Axel Pelster, Florian Weissbach
We evaluate perturbatively the density matrix in the low-temperature limit and thus the ground-state wave function of the anharmonic oscillator up to second order in the coupling constant. We then employ Kleinert's variational perturbation theory to determine the ground-state wave function for all coupling strengths.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Variational Quantum Algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In variational quantum algorithm, wavefunction represented by a parametrized ansatz and variational parameters are updated iteratively with a classical computer based on the measurement outputs from the quantum computer. In this paper, we investigate perturbation theory with these algorithms and prospect the possibility of using the variational quantum algorithm to simulate quantum dynamics in perturbation theory. We illustrate the use…
We derive recursively the perturbation series for the ground-state energy of the D-dimensional anharmonic oscillator and resum it using variational perturbation theory (VPT). From the exponentially fast converging approximants, we extract the coefficients of the large-D expansion to higher orders. The calculation effort is much smaller than in the standard field-theoretic approach based on the Hubbard-Stratonovich transformation.
We develop convergent variational perturbation theory for quantum statistical density matrices. The theory is applicable to polynomial as well as nonpolynomial interactions. Illustrating the power of the theory, we calculate the temperature-dependent density of a particle in a double-well and of the electron in a hydrogen atom.
Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we explain the physical origin of the empirically observed convergence behavior which is exponentially fast with superimposed oscillations.
Variational perturbation theory is used to determine the decay rates of metastable states across a cubic barrier of arbitrary height. For high barriers, a variational resummation procedure is applied to the complex energy eigenvalues obtained from a WKB expansion; for low barriers, the variational resummation procedure converts the non-Borel-summable Rayleigh-Schrö\-din\-ger expansion into an exponentially fast convergent one. The results in the two regimes match and yield very accurate imaginary parts of the energy eigenvalues. This is demonstrated by comparison with the complex eigenvalues f…
The newly developed iterative method based on Green function defined by quadratures along a single trajectory is combined with the variational method to solve the ground state quantum wave function for central potentials. As an example, the method is applied to discuss the ground state solution of Yukawa potential, using Hulthen solution as the trial function.
Variational Quantum Homotopy Perturbation Method to Solve Nonlinear Partial Differential Equations
本文提出量子同伦摄动方法（QHPM），通过保持希尔伯特空间维度并利用变分量子模拟减少量子比特和电路深度，提高非线性PDE求解的可扩展性，并用涡量输运方程等示例验证。
Variational perturbation expansions have recently been used to calculate directly the strong-coupling expansion coefficients of the anharmonic oscillator. The convergence is exponentially fast with superimposed oscillations, as recently observed empirically by the authors. In this note, the observed behavior is explained and used to determine accurately the magnitude and phase of the leading Bender-Wu singularity which is responsible for the finite convergence radius in the complex coupling constant plane.
In this paper we introduce a generalization to the algebraic Bender-Wu recursion relation for the eigenvalues and the eigenfunctions of the anharmonic oscillator. We extend this well known formalism to the time-dependent quantum statistical Schroedinger equation, thus obtaining the imaginary-time evolution amplitude by solving a recursive set of ordinary differential equations. This approach enables us to evaluate global and local quantum statistical quantities of the anharmonic oscillator to much higher orders than by evaluating Feynman diagrams. We probe our perturbative results by deriving …
As an application of a recently developed variational perturbation theory we find the first 22 terms of the convergent strong-coupling series expansion for the ground state energy of the quartic anharmonic oscillator.
Robustness of Variational Quantum Algorithms against stochastic parameter perturbation
本文通过微扰分析研究了变分量子算法在随机门误差下的去相干与能量估计偏差，确定了满足稳定性引理的噪声阈值，并在最多14量子比特问题上验证了不同门误差对相干性的影响差异。
We prove a powerful scaling property for the extremality condition in the recently developed variational perturbation theory which converts divergent perturbation expansions into exponentially fast convergent ones. The proof is given for the energy eigenvalues of an anharmonic oscillator with an arbitrary $x^p$-potential. The scaling property greatly increases the accuracy of the results.
