Balancing the Quantum Speed Limit and Instantaneous Energy Cost in Adiabatic Quantum Evolution

Adiabatic time-optimal quantum controls are extensively used in quantum technologies to break the constraints imposed by short coherence times.However,practically it is crucial to consider the trade-off between the quantum evolution speed and instantaneous energy cost of process because of the constraints in the available control Hamiltonian.Here,we experimentally show that using a transmon qubit that,even in the presence of vanishing energy gaps,it is possible to reach a highly time-optimal adiabatic quantum driving at low energy cost in the whole evolution process.This validates the recently derived general solution of the quantum Zermelo navigation problem,paving the way for energy-efficient quantum control which is usually overlooked in conventional speed-up schemes,including the well-known counter-diabatic driving.By designing the control Hamiltonian based on the quantum speed limit bound quantified by the changing rate of phase in the interaction picture,we reveal the relationship between the quantum speed limit and instantaneous energy cost.Consequently,we demonstrate fast and high-fidelity quantum adiabatic processes by employing energy-efficient driving strengths,indicating a promising strategy for expanding the applications of time-optimal quantum controls in superconducting quantum circuits.

Quantum State-Resolved Nonadiabatic Dynamics of the H+NaF→Na+HF Reaction

The H+NaF reaction is investigated at the quantum state-resolved level using the time-dependent wavepacket method based on a set of accurate diabatic potential energy surfaces.Oscillatory structures in the total reaction probability indicate the presence of the short-lived intermediate complex.

Fast population transfer with a superconducting qutrit via non-Hermitian shortcut to adiabaticity

Non-Hermitian dissipation dynamics,capable of turning the conventionally detrimental decoherence effects to useful resources for state engineering,is highly attractive to quantum information processing.In this work,an effective scheme is developed for implementing fast population transfer with a superconducting qutrit via the non-Hermitian shortcut to adiabaticity(STA).We first deal with aΛ-configuration interaction between the qutrit and microwave drivings,in which the dephasing-assisted qubit state inversion requiring an overlarge dephasing rate is constructed non-adiabatically.After introducing a feasible ancillary driving that directly acts upon the qubit states,the target state transfer can be well realized but with an accessible qubit dephasing rate.Moreover,a high fidelity could be numerically obtained in the considered system.The strategy could provide a new route towards the non-Hermitian shortcut operations on superconducting quantum circuits.

Comparative study on the flame retardancy of CO_(2) and N_(2) during coal adiabatic oxidation process

To test the effectiveness of N_(2) and CO_(2) in preventing coal from spontaneously combusting,researchers used an adiabatic oxidation apparatus to conduct an experiment with different temperature starting points.Non-adsorbed helium(He)was used as a reference gas,and coal and oxygen concentration temperature variations were analyzed after inerting.The results showed that He had the best cooling effect,N_(2) was second,and CO_(2) was the worst.At 70℃and 110℃,the impact of different gases on reducing oxygen concentration and the cooling effect was the same.However,at the starting temperature of 150℃,CO_(2) was less effective in lowering oxygen concentration at the later stage than He and N_(2).N_(2) and CO_(2) can prolong the flame retardation time of inert gas and reduce oxygen displacement with an initial temperature increase.When the starting temperature is the same,N_(2) injection cools coal samples and replaces oxygen more effectively than CO_(2) injection.The flame retardancy of inert gas is the combined result of the cooling effect of inert gas and the replacement of oxygen.These findings are essential for using inert flame retardant technology in the goaf.

Charge self-trapping in two strand biomolecules:Adiabatic polaron approach

We investigate the properties of the excess charge(electron, hole) introduced into a two-strand biomolecule. We consider the possibility that the stable soliton excitation can be formed due to interaction of excess charge with the phonon subsystem. The influence of overlap of the molecular orbitals between adjacent structure elements of the macromolecular chain on the soliton properties is discussed. Special attention is paid to the influence of the overlapping of the molecular orbitals between structure elements placed on the different chains. Using the literature values of the basic energy parameters of the two-chain biomolecular structures, possible types of soliton solutions are discussed.

