Dynamic Ansatz Research Articles

Solving the vehicle routing problem via quantum support vector machines

The vehicle routing problem (VRP) is an example of a combinatorial optimization problem that has attracted academic attention due to its potential use in various contexts. VRP aims to arrange vehicle deliveries to several sites in the most efficient and economical manner possible. Quantum machine learning offers a new way to obtain solutions by harnessing the natural speedups of quantum effects, although many solutions and methodologies are modified using classical tools to provide excellent approximations of the VRP. In this paper, we employ 6 and 12 qubit circuits, respectively, to build and evaluate a hybrid quantum machine learning approach for solving VRP of 3- and 4-city scenarios. The approach employs quantum support vector machines (QSVMs) trained using a variational quantum eigensolver on a static or dynamic ansatz. Different encoding strategies are used in the experiment to transform the VRP formulation into a QSVM and solve it. Multiple optimizers from the IBM Qiskit framework are also evaluated and compared

Machine learning assisted construction of a shallow depth dynamic ansatz for noisy quantum hardware.

The development of various dynamic ansatz-constructing techniques has ushered in a new era, making the practical exploitation of Noisy Intermediate-Scale Quantum (NISQ) hardware for molecular simulations increasingly viable. However, such ansatz construction protocols incur substantial measurement costs during their execution. This work involves the development of a novel protocol that capitalizes on regenerative machine learning methodologies and many-body perturbation theoretical measures to construct a highly expressive and shallow ansatz within the variational quantum eigensolver (VQE) framework with limited measurement costs. The regenerative machine learning model used in our work is trained with the basis vectors of a low-rank expansion of the N-electron Hilbert space to identify the dominant high-rank excited determinants without requiring a large number of quantum measurements. These selected excited determinants are iteratively incorporated within the ansatz through their low-rank decomposition. The reduction in the number of quantum measurements and ansatz depth manifests in the robustness of our method towards hardware noise, as demonstrated through numerical applications. Furthermore, the proposed method is highly compatible with state-of-the-art neural error mitigation techniques. This resource-efficient approach is quintessential for determining spectroscopic and other molecular properties, thereby facilitating the study of emerging chemical phenomena in the near-term quantum computing framework.

Development of a compact Ansatz via operator commutativity screening: Digital quantum simulation of molecular systems.

Recent advancements in quantum information and quantum technology have stimulated a good deal of interest in the development of quantum algorithms toward the determination of the energetics and properties of many-fermionic systems. While the variational quantum eigensolver is the most optimal algorithm in the noisy intermediate scale quantum era, it is imperative to develop compact Ansätze with low-depth quantum circuits that are physically realizable in quantum devices. Within the unitary coupled cluster framework, we develop a disentangled Ansatz construction protocol that can dynamically tailor an optimal Ansatz using the one- and two-body cluster operators and a selection of rank-two scatterers. The construction of the Ansatz may potentially be performed in parallel over multiple quantum processors through energy sorting and operator commutativity prescreening. With a significant reduction in the circuit depth toward the simulation of molecular strong correlation, our dynamic Ansatz construction protocol is shown to be highly accurate and resilient to the noisy circumstances of the near-term quantum hardware.

Variational quantum linear solver with a dynamic ansatz

Variational quantum algorithms have found success in the noisy intermediate-scale quantum era owing to their hybrid quantum-classical approach which mitigate the problems of noise in quantum computers. In our paper, we introduce the dynamic ansatz in the variational quantum linear solver for a system of linear algebraic equations. In this improved algorithm, the number of layers in the hardware efficient ansatz circuit is evolved, starting from a small and gradually increasing until convergence of the solution is reached. We demonstrate the algorithm advantage in comparison to the standard static ansatz by utilizing fewer quantum resources and with a smaller quantum depth on average in the presence and absence of quantum noise and in cases when the number of qubits or condition number of the system matrices are increased. The numbers of iterations and layers can be altered by a switching parameter. The performance of the algorithm in using quantum resources is quantified by a newly defined metric.

Gaussian time-dependent variational principle for the finite-temperature anharmonic lattice dynamics

The anharmonic lattice is a representative example of an interacting bosonic many-body system. The self-consistent harmonic approximation has proven versatile for the study of the equilibrium properties of anharmonic lattices. However, the study of dynamical properties therewithin resorts to an ansatz, whose validity has not yet been theoretically proven. Here, we apply the time-dependent variational principle, a recently emerging useful tool for studying the dynamic properties of interacting many-body systems, to the anharmonic lattice Hamiltonian at finite temperature using the Gaussian states as the variational manifold. We derive an analytic formula for the position-position correlation function and the phonon self-energy, proving the dynamical ansatz of the self-consistent harmonic approximation. We establish a fruitful connection between time-dependent variational principle and the anharmonic lattice Hamiltonian, providing insights in both fields. Our work expands the range of applicability of time-dependent variational principle to first-principles lattice Hamiltonians and lays the groundwork for the study of dynamical properties of the anharmonic lattice using a fully variational framework.