Ground-state preparation for a given Hamiltonian is a common quantum-computing task of great importance and has relevant applications in quantum chemistry, computational material modeling, and combinatorial optimization. We consider an approach to simulate dissipative non-Hermitian Hamiltonian quantum dynamics using Hamiltonian simulation techniques to efficiently recover the ground state of a target Hamiltonian. The proposed method facilitates the energy transfer by repeatedly projecting ancilla qubits to the desired state, rendering the effective non-Hermitian Hamiltonian evolution on the sy…
In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantit…
A new variational perturbation theory is developed based on the $q-$deformed oscillator. It is shown that the new variational perturbation method provides 200 or 10 times better accuracy for the ground state energy of anharmonic oscillator than the Gaussian and the improved Gaussian approximation, respectively.
Variational post-selection for ground states and thermal states simulation
针对NISQ时代变分量子算法受硬件限制的问题，提出结合变分后选择与神经网络后处理的框架，提升量子自旋及分子系统的基态、热态制备精度，并在热态局域性质估计上实现更优的可扩展方案。
We discuss a novel form of the variational approach in Quantum Field Theory in which the trial quantum configuration is represented directly in terms of relevant expectation values rather than, e.g., increasingly complicated structure from Fock space. The quantum algebra imposes constraints on such expectation values so that the variational problem is formulated here as an optimization under constraints. As an example of application of such approach we consider the study of ground state and critical properties in a variant of nonlinear sigma model.
Preparing the ground states of a many-body system is essential for evaluating physical quantities and determining the properties of materials. This work provides a quantum ground state preparation scheme with shallow variational warm-start to tackle the bottlenecks of current algorithms, i.e., demand for prior ground state energy information and lack of demonstration of efficient initial state preparation. Particularly, our methods would not experience the instability for small spectral gap $Δ$ during pre-encoding the phase factors since our methods involve only $\widetilde{O}(1)$ factors whil…
Benchmarking Variational Quantum Eigensolvers for Entanglement Detection in Many-Body Hamiltonian Ground States
本文使用变分量子特征求解器（VQEs）对由Heisenberg哈密顿量描述的多体系统进行纠缠检测基准测试，发现受哈密顿量相互作用启发的参数化量子电路在代价函数估计上优于问题无关电路。
Finding and probing the ground states of spin lattices, such as the antiferromagnetic Heisenberg model on the kagome lattice (KAFH), is a very challenging problem on classical computers and only possible for relatively small systems. We propose using the Variational Quantum Eigensolver (VQE) to find the ground state of the KAFH on a quantum computer. We find efficient ansatz circuits and show how physically interesting observables can be measured efficiently. To investigate the expressiveness and scaling of our ansatz circuits we used classical, exact simulations of VQE for the KAFH for differ…
One of the key applications for the emerging quantum simulators is to emulate the ground state of many-body systems, as it is of great interest in various fields from condensed matter physics to material science. Traditionally, in an analog sense, adiabatic evolution has been proposed to slowly evolve a simple Hamiltonian, initialized in its ground state, to the Hamiltonian of interest such that the final state becomes the desired ground state. Recently, variational methods have also been proposed and realized in quantum simulators for emulating the ground state of many-body systems. Here, we …
A scalable quantum-neural hybrid variational algorithm for ground state estimation
本文提出了一种可扩展的量子-神经混合变分算法，通过强制单位ary神经变换解决了原始VQNHE的归一化问题和损失函数发散问题，显著减少了测量次数并提高了算法的准确性和稳定性。
Ground and excited state energy calculations of the H2 molecule using a variational quantum eigensolver algorithm on an NMR quantum simulator