Quantum adiabatic algorithms using unitary interpolation

We present two efficient quantum adiabatic algorithms for Bernstein–Vazirani problem and Simon’s problem.We show that the time complexities of the algorithms for Bernstein–Vazirani problem and Simon’s problem are O(1)and O(n),respectively,which are the same complexities as the corresponding algorithms in quantum circuit model.In these two algorithms,the adiabatic Hamiltonians are realized by unitary interpolation instead of standard linear interpolation.Comparing with the adiabatic algorithms using linear interpolation,the energy gaps of our algorithms keep constant.Therefore,the complexities are much easier to analyze using this method.

Effects of constitutive parameters on adiabatic shear localization for ductile metal based on JOHNSON-COOK and gradient plasticity models

By using the widely used JOHNSON-COOK model and the gradient-dependent plasticity to consider microstructural effect beyond the occurrence of shear strain localization,the distributions of local plastic shear strain and deformation in adiabatic shear band(ASB)were analyzed.The peak local plastic shear strain is proportional to the average plastic shear strain,while it is inversely proportional to the critical plastic shear strain corresponding to the peak flow shear stress.The relative plastic shear deformation between the top and base of ASB depends on the thickness of ASB and the average plastic shear strain.A parametric study was carried out to study the influence of constitutive parameters on shear strain localization.Higher values of static shear strength and work to heat conversion factor lead to lower critical plastic shear strain so that the shear localization is more apparent at the same average plastic shear strain.Higher values of strain-hardening exponent,strain rate sensitive coefficient,melting point,thermal capacity and mass density result in higher critical plastic shear strain,leading to less apparent shear localization at the same average plastic shear strain.The strain rate sensitive coefficient has a minor influence on the critical plastic shear strain,the distributions of local plastic shear strain and deformation in ASB.The effect of strain-hardening modulus on the critical plastic shear strain is not monotonous.When the maximum critical plastic shear strain is reached,the least apparent shear localization occurs.

PERTURBATION OF SYMMETRIES OF BIRKHOFF SYSTEM AND ADIABATIC INVARIANTS

The perturbation of symmetries of the free Birkhoff system undersmall excitation is discussed.The concept of high-order adiabatic invariant is pre-sented,and the form of adiabatic invariants and the conditions for their existence aregiven.Then these results are generalized to the constrained Birkhoff system.Oneexample is presented to illustrate these results.

Dynamic Mechanical Behavior and Adiabatic Shear Bands of Ultrafine Grained Pure Zirconium

Dynamic compression tests were carried out to investigate dynamic mechanical behavior and adiabatic shear bands in ultrafine grained(UFG)pure zirconium prepared by equal channel angular pressing(ECAP)and rotary swaying.The cylindrical specimens were deformed dynamically on the split Hopkinson pressure bar(SHPB)at different strain rates of 800 to 4000s^-1 at room temperature.The temperature distribution of the shear bands was estimated on the basis of temperature rise of uniform plastic deformation stage and thermal diffusion effect.The results show that the true stress-true strain curves of UFG pure zirconium are concave upward trend of strain in range of 0.02-0.16 due to the effects of strain hardening,strain rate hardening and thermal softening.The formation of the adiabatic shear bands is the main reason of UFG pure zirconium failure.A large number of micro-voids are observed in the adiabatic shear bands,and the macroscopic cracks develop from the micro-voids coalescence.The fracture surface of UFG pure zirconium exhibits quasi cleavage fracture with the characteristic features of shear dimples and river pattern.The highest temperature within the shear bands of UFG pure zirconium is about 592 K.

Perturbation to Noether Quasi-Symmetry and Adiabatic Invariants for Nonholonomic Systems on Time Scales

Perturbation to Noether quasi-symmetry and adiabatic invariants for the nonholonomic system on time scales are studied. Firstly, some properties of time scale calculus are reviewed. Secondly, the differential equations of motion for the nonholonomic system on time scales, Noether quasi-symmetry and conserved quantity are given. Thirdly, perturbation to Noether quasi-symmetry and adiabatic invariants, which are the main results of this paper, are investigated. The main results are achieved by two steps, the first step is to obtain adiabatic invariants without transforming the time, and the next is to obtain adiabatic invariants under the infinitesimal transformations of both the time and the coordinates. And in the end, an example is given to illustrate the methods and results.

