distance between the normalized…
We propose Quantum Riemannian Hamiltonian Descent (QRHD), a quantum algorithm for continuous optimization on Riemannian manifolds that extends Quantum Hamiltonian Descent (QHD) by incorporating geometric structure of the parameter space via…
A fundamental problem in quantum engineering is determining the lowest time required to ensure that all possible unitaries can be generated with the tools available, which is one of a number of possible quantum speed limits. We examine this…
The dynamics of a closed quantum system is often studied with the direct evolution of the Schrodinger equation. In this paper, we propose that the gauge choice (i.e. degrees of freedom irrelevant to physical observables) of the Schrodinger…
We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider…
We present a unifying variational calculus derivation of Groverian geodesics for both quantum state vectors and quantum probability amplitudes. In the first case, we show that horizontal affinely parametrized geodesic paths on the Hilbert…
We consider how different choices of kinetic energy in Hamiltonian Monte Carlo affect algorithm performance. To this end, we introduce two quantities which can be easily evaluated, the composite gradient and the implicit noise. Results are…
It is known that mixed quantum states are highly entropic states of imperfect knowledge (i.e., incomplete information) about a quantum system, while pure quantum states are states of perfect knowledge (i.e., complete information) with…
Big Data is characterized by Volume, Velocity, Veracity and Complexity. The interaction between this huge data is complex with an associated free will having dynamic and non linear nature. We reduced big data based on its characteristics,…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
Many optimally scaling quantum simulation algorithms employ controlled time evolution of the Hamiltonian, which is typically the major bottleneck for their efficient implementation. This work establishes a compression protocol for encoding…
In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is…
One often needs to estimate how fast an evolving state of a quantum system can depart from some target state or target subspace of a Hilbert space. Such estimates are known as quantum speed limits. We derive a quantum speed limit for a…
High-dimensional portfolio optimization faces significant computational challenges under complex constraints, with traditional optimization methods struggling to balance convergence speed and global exploration capability. To address this,…
Recently, Bender et al. have considered the quantum brachistochrone problem for the non-Hermitian $\cal PT$-symmetric quantum system and have shown that the optimal time evolution required to transform a given initial state $|\psi_i\rangle$…
Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using…
Shortcuts to adiabaticity provide a general approach to mimic adiabatic quantum processes via arbitrarily fast evolutions in Hilbert space. For these counter-diabatic evolutions, higher speed comes at higher energy cost. Here, the…
It is expected that a quantum theory of gravity will radically alter our current notion of spacetime geometry. However, contrary to what was commonly assumed for many decades, quantum gravity effects could manifest in scales much larger…
We study quantum brachistochrone problem for the spin-1 system in a magnetic field of a constant absolute value. Such system gives us a possibility to examine in detail the statement of papers [A. Carlini {\it et al.}, Phys. Rev. Lett. {\bf…