本文在NMR量子处理器上实验实现了变分量子本征求解器与变分量子紧缩算法，分别计算H2分子的基态和激发态能量，并首次证明单个NMR量子比特即可达到所需精度。
Variational ground-state quantum adiabatic theorem
本文提出变分量子绝热定理，证明在低纠缠变分流形上演化可绕过量子退火中的高纠缠中间态并收敛到经典目标基态。
Quantum computers have been widely speculated to offer significant advantages in obtaining the ground state of difficult Hamiltonian in chemistry and physics. In this work, we first propose a Lyapunov control-inspired strategy to accelerate the well-established imaginary-time method for ground-state preparation. We also dig for the source of acceleration of the imaginary-time process under Lyapunov control with theoretical understanding and dynamic process visualization. To make the method accessible in the noisy intermediate-scale quantum era, we further propose a variational form of the algo…
A variational upper bound on the ground state energy $E_{\rm gs}$ of a quantum system, $E_{\rm gs} \leqslant \langle Ψ|H| Ψ\rangle$, is well-known (here $H$ is the Hamiltonian of the system and $Ψ$ is an arbitrary wave function). Much less known are variational {\it lower} bounds on the ground state. We consider one such bound which is valid for a many-body translation-invariant lattice system. Such a lattice can be divided into clusters which are identical up to translations. The Hamiltonian of such a system can be written as $H=\sum_{i=1}^M H_i$, where a term $H_i$ is supported on the $i$'th…
Using Variational Eigensolvers on Low-End Hardware to Find the Ground State Energy of Simple Molecules
本文研究在低端硬件上用变分量子特征求解器计算简单分子基态能量，并比较不同优化器在精度和代码效率上的表现。
Probing the limits of variational quantum algorithms for nonlinear ground states on real quantum hardware: The effects of noise
该研究在真实超导量子处理器上探究了变分量子算法求解非线性薛定谔方程基态的能力，发现量子硬件噪声虽影响能量代价函数评估，但小规模实例仍能收敛，且浅态制备电路避免了保真度估计的差异。
Ground-state reachability for variational quantum eigensolvers: a Rydberg-atom case study
本研究通过分析固有对称性，探讨了变分量子特征求解器（VQE）的基态可达性条件，并在里德堡原子量子模拟器上验证了其预测基态可达性的可靠性，提出了克服对称性限制的实用方法。
The variational perturbation theory for wave functions, which has been shown to work well for bound states of the anharmonic oscillator, is applied to resonance states of the anharmonic oscillator with negative coupling constant. We obtain uniformly accurate wave functions starting from the bound states.
Robust Variational Ground-State Solvers via Dissipative Quantum Feedback Models
本文提出了一种基于耗散量子反馈模型的变分基态求解器，通过H-infinity控制提升鲁棒性，适用于量子化学和光学实验平台。
Variational Quantum Eigensolvers with Quantum Gaussian Filters for solving ground-state problems in quantum many-body systems
提出一种结合变分量子本征求解器与量子高斯滤波器的量子算法，用于在NISQ设备上高效求解多体系统基态，在横场伊辛模型上展现出更快的收敛和更高的精度。
A key goal of digital quantum computing is the simulation of fermionic systems such as molecules or the Hubbard model. Unfortunately, for present and near-future quantum computers the use of quantum error correction schemes is still out of reach. Hence, the finite error rate limits the use of quantum computers to algorithms with a low number of gates. The variational Hamiltonian ansatz (VHA) has been shown to produce the ground state in good approximation in a manageable number of steps. Here we study explicitly the effect of gate errors on its performance. The VHA is inspired by the adiabatic…
Variational quantum simulation of ground states and thermal states for lattice gauge theory with multi-objective optimization
本文针对格点规范理论中局域规范不变性约束带来的变分量子模拟困难，提出将能量（自由能）最小化与规范不变性惩罚作为两个目标进行多目标优化，并设计变分量子本征求解器和热化器，在$Z_2$格点规范理论中数值验证了零温与有限温度下同时实现能量优化和规范约束的可行性。
Variational Perturbation Theory in Open Quantum Systems for Efficient Steady State Computation
本文提出变分扰动理论及多点泛化方法，扩展收敛半径并消除伪逆计算需求，提升开放量子系统稳态计算效率。
We propose a variational perturbation method based on the observation that eigenvalues of each parity sector of both the anharmonic and double-well oscillators are approximately equi-distanced. The generalized deformed algebra satisfied by the invariant operators of the systems provides well defined Hilbert spaces to both of the oscillators. There appears a natural expansion parameter defined by the ratios of three distance scales of the trial wavefunctions. The energies of the ground state and the first order excited state, in the $0^{th}$ order variational approximation, are obtained with er…
