Improving the Variational Quantum Eigensolver Using Variational Adiabatic Quantum Computing

The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm for finding the minimum eigenvalue of a Hamiltonian that involves the optimization of a parameterized quantum circuit. Since the resulting optimization problem is in general nonconvex, the method can converge to suboptimal parameter values that do not yield the minimum eigenvalue. In this work, we address this shortcoming by adopting the concept of variational adiabatic quantum computing (VAQC) as a procedure to improve VQE. In VAQC, the ground state of a continuously parameterized Hamiltonian is approximated via a parameterized quantum circuit. We discuss some basic theory of VAQC to motivate the development of a hybrid quantum-classical homotopy continuation method. The proposed method has parallels with a predictor-corrector method for numerical integration of differential equations. While there are theoretical limitations to the procedure, we see in practice that VAQC can successfully find good initial circuit parameters to initialize VQE. We demonstrate this with two examples from quantum chemistry. Through these examples, we provide empirical evidence that VAQC, combined with other techniques (an adaptive termination criteria for the classical optimizer and a variance-based resampling method for the expectation evaluation), can provide more accurate solutions than “plain” VQE, for the same amount of effort.

Parametric estimation of gyrotactic microorganism hybrid nanofluid flow between the conical gap of spinning disk-cone apparatus

The silver, magnesium oxide and gyrotactic microorganism-based hybrid nanofluid flow inside the conical space between disc and cone is addressed in the perspective of thermal energy stabilization. Different cases have been discussed between the spinning of cone and disc in the same or counter wise directions. The hybrid nanofluid has been synthesized in the presence of silver Ag and magnesium oxide MgO nanoparticulate. The viscous dissipation and the magnetic field factors are introduced to the modeled equations. The parametric continuation method (PCM) is utilized to numerically handle the modeled problem. Magnesium oxide is chemically made up of Mg2+ and O2- ions that are bound by a strong ionic connection and can be made by pyrolyzing Mg(OH)2 (magnesium hydroxide) and MgCO3 (magnesium carbonate) at high temperature (700–1500 °C). For metallurgical, biomedical and electrical implementations, it is more efficient. Similarly, silver nanoparticle's antibacterial properties could be employed to control bacterial growth. It has been observed that a circulating disc with a stationary cone can achieve the optimum cooling of the cone-disk apparatus while the outer edge temperature remains fixed. The thermal energy profile remarkably upgraded with the magnetic effect, the addition of nanoparticulate in base fluid and Eckert number.

Casimir free energy for massive fermions: a comparative study of various approaches

We compute the Casimir thermodynamic quantities for a massive fermion field between two parallel plates with the MIT boundary conditions, using three different general approaches and present explicit solutions for each. The Casimir thermodynamic quantities include the Casimir Helmholtz free energy, pressure, energy and entropy. The three general approaches that we use are based on the fundamental definition of Casimir thermodynamic quantities, the analytic continuation method represented by the zeta function method, and the zero temperature subtraction method. We include the renormalized versions of the latter two approaches as well, whereas the first approach does not require one. Within each general approach, we obtain the same results in a few different ways to ascertain the selected cancellations of infinities have been done correctly. We then do a comparative study of the three different general approaches and their results, and show that they are in principle not equivalent to each other and they yield in general different results. In particular, we show that the Casimir thermodynamic quantities calculated only by the first approach have all three properties of going to zero as the temperature, the mass of the field, or the distance between the plates increases.

Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model

We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized T$$ \overline{\mathrm{T}} $$ T ¯ deformations. We focus on the sinh-Gordon model and its elliptic deformation in both its fermionic and bosonic realizations. We confirm that the determining factor for a turning point in the TBA, interpreted as a finite Hagedorn temperature, is the difference between the number of bound states and resonances in the theory. Implementing the numerical pseudo-arclength continuation method, we are able to follow the solutions to the TBA equations past the turning point all the way to the ultraviolet regime. We find that for any number k of resonances the pair of complex conjugate solutions below the turning point is such that the effective central charge is minimized. As k → ∞ the UV effective central charge goes to zero as in the elliptic sinh-Gordon model. Finally we uncover a new family of UV complete integrable theories defined by the bosonic counterparts of the S-matrices describing the Φ1,3 integrable deformation of non-unitary minimal models $$ \mathcal{M} $$ M 2,2n+3.

Rotational nonlinear double-beam energy harvesting

This paper presents an investigation of the performance of a coupled rotational double-beam energy harvester (DBEH) with magnetic nonlinearity. Two spring-connected cantilever beams are fixed on a rotating disc. Repelling magnets are attached to the frame and to the lower beam tip, and an equal-mass block is attached to the tip of the upper beam. To describe the dynamic response, a theoretical model related to the rotational motion of the coupled cantilever beam is derived from the Lagrange equations. In addition, the harmonic balance method, together with the arc-length continuation method, is applied to obtain the frequency response functions (FRFs). Parametric studies are then conducted to analyze the effect of varying the parameters on the energy harvesting performance, and numerical analysis is performed to validate the analytical solutions. Finally, the theoretical model is verified by forward- and reverse-frequency-sweeping experiments. The DBEH in rotational motion can perform effective energy harvesting over a wide range of rotational frequencies (10 to 35 rad/s). The upper beam is found to exhibit better energy harvesting efficiency than the lower beam around the resonant frequency. This study effectively broadens the energy harvesting bandwidth and provides a theoretical model for the design of nonlinear magnet-coupled double-beam structure in rotational energy harvesting.

Flow Analysis of Hybridized Nanomaterial Liquid Flow in the Existence of Multiple Slips and Hall Current Effect over a Slendering Stretching Surface

Carbon nanotubes (CNTs) are favored materials in the manufacture of electrochemical devices because of their mechanical and chemical stability, good thermal and electrical conductivities, physiochemical consistency, and featherweight. With such intriguing carbon nanotubes properties in mind, the current research aims to investigate the flow of hybridized nano liquid containing MWCNTs (multi-wall carbon nanotubes) and SWCNTs (single-wall carbon nanotubes) across a slendering surface in the presence of a gyrotactic-microorganism. The temperature and solutal energy equation are modified with the impact of the modified Fourier and Fick’s law, binary chemical reaction, viscous dissipation, and joule heating. The slip conditions are imposed on the surface boundaries. The flow equations are converted into ODEs by applying similarity variables. The bvp4c approach is applied to tackle the coupled and extremely nonlinear boundary value problem. The outputs are compared with the PCM (Parametric continuation method) to ensure that the results are accurate. The influence of involved characteristics on energy distribution, velocity profiles, concentration, and microorganism field are presented graphically. It is noted that the stronger values of the wall thickness parameter and the Hartmann number produce a retardation effect; as a result, the fluid velocity declines for MWCNT and SWCNT hybrid nano liquid. Furthermore, the transport of the mass and heat rate improves with a higher amount of both the hybrid and simple nanofluids. The amount of local skin friction and the motile density of microorganisms are discussed and tabulated. Furthermore, the findings are validated by comparing them to the published literature, which is a notable feature of the present results. In this aspect, venerable stability has been accomplished.