Approximated center-of-mass motion for systems of interacting particles with space- and velocity-dependent friction and anharmonic potential.

We study the center-of-mass motion in systems of trapped interacting particles with space- and velocity-dependent friction and anharmonic traps. Our approach, based on a dynamical ansatz assuming a fixed density profile, allows us to obtain information at once for a wide range of binary interactions and interaction strengths, at linear and nonlinear levels. Our findings are first tested on different simple models by comparison with direct numerical simulations. Then, we apply the method to characterize the motion of the center of mass of a magneto-optical trap and its dependence on the number of trapped atoms. Our predictions are compared with experiments performed on a large Rb(85) magneto-optical trap.

Breathing Dynamics for Systems of Interacting Particles in the Microcanonical and Canonical Descriptions

By means of a dynamical ansatz, we study the breathing dynamics in systems of trapped interacting particles in a unified context, including a wide range of power law interactions and interaction strengths, at linear and nonlinear levels. We present detailed numerical tests of the general theory, and, motivated by Magneto-Optical Traps modeling, we extend it to the case of space-dependent friction and diffusion.

Breathing Mode for Systems of Interacting Particles

We study the breathing mode in systems of trapped interacting particles. Our approach, based on a dynamical ansatz in the first equation of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy allows us to tackle at once a wide range of power-law interactions and interaction strengths, at linear and nonlinear levels. This both puts in a common framework various results scattered in the literature, and by widely generalizing these, emphasizes universal characters of this breathing mode. Our findings are supported by direct numerical simulations.

A phenomenological model for the dynamic response of wind turbines to turbulent wind

To predict the average power output of a wind turbine, a response model is proposed which takes into account: (i) the delayed response to the longitudinal wind speed fluctuations; (ii) a response function of the turbine with arbitrary frequency dependence; (iii) wind fields of arbitrary turbulence intensity. In the limit of low turbulence intensity, the dynamical ansatz as proposed in 1992 by Rosen and Sheinman is reproduced. It is shown, how the response function of the turbine can be obtained from simulation experiments of a specific wind turbine. For two idealized situations the dynamic effect of fluctuating wind is estimated at turbulence intensities 0⩽ I u ⩽0.5. At the special mean wind speed V=8 m/s , the turbine response function is determined from simulation data published by Sheinman and Rosen in 1992 and 1994.

Dynamical ansatz for path integrals and nonperturbative trace formulas.

It is shown that a recently discovered representation of the Green's function is equivalent to a certain "dynamical ansatz" for the corresponding path integral, which brings about a convenient method of nonperturbative approximations. Based on this observation, a set of nonperturbative approximations to the trace of the Green's function is established.

Energy dependence of KNO moments using the Novero–Predazzi method with a new ansatz

The method of Novero–Predazzi is applied to a new ansatz with three constraints. Hadronic production cross sections σn(s) satisfying Koba–Nielsen–Olesen (KNO)-like constraints are determined; σn(s) and [Formula: see text] automatically have the KNO scaling property. The multiplicity distribution Pn obtained is identical with the empirical formula used by Bozóki et al. The generalization of the method is investigated for more than three constraints. Assuming a given energy dependence of the parameter in the KNO function, we find that all calculated higher moments ck of the KNO function are in excellent agreement with the observed values of ck – s for proton–proton (pp) interactions at Serpukhov, the Fermi National Accelerator Laboratory (FNAL), and intersecting storage rings' (ISR) energies.A zero parameter empirical formula is presented, which gives good results at a 95% confidence level for pp interactions. This KNO function describes the multiplicity distributions e+e− at positron–electron tandem ring accelerator (PETRA) energies. We give a dynamical ansatz leading to this KNO function within the framework of a parton model.

New evaluation of the strongΔΔπcoupling constant and the weak axial-vector coupling constant[gA(0)]ΔΔ

We calculate the strong ..delta delta pi.. coupling constant g/sup 2//4..pi.. and the weak axial-vector coupling constant (g/sub A/(0))/sub DeltaDelta/ without using SU(6) symmetry. The method is based on the dynamical ansatz of level realization of asymptotic flavor SU(2) symmetry, applied to the charge-charge and charge-current SU(2)xSU(2) chiral algebras. We predict that g/sup 2//4..pi..approx. =125 and (g/sub A/(0))++..delta../sup +/approx. =1.30.

A derivation of the [formula omitted] rule for the non-leptonic k-meson decays

It is shown that the presence and violations of the |ΔI| = 1 2 rule in the K-meson non-leptonic decays as well as those of the quark-line selection rule can be explained, together with other important physical quantities, in terms of the single dynamical ansatz, called level realization of asympottic SU(3) symmetry in certain classes of quark chiral SU(2) ⊗ SU(2) algebras.

Hadrons from jets

A dynamical ansatz on the nature of the interaction that binds the constituents into physical hadrons makes it possible to compute perturbatively the spectrum and the quantum numbers of hadrons near the phase space boundary of a QCD jet. Nonperturbative effects are important for less extreme values of the momentum of the detected hadrons. They can be incorporated in the model using the algorithm of the jet calculus.