We use the Variational Quantum Eigensolver (VQE) as implemented in the Qiskit software package to compute the ground state energy of small molecules derived from water, H$_2$O, and hydrogen cyanide, HCN. The work aims to benchmark algorithms for calculating the electronic structure and energy surfaces of molecules of relevance to prebiotic chemistry, beginning with water and hydrogen cyanide, and to run them on the available simulated and physical quantum hardware. The numerical calculations of the algorithms for small quantum processors allow us to design more efficient protocols to be run in…
We introduce a simple, physically-motivated variational ground state for the quantum Rabi model, and demonstrate that it provides a high-fidelity approximation of the true ground state in all parameter regimes (including intermediate and strong coupling regimes). Our variational state is constructed using Gaussian cavity states and nonorthogonal qubit pointer states, and contains only three variational parameters. We use our state to develop a heuristic understanding of how the ground state evolves with increasing coupling, and find a previously unexplored regime where the ground state corresp…
We compute the shift of the transition temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length a for given particle density n. Using variational perturbation theory through six loops in a classical three-dimensional scalar field theory, we obtain Delta T_c/T_c = 1.25+/-0.13 a n^(1/3), in agreement with recent Monte-Carlo results.
Detecting quasi-degenerate ground states in topological models via variational quantum eigensolver
本研究通过改进VQE算法，施加约束限制希尔伯特空间探测，成功解决了拓扑模型中准简并基态导致的收敛问题，实现了对精确基态的高保真度检测。
The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Quantum Natural Gradient Descent and Variational Quantum Imaginary Time Evolution. Computing the full QFIM for a model with $d$ parameters, however, is computationally expensive and generally requires $\mathcal{O}(d^2)$ function evaluations. To remedy these increasing costs in high-dimensional parameter spaces, we propose using simultaneous perturbation stochastic approximation techniques to approximate the QFIM at a constant cost. We present the resulting algorithm and successfully apply it to pr…
Post-Variational Ground State Estimation via QPE-Based Quantum Imaginary Time Evolution
针对容错量子计算机的后变分基态估计问题，提出无需参数优化的QPE-QITE算法，通过辅助量子比特投影低能本征态，在LABS问题验证能力并提供魔法态缩放估计，为量子优势建立基准。
Accelerated spin-adapted ground state preparation with non-variational quantum algorithms
本文提出一种非变分量子算法方法，通过两步流程制备自旋适应基态，减少惩罚项数量，验证了在Heisenberg环模型和锰三元系统中的有效性。
Multi-Reference UCCSD Variational Quantum Algorithm for Molecular Ground State Energies
本文提出一种粒子数守恒量子线路实现的多参考UCCSD变分量子算法，在LiH、BeH₂和H₆上以数百个CNOT门实现低于10⁻⁵ Hartree的基态能量精度，兼顾计算精度与量子资源缩减。
Some effective operators for graphene monolayer superlattices, from variational perturbation theory
本文通过变分微扰理论和多尺度方法，为石墨烯单层超晶格在费米能级下的有效算子提供了精确计算。
The shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length `a' is computed for given particle density `n.' Variational perturbation theory is used to resum the corresponding perturbative series for Delta<phi^2>/Nu in a classical three-dimensional scalar field theory with coupling `u' and where the physical case of N=2 field components is generalized to arbitrary N. Our results for N=1,2,4 are in agreement with recent Monte-Carlo simulations; for N=2, we obtain Delta T_c/T_c = 1.27 +/- 0.11 a n^(1/3). We use sev…
Efficient ground state preparation in variational quantum eigensolver with symmetry-breaking layers
针对哈密顿量变分拟设（HVA）难以求解对称破缺基态的局限，提出带对称破缺层的量子电路拟设，数值模拟显示其在对称破缺系统中所需基态制备深度远低于纯HVA。
