相关论文: Simple parallel estimation of the partition ratio …
We consider the problem of estimating the partition function $Z(\beta)=\sum_x \exp(-\beta(H(x))$ of a Gibbs distribution with a Hamilton $H(\cdot)$, or more precisely the logarithm of the ratio $q=\ln Z(0)/Z(\beta)$. It has been recently…
A central problem in computational statistics is to convert a procedure for sampling combinatorial from an objects into a procedure for counting those objects, and vice versa. Weconsider sampling problems coming from *Gibbs distributions*,…
We consider Gibbs distributions, which are families of probability distributions over a discrete space $\Omega$ with probability mass function of the form $\mu^\Omega_\beta(\omega) \propto e^{\beta H(\omega)}$ for $\beta$ in an interval…
Consider a family of distributions $\{\pi_{\beta}\}$ where $X\sim\pi_{\beta}$ means that $\mathbb{P}(X=x)=\exp(-\beta H(x))/Z(\beta)$. Here $Z(\beta)$ is the proper normalizing constant, equal to $\sum_x\exp(-\beta H(x))$. Then…
We study the complexity of estimating the partition function $\mathsf{Z}(\beta)=\sum_{x\in\chi} e^{-\beta H(x)}$ for a Gibbs distribution characterized by the Hamiltonian $H(x)$. We provide a simple and natural lower bound for quantum…
Estimating quantum partition functions is a critical task in a variety of fields. However, the problem is classically intractable in general due to the exponential scaling of the Hamiltonian dimension $N$ in the number of particles. This…
The computational equivalence between approximate counting and sampling is well established for polynomial-time algorithms. The most efficient general reduction from counting to sampling is achieved via simulated annealing, where the…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
There are well established reductions between combinatorial sampling and counting problems (Jerrum, Valiant, Vazirani TCS 1986). Building off of a very recent parallel algorithm utilizing this connection (Liu, Yin, Zhang arxiv 2024), we…
Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…
We present new algorithms for estimating and testing \emph{collision probability}, a fundamental measure of the spread of a discrete distribution that is widely used in many scientific fields. We describe an algorithm that satisfies…
We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in $\sqrt{N \beta/{\cal Z}}$ and polynomial in…
A canonical approach to approximating the partition function of a Gibbs distribution via sampling is simulated annealing. This method has led to efficient reductions from counting to sampling, including: $\bullet$ classic non-adaptive…
We study the problem of learning a Hamiltonian $H$ to precision $\varepsilon$, supposing we are given copies of its Gibbs state $\rho=\exp(-\beta H)/\operatorname{Tr}(\exp(-\beta H))$ at a known inverse temperature $\beta$. Anshu,…
We present a novel quantum algorithm for estimating Gibbs partition functions in sublinear time with respect to the logarithm of the size of the state space. This is the first speed-up of this type to be obtained over the seminal…
We establish a systematic framework of unbiased quantum sampling and estimation protocols for the classical Gibbs expectation. This framework generalizes existing approaches to the partition function estimation and has broader applications…
To minimize data movement, state-of-the-art parallel sorting algorithms use techniques based on sampling and histogramming to partition keys prior to redistribution. Sampling enables partitioning to be done using a representative subset of…
Log-linear models are arguably the most successful class of graphical models for large-scale applications because of their simplicity and tractability. Learning and inference with these models require calculating the partition function,…
Randomized approximation algorithms for many #P-complete problems (such as the partition function of a Gibbs distribution, the volume of a convex body, the permanent of a $\{0,1\}$-matrix, and many others) reduce to creating random…
We present classical and quantum algorithms for approximating partition functions of classical Hamiltonians at a given temperature. Our work has two main contributions: first, we modify the classical algorithm of \v{S}tefankovi\v{c},…