Related papers: Optimized regulator for the quantized anharmonic o…
We consider optimization of linear stability of synchronized states between a pair of weakly coupled limit-cycle oscillators with cross coupling, where different components of state variables of the oscillators are allowed to interact. On…
In this work, the energy eigenvalues are calculated for the quadratic ($\frac{g^2 x^2}{2}$), pure quartic ($\lambda x^4 $), and quartic anharmonic oscillators ($\frac{g^2 x^2}{2} + \lambda x^4 $) by applying variational method. For this,…
The initial states which minimize the predictability loss for a damped harmonic oscillator are identified as quasi-free states with a symmetry dictated by the environment's diffusion coefficients. For an isotropic diffusion in phase space,…
The quantum phase estimation algorithm stands as the primary method for determining the ground state energy of a molecular electronic Hamiltonian on a quantum computer. In this context, the ability to initialize a classically tractable…
Two possibile applications of the optimized expansion for the free energy of the quantum-mechanical anharmonic oscillator are discussed. The first method is for the finite temperature effective potential; the second one, for the classical…
In this article, we derived a rigorous lower bound on the ground-state energy for a class of one-dimensional quantum systems in deformed space with minimal coordinate and momentum uncertainties, representing the absolute minimum energy that…
Oscillator Ising machines (OIMs) are networks of coupled oscillators that seek the minimum energy state of an Ising model. Since many NP-hard problems are equivalent to the minimization of an Ising Hamiltonian, OIMs have emerged as a…
We study the bound states of a quantum mechanical system consisting of a simple harmonic oscillator with an inverse square interaction, whose interaction strength is governed by a constant $\alpha$. The singular form of this potential has…
We investigate the relationship between the gap between the energy of the ground state and the first excited state and the decay of correlation functions in harmonic lattice systems. We prove that in gapped systems, the exponential decay of…
We perform a study of various anharmonic potentials using a recently developed method. We calculate both the wave functions and the energy eigenvalues for the ground and first excited states of the quartic, sextic and octic potentials with…
The quantum formalism permits one to discriminate sometimes between any set of linearly-independent pure states with certainty. We obtain the maximum probability with which a set of equally-likely, symmetric, linearly-independent states can…
We show that the rate of closing of the energy gap between the ground state and the first excited state, as a function of system size, behaves in many qualitatively different ways at first-order quantum phase transitions of the…
Quantum annealing is a promising algorithm for solving combinatorial optimization problems. It searches for the ground state of the Ising model, which corresponds to the optimal solution of a given combinatorial optimization problem. The…
The quantum quartic anharmonic oscillator with the Hamiltonian $H=\frac{1}{2}\left( p^{2}+x^{2}\right) +\lambda x^{4}$ is a classical and fundamental model that plays a key role in various branches of physics, including quantum mechanics,…
Genetic regulatory circuits universally cope with different sources of noise that limit their ability to coordinate input and output signals. In many cases, optimal regulatory performance can be thought to correspond to configurations of…
Optimal control problems with oscillations (chattering controls) and concentrations (impulsive controls) can have integral performance criteria such that concentration of the control signal occurs at a discontinuity of the state signal.…
One of the bottlenecks in solving combinatorial optimisation problems using quantum annealers is the emergence of exponentially-closing energy gaps between the ground state and the first excited state during the annealing, which indicates…
The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground…
We probe both the unidimensional quartic harmonic oscillator and the double well potential through a numerical analysis of the Functional Renormalization Group flow equations truncated at first order in the derivative expansion. The two…
In this article, we use geometric optimal control to completely solve the problem of minimum-time transitions between thermal equilibrium states of the quantum parametric oscillator, which finds applications in various physical contexts. We…