We propose a ground-state ansatz for the Ohmic spin-boson model that improves upon the variational treatment of Silbey and Harris for biased systems in the scaling limit. In particular, it correctly captures the smooth crossover behaviour expected for the ground-state magnetisation when moving between the delocalised and localised regimes of the model, a feature that the variational treatment is unable to properly reproduce, while it also provides a lower ground-state energy estimate in the crossover region. We further demonstrate the validity of our intuitive ground-state by showing that it l…
Ground-State Energy Solutions of the Lithium Atom: Zeroth-, First-, and Second-Order Perturbation Theory and the Variational Method
本文通过微扰理论和变分法系统计算锂原子基态能量，比较电子关联和屏蔽效应，得到-201.187 eV的变分上界。
We propose a variational quantum algorithm to study the real time dynamics of quantum systems as a ground-state problem. The method is based on the original proposal of Feynman and Kitaev to encode time into a register of auxiliary qubits. We prepare the Feynman-Kitaev Hamiltonian acting on the composed system as a qubit operator and find an approximate ground state using the Variational Quantum Eigensolver. We apply the algorithm to the study of the dynamics of a transverse field Ising chain with an increasing number of spins and time steps, proving a favorable scaling in terms of the number …
We present an ansatz for the ground states of the Quantum Sherrington-Kirkpatrick model, a paradigmatic model for quantum spin glasses. Our ansatz, based on the concept of generalized coherent states, very well captures the fundamental aspects of the model, including the ground state energy and the position of the spin glass phase transition. It further enables us to study some previously unexplored features, such as the non-vanishing longitudinal field regime and the entanglement structure of the ground states. We find that the ground state entanglement can be captured by a simple ensemble of…
Variationally Optimized Imaginary-time Polynomial Filters for Ground State Projection
该研究开发了基于多项式滤波的变分虚时演化框架，推导了严格误差界，经横场伊辛模型基准测试，可提升基态投影的精度、稳定性与收敛速度，为近期量子设备的基态制备提供了实用方案。
An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near-term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan dista…
Variational quantum eigensolver for chemical molecules
本文提出利用变分量子特征解算器计算H2O和He-H+分子的基态能量，并通过经典方法验证结果。
Quantum variational embedding for ground-state energy problems: sum of squares and cluster selection
本文提出一种平方和SDP层次结构从下方近似量子多体基态能量，并利用量子信息理论优化簇选择以在有限计算预算内收紧松弛，数值实验验证了其有效性。
Hardware-Efficient Ground-State Preparation using Variational Imaginary-Time Majorana Evolution
VIME算法结合c-tUPS拟设，通过经典预训练实现资源高效的分子基态制备，在强关联体系中以更少门数达到化学精度。
An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
本文综述基于自动微分的变分 iPEPS 框架，介绍其原理、可适配二维晶格的通用基础及基准结果，以提升基态与激发态模拟的灵活性和精度。
Counterdiabatic (CD) protocols enable fast driving of quantum states by invoking an auxiliary adiabatic gauge potential (AGP) that suppresses transitions to excited states throughout the driving process. Usually, the full spectrum of the original unassisted Hamiltonian is a prerequisite for constructing the exact AGP, which implies that CD protocols are extremely difficult for many-body systems. Here, we apply a variational CD protocol recently proposed by P. W. Claeys et al. [Phys. Rev. Lett. 123, 090602 (2019)] to a two-component fermionic Hubbard model in one spatial dimension. This protoco…
We introduce a new discrete-time variational principle inspired by the quantum clock originally proposed by Feynman, and use it to write down quantum evolution as a ground state eigenvalue problem. The construction allows one to apply ground state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. Moreover this formalism naturally leads to an algorithm to parallelize quantum simulation over time. We draw an explicit connection between previously known time-dependent variational principles and the new time embedded v…
Predicting quantum ground-state energy by data-driven Koopman analysis of variational parameter nonlinear dynamics
本文提出利用数据驱动的Koopman分析方法估计量子哈密顿量基态能量，通过非线性动力学的变分参数向量线性化，结合扩展动态模式分解估算四站点横向磁场Ising模型的基态能量。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。