Conserved quantities and adiabatic invariants of fractional Birkhoffian system of Herglotz type

In order to further study the dynamical behavior of nonconservative systems,we study the conserved quantities and the adiabatic invariants of fractional Brikhoffian systems with four kinds of different fractional derivatives based on Herglotz differential variational principle.Firstly,the conserved quantities of Herglotz type for the fractional Brikhoffian systems based on Riemann-Liouville derivatives and their existence conditions are established by using the fractional Pfaff-Birkhoff-d Alembert principle of Herglotz type.Secondly,the effects of small perturbations on fractional Birkhoffian systems are studied,the conditions for the existence of adiabatic invariants for the Birkhoffian systems of Herglotz type based on Riemann-Liouville derivatives are established,and the adiabatic invariants of Herglotz type are obtained.Thirdly,the conserved quantities and adiabatic invariants for the fractional Birkhoffian systems of Herglotz type under other three kinds of fractional derivatives are established,namely Caputo derivative,Riesz-Riemann-Liouville derivative and Riesz-Caputo derivative.Finally,an example is given to illustrate the application of the results.

Experiment on Adiabatic Film Cooling Effectiveness in Front Zone of Effusion Cooling Configuration

Experimental investigation is performed to investigate the cooling characteristics in the front zone of effusion configuration. Effects of blowing ratio,multi-hole arrangement mode,hole-to-hole pitch and jet orientation angle on the adiabatic film cooling effectiveness are concentrated on. The results show that the film layer displays an obvious"developing"feature in the front zone of effusion cooling scheme,for either the staggered or inline multi-hole arrangement. The varying gradient of the laterally-averaged adiabatic cooling effectiveness along the streamwise direction is greater for the staggered arrangement than that for the inline arrangement. The holes array arranged in staggered mode with small hole-tohole pitches is in favor of obtaining developed film coverage layer rapidly.

Perturbation to Noether Symmetries and Adiabatic Invariants for Generalized Birkhoff Systems Based on El-Nabulsi Dynamical Model

With the action of small perturbation on generalized El-Nabulsi-Birkhoff fractional equations,the perturbation to Noether symmetries and adiabatic invariants are studied under the framework of El-Nabulsi′s fractional model.Firstly,based on the invariance of El-Nabulsi-Pfaff action under the infinitesimal transformations of group,the exact invariants are given.Secondly,on the basis of the definition of higher order adiabatic invariants of a dynamical system,the adiabatic invariants of the Noether symmetric perturbation for disturbed generalized El-Nabulsi′s fractional Birkhoff system are presented under some conditions,and some special cases are discussed.Finally,an example known as Hojman-Urrutia problem is given to illustrate the application of the results.

Hojman Exact Invariants and Adiabatic Invariants of Hamilton System

The perturbation to Lie symmetry and adiabatic invariants are studied.Based on the concept of higher-order adiabatic invariants of mechanical systems with action of a small perturbation,the perturbation to Lie symmetryis studied,and Hojman adiabatic invariants of Hamilton system are obtained.An example is given to illustrate theapplication of the results.

Formation of adiabatic shearing band for high-strength Ti-5553 alloy:A dramatic thermoplastic microstructural evolution

By using split Hopkinson pressure bar, optical microscopy and electronic microscopy, we investigate the influence of initial microstructures on the adiabatic shear behavior of high-strength Ti-5Al-5V-5Mo-3Cr(Ti-5553) alloy with lamellar microstructure and bimodal microstructure. Lamellar alloy tends to form adiabatic shearing band(ASB) at low compression strain, while bimodal alloy is considerably ASBresistant. Comparing with the initial microstructure of Ti-5553 alloy, we find that the microstructure of the ASB changes dramatically. Adiabatic shear of lamellar Ti-5553 alloy not only results in the formation of recrystallized β nano-grains within the ASB, but also leads to the chemical redistribution of the alloying elements such as Al, V, Cr and Mo. As a result, the alloying elements distribute evenly in the ASB.In contrast, the dramatic adiabatic shear of bimodal alloy might give rise to the complete lamination of the globular primary a grain and the equiaxial prior β grain, which is accompanied by the dynamic recrystallization of a lamellae and β lamellae. As a result, ASB of bimodal alloy is composed of a/β nanomultilayers. Chemical redistribution does not occur in ASB of bimodal alloy. Bimodal Ti-5553 alloy should be a promising candidate for high performance armors with high mass efficiency due to the processes high dynamic flow stress and excellent ASB-resistance.

