scholarly journals Locally Accurate Tensor Networks for Thermal States and Time Evolution

PRX Quantum ◽  
2021 ◽  
Vol 2 (4) ◽  
Author(s):  
Álvaro M. Alhambra ◽  
J. Ignacio Cirac
Keyword(s):  
Time Evolution ◽  
Tensor Networks ◽  
Thermal States

scholarly journals Publisher Correction: Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution

2020 ◽  
Vol 16 (2) ◽  
pp. 231-231 ◽  
Author(s):  
Mario Motta ◽  
Chong Sun ◽  
Adrian T. K. Tan ◽  
Matthew J. O’Rourke ◽  
Erika Ye ◽  
...  
Keyword(s):  
Time Evolution ◽  