Related papers: Simple variational approaches to quantum wells
We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the…
Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…
Using the formalism of extended N=4 supersymmetric quantum mechanics we consider the procedure of the construction of multi-well potentials. We demonstrate the form-invariance of Hamiltonians entering the supermultiplet, using the presented…
We present a simple scheme to evaluate linear response functions including quantum fluctuation corrections on top of the Gutzwiller approximation. The method is derived for a generic multi-band lattice Hamiltonian without any assumption…
Quantum tunneling between two potential wells in a magnetic field can be strongly increased when the potential barrier varies in the direction perpendicular to the line connecting the two wells and remains constant along this line. An…
We study the physics of $\nu=1/2$ bosonic fractional quantum Hall droplets confined in a ring-shaped region delimited by two concentric cylindrically symmetric hard-wall potentials. Trial wave functions based on an extension of the Jack…
We apply power series expansion to symmetric multi-well oscillators bounded by two infinite walls. The spectrum and expectation values obtained are compared with available exact and approximate values for the unbounded ones. It is shown…
We investigate theoretically the fractional quantum Hall effect at half-filling in the lowest Landau level observed in asymmetric wide quantum wells. The asymmetry can be achieved by a potential bias applied between the two sides of the…
We present a variational quantum algorithm for differentiating several hypotheses encoded as quantum channels. Both state preparation and measurement are simultaneously optimized using success probability of single-shot discrimination as an…
Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique solution for all…
This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are…
The problem of topology change transitions in quantum gravity is investigated from the Wheeler-de Witt wave function point of view. It is argued that for all theories allowing wormhole effects the wave function of the universe is…
One of the most important properties of classical neural networks is how surprisingly trainable they are, though their training algorithms typically rely on optimizing complicated, nonconvex loss functions. Previous results have shown that…
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…
The development of quantum computational techniques has advanced greatly in recent years, parallel to the advancements in techniques for deep reinforcement learning. This work explores the potential for quantum computing to facilitate…
Hybrid quantum-classical variational algorithms such as the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA) are promising applications for noisy, intermediate-scale quantum (NISQ) computers.…
We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining…
This paper investigates quantized thin vortex rings with an internal structure. The quantization scheme of this dynamical system is based on an earlier the approach proposed by the author. Both energy spectrum and circulation spectrum are…
Quantum reservoir computing (QRC) is an emerging framework for near-term quantum machine learning that offers in-memory processing, platform versatility across analogue and digital systems, and avoids typical trainability challenges such as…
We present a variational method which uses a quartic exponential function as a trial wave-function to describe time-dependent quantum mechanical systems. We introduce a new physical variable $y$ which is appropriate to describe the shape of…