arXiv 2201.033582022-01quant-ph

Quantum Approximate Optimization Algorithm pseudo-Boltzmann states

Pablo Díez-Valle, Diego Porras, Juan José García-Ripoll

备注：: 6 pages, 5 figures + Supplementary material (7 pages, 6 figures). v3: close to the published version
发表信息：: Phys. Rev. Lett. 130, 050601 (2023)
DOI：: 10.1103/PhysRevLett.130.050601

英文摘要：

In this letter, we provide analytical and numerical evidence that the single-layer Quantum Approximate Optimization Algorithm (QAOA) on universal Ising spin models produces thermal-like states. We find that these pseudo-Boltzmann states can not be efficiently simulated on classical computers according to the general state-of-the-art condition that ensures rapid mixing for Ising models. Moreover, we observe that the temperature depends on a hidden universal correlation between the energy of a state and the covariance of other energy levels and the Hamming distances of the state to those energies.

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。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

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

相关论文

量子近似优化中的近似玻尔兹曼分布

Approximate Boltzmann Distributions in Quantum Approximate Optimization

该研究分析不同规模MaxCut问题的QAOA输出，发现其平均基态概率遵循近似玻尔兹曼分布，推导了有效温度的首项标度关系，并据此生成的大规模近似分布可准确预测性能指标。

2023-11-07physics.comp-phquant-ph

Realizing Quantum Boltzmann Machines Through Eigenstate Thermalization

Quantum Boltzmann machines are natural quantum generalizations of Boltzmann machines that are expected to be more expressive than their classical counterparts, as evidenced both numerically for small systems and asymptotically under various complexity theoretic assumptions. However, training quantum Boltzmann machines using gradient-based methods requires sampling observables in quantum thermal distributions, a problem that is NP-hard. In this work, we find that the locality of the gradient observables gives rise to an efficient sampling method based on the Eigenstate Thermalization Hypothesis…

2019-03-04quant-ph

Boltzmann machine learning with a variational quantum algorithm

Boltzmann machine is a powerful tool for modeling probability distributions that govern the training data. A thermal equilibrium state is typically used for Boltzmann machine learning to obtain a suitable probability distribution. The Boltzmann machine learning consists of calculating the gradient of the loss function given in terms of the thermal average, which is the most time consuming procedure. Here, we propose a method to implement the Boltzmann machine learning by using Noisy Intermediate-Scale Quantum (NISQ) devices. We prepare an initial pure state that contains all possible computati…

2021-10-11quant-ph

Approximate analytical solutions of Dirac Equation with spin and pseudo spin symmetries for the diatomic molecular potentials plus a tensor term with any angular momentum

Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in the closed form and the spinor wave functions by using an algebraic method. We also perform numerical calculations for the Pöschl-Teller potential to show the effect of the tensor interaction. Our results are consistent with ones obtained before.

2012-12-21quant-ph

Ergodic Properties of the Quantum Ideal Gas in the Maxwell-Boltzmann Statistics

It is proved that the quantization of the Volkovyski-Sinai model of ideal gas (in the Maxwell-Boltzmann statistics) enjoys at the thermodynamical limit the properties of mixing and ergodicity with respect to the quantum canonical Gibbs state. Plus, the average over the quantum state of a pseudo-differential operator is exactly the average over the classical canonical measure of its Weyl symbol.

1996-05-09chao-dynnlin.CDnlin.SI

Approximate Analytical Solutions of the Pseudospin Symmetric Dirac Equation for Exponential-type Potentials

The solvability of The Dirac equation is studied for the exponential-type potentials with the pseudospin symmetry by using the parametric generalization of the Nikiforov-Uvarov method. The energy eigenvalue equation, and the corresponding Dirac spinors for Morse, Hulthen, and q-deformed Rosen-Morse potentials are obtained within the framework of an approximation to the spin-orbit coupling term, so the solutions are given for any value of the spin-orbit quantum number $κ=0$, or $κ\neq 0$.

2009-09-04quant-ph

更多相关论文收起更多论文

深度为一的量子交替算子拟设作为近似Gibbs分布采样器

Depth One Quantum Alternating Operator Ansatz as an Approximate Gibbs Distribution Sampler

本研究数值调查了深度为一的QAOA从经典Ising模型定义的Boltzmann分布采样的能力，发现Grover混合器在高温下比标准X混合器更准确，两者均可作为近似采样器且效果取决于角度选择。

2025-10-11cond-mat.stat-mechcs.ITmath.IT

最大熵形式化与受限玻尔兹曼机

Maximal Entropy Formalism and the Restricted Boltzmann Machine

本文将受限玻尔兹曼机（RBM）与最大熵形式化结合，提出一种计算高效的量子态层析框架，利用多项式高效量子采样技术增强 RBM 训练，实现可扩展、高保真地重建任意混合量子态。

2025-04-04quant-ph

Multi-Layer Restricted Boltzmann Machine Representation of 1D Quantum Many-Body Wave Functions

We consider representing two classes of 1D quantum wave functions of spin systems, including the AKLT and CFT correlator wave functions, in terms of multi-layer restricted Boltzmann machines. In our prescription, the AKLT wave function can be exactly represented by a 2-layer restricted Boltzmann machine with five hidden spins per visible spin. The construction can be generalized to prove that any MPS wave function on $N$ unit cells with finite bond dimension can be approximated by a 2-layer restricted Boltzmann machine with $\mathcal{O}(N)$ hidden spins within an error which scales linearly wi…

2019-10-29cond-mat.str-elquant-ph

面向量子机器学习的晶格玻尔兹曼碰撞算子的流体动力学模拟

Towards Quantum Machine Learning of Lattice Boltzmann Collision Operators for Fluid Dynamic Simulations

本文提出利用量子机器学习近似晶格玻尔兹曼碰撞算子，探讨其在流体动力学模拟中的应用与限制。

2026-01-07physics.flu-dynquant-ph

Quantum Inspired Training for Boltzmann Machines

Microsoft Research（微软研究院）；University of Sydney（悉尼大学）

We present an efficient classical algorithm for training deep Boltzmann machines (DBMs) that uses rejection sampling in concert with variational approximations to estimate the gradients of the training objective function. Our algorithm is inspired by a recent quantum algorithm for training DBMs. We obtain rigorous bounds on the errors in the approximate gradients; in turn, we find that choosing the instrumental distribution to minimize the alpha=2 divergence with the Gibbs state minimizes the asymptotic algorithmic complexity. Our rejection sampling approach can yield more accurate gradients t…

2015-07-09cs.LGquant-ph

Generative training of quantum Boltzmann machines with hidden units

Microsoft Research（微软研究院）；University College London（伦敦大学学院）；Rahko

In this article we provide a method for fully quantum generative training of quantum Boltzmann machines with both visible and hidden units while using quantum relative entropy as an objective. This is significant because prior methods were not able to do so due to mathematical challenges posed by the gradient evaluation. We present two novel methods for solving this problem. The first proposal addresses it, for a class of restricted quantum Boltzmann machines with mutually commuting Hamiltonians on the hidden units, by using a variational upper bound on the quantum relative entropy. The second…

2019-05-23cs.LGquant-ph

The Boltzmann Equation from Quantum Field Theory

We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff-Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff-Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradien…

2012-12-11astro-ph.COcond-mat.stat-mechhep-ph