相关论文: Quantum Gibbs states are locally Markovian

We prove that any one-dimensional (1D) quantum state with small quantum conditional mutual information in all certain tripartite splits of the system, which we call a quantum approximate Markov chain, can be well-approximated by a Gibbs…

Classical and quantum Markov networks -- including Gibbs states of commuting local Hamiltonians -- are characterized by the vanishing of conditional mutual information (CMI) between spatially separated subsystems. Adding local dissipation…

We prove that the quantum Gibbs states of spin systems above a certain threshold temperature are approximate quantum Markov networks, meaning that the conditional mutual information decays rapidly with distance. We demonstrate the…

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…

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…

Quantum systems in thermal equilibrium are described using Gibbs states. The correlations in such states determine how difficult it is to describe or simulate them. In this article, we show that if the Gibbs state of a quantum system…

Statistical mechanics assumes that a quantum many-body system at low temperature can be effectively described by its Gibbs state. However, many complex quantum systems exist only as metastable states of dissipative open system dynamics,…

Efficient simulation of a quantum system generally relies on structural properties of the quantum state. Motivated by the recent results by Bakshi et al. on the sudden death of entanglement in high-temperature Gibbs states of quantum spin…

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…

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…

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…

Recent works have shown that generic local Hamiltonians can be efficiently inferred from local measurements performed on their eigenstates or thermal states. Realistic quantum systems are often affected by dissipation and decoherence due to…

For quantum phases of Hamiltonian ground states, the energy gap plays a central role in ensuring the stability of the phase as long as the gap remains finite. We propose Markov length, the length scale at which the quantum conditional…

Conditional mutual information (CMI) has recently attracted significant attention as a key quantity for characterizing quantum correlations in many-body systems. While it is conjectured that CMI decays rapidly in finite-temperature Gibbs…

It is known that any locally faithful quantum Markov state (QMS) on one dimensional setting can be considered as a Gibbs state associated with Hamiltonian with commuting nearest-neighbor interactions. In our previous results, we have…

Preparing thermal and ground states is an essential quantum algorithmic task for quantum simulation. In this work, we construct the first efficiently implementable and exactly detailed-balanced Lindbladian for Gibbs states of arbitrary…

Gibbs states are a natural model of quantum matter at thermal equilibrium. We investigate the role of external fields in shaping the entanglement structure and computational complexity of high-temperature Gibbs states. External fields can…

Quantum Markov networks are a generalization of quantum Markov chains to arbitrary graphs. They provide a powerful classification of correlations in quantum many-body systems---complementing the area law at finite temperature---and are…

We show that the norm squared amplitudes with respect to a local orthonormal basis (the classical restriction) of finite quantum systems on one-dimensional lattices can be exponentially well approximated by Gibbs states of local…

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,…