Calculation of a Nonuniform and Nonadiabatic Model of Sonoluminescence

A nonuniform and nonadiabatic model has been developed to research the gas dynamics within a bubble of sonoluminescence.The model includes three diffusive effects of gas viscosity,thermal conduction and radiative transport simultaneously,and calculations prove that they have important influences on the characteristics of sonoluminescence.The model has been solved numerically and gives the results of about 104 K peak temperature and l00ps pulse duration which are consistent with recent experiments.

Perturbation to Noether Symmetry and Noether adiabatic Invariants of Discrete Mechanico-Electrical Systems

Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is investigated.First,Noether theorem of a system is presented.Secondly,the criterion of perturbation to Noether symmetry of the system is given.Based on the definition of adiabatic invariants,Noether adiabatic invariants of the system are obtained.Finally,An example is given to support these results.

Estimation of Time to Maximum Rate Under Adiabatic Conditions(TMR_(ad)) Using Kinetic Parameters Derived From DSC-Investigation of Thermal Behavior of 3-Methyl-4-Nitrophenol

Kinetic parameters of the decomposition of hazardous chemicals can be applied for the estimation of their thermal behavior under any temperature profile.Presented paper describes the application of the advanced kinetic approach for the determination of the thermal behavior also under adiabatic conditions occurring e.g.in batch reactors in case of cooling failure.The kinetics of the decomposition of different samples(different manufacturers and batches) of 3-methyl-4-nitrophenol were investigated by conventional DSC in non-isothermal(few heating rates varying from 0.25 to 8.0K/min) and isothermal(range of 200~260℃) modes.The kinetic parameters obtained with AKTS-Thermokinetics Software were applied for calculating reaction rate and progress under different heating rates and temperatures and verified by comparing simulated and experimental signals.After application of the heat balance to compare the amount of heat generated during reaction and its removal from the system,the knowledge of reaction rate at any temperature profiles allowed the determination of the temperature increase due to the self-heating in adiabatic and pseudo-adiabatic conditions.Applied advanced kinetic approach allowed simulation the course of the Heat-Wait-Search(HWS) mode of operation of adiabatic calorimeters.The thermal safety diagram depicting dependence of Time to Maximum Rate(TMR) on the initial temperature was calculated and compared with the results of HWS experiments carried out in the system with Ф-factor amounting to 3.2.The influence of the Ф-factor and reaction progress reached at the end of the HWS monitoring on the TMR is discussed.Presented calculations clearly indicate that even very minor reaction progress reduces the TMRad of 24h characteristic for a sample with initial reaction progress amounting to zero.Described estimation method can be verified by just one HWS-ARC,or by one correctly chosen ISO-ARC run of reasonable duration by knowing in advance the dependence of the TMR on the initial temperature for any Ф-factor.Proposed procedure results in significant shortening of the measuring time compared to a safety hazard approach based on series of ARC experiments carried out at the beginning of a process safety evaluation.

DESIGN OF TERNARY ADIABATIC MULTIPLIER ON SWITCH-LEVEL

The design of ternary adiabatic multiplier adopting switch-level design techniques is proposed in this paper. First by using the theory of three essential circuit elements, the switch-level functional expressions of the carry and product circuit models, which compose one bit ternary adiabatic multiplier, are derived. Consequently, the corresponding circuit structures can be ob-tained, and the evaluation and energy recovery for ternary circuit can be realized by bootstrapped NMOS transistors and cross-memory structure. Based on the designed circuits, the four bits ter-nary adiabatic multiplier is further realized by adopting the ripple carry manner. The PSPICE simulation results indicate that the designed circuits have correct logic function and are charac-terized with distinctive low power consumption.

Perturbation to Noether Symmetry and Adiabatic Invariants for Dynamical Systems with Nonstandard Lagrangians

The perturbation to Noether symmetry and adiabatic invariants for dynamical systems with nonstandard Lagrangians are studied. Based on two kinds of nonstandard Lagrangians( i. e.exponential Lagrangians and power-law Lagrangians),the exact invariants of Noether type are given. Based on the definition of highorder adiabatic invariants,the relationship between the perturbation of Noether symmetry and the adiabatic invariants of the system under a small disturbance is studied,and then the corresponding theorems of adiabatic invariants are established. Finally, two examples are given to illustrate the methods and results appear in this paper.