Related papers: Slow Mixing of Quantum Gibbs Samplers
We prove an analogue of the "bottleneck theorem", well-known for classical Markov chains, for Markovian quantum channels. In particular, we show that if two regions (subspaces) of Hilbert space are separated by a region that has very low…
Gibbs state preparation, or Gibbs sampling, is a key computational technique extensively used in physics, statistics, and other scientific fields. Recent efforts for designing fast mixing Gibbs samplers for quantum Hamiltonians have largely…
Providing evidence that quantum computers can efficiently prepare low-energy or thermal states of physically relevant interacting quantum systems is a major challenge in quantum information science. A newly developed quantum Gibbs sampling…
A quantum system coupled to a bath at some fixed, finite temperature converges to its Gibbs state. This thermalization process defines a natural, physically-motivated model of quantum computation. However, whether quantum computational…
We analyze the problem of preparing quantum Gibbs states of lattice spin Hamiltonians with local and commuting terms on a quantum computer and in nature. Our central result is an equivalence between the behavior of correlations in the Gibbs…
Many physical phenomena, including thermalization in open quantum systems and quantum Gibbs sampling, are modeled by Lindbladians approximating a system weakly coupled to a bath. Understanding the convergence speed of these Lindbladians to…
Systems in thermal equilibrium at non-zero temperature are described by their Gibbs state. For classical many-body systems, the Metropolis-Hastings algorithm gives a Markov process with a local update rule that samples from the Gibbs…
Dissipative quantum algorithms for state preparation in many-body systems are increasingly recognised as promising candidates for achieving large quantum advantages in application-relevant tasks. Recent advances in algorithmic,…
Sampling from Gibbs states -- states corresponding to system in thermal equilibrium -- has recently been shown to be a task for which quantum computers are expected to achieve super-polynomial speed-up compared to classical computers,…
Gibbs sampling is a crucial computational technique used in physics, statistics, and many other scientific fields. For classical Hamiltonians, the most commonly used Gibbs sampler is the Metropolis algorithm, known for having the Gibbs…
It is of great interest to understand the thermalization of open quantum many-body systems, and how quantum computers are able to efficiently simulate that process. A recently introduced disispative evolution, inspired by existing models of…
Quantum systems typically reach thermal equilibrium rather quickly when coupled to a thermal environment. The usual way of bounding the speed of this process is by estimating the spectral gap of the dissipative generator. However the gap,…
The computational complexity of simulating quantum many-body systems generally scales exponentially with the number of particles. This enormous computational cost prohibits first principles simulations of many important problems throughout…
Estimating thermal expectation values of quantum many-body systems is a central challenge in physics, chemistry, and materials science. Standard quantum Gibbs sampling protocols address this task by preparing the Gibbs state from scratch…
Recently, there have been several advancements in quantum algorithms for Gibbs sampling. These algorithms simulate the dynamics generated by an artificial Lindbladian, which is meticulously constructed to obey a detailed-balance condition…
We study the problem of sampling from and preparing quantum Gibbs states of local commuting Hamiltonians on hypercubic lattices of arbitrary dimension. We prove that any such Gibbs state which satisfies a clustering condition that we coin…
Estimating thermal expectation values of observables is a fundamental task in quantum physics, quantum chemistry, and materials science. While recent quantum algorithms have enabled efficient quantum preparation of thermal states,…
The preparation of thermal states of matter is a crucial task in quantum simulation. In this work, we prove that a recently introduced, efficiently implementable dissipative evolution thermalizes to the Gibbs state in time scaling…
We develop a quantum algorithm for estimating the free energy as well as the total Gibbs state of interacting quantum Coulomb gases and molecular systems in dimensions $d \in \{2,3\}$ at finite temperature. These systems lie beyond the…
It is shown that every one-dimensional Hamiltonian with short-range interaction admits a quantum Gibbs sampler [CKG23] with a system-size independent spectral gap at all finite temperatures. Consequently, their Gibbs states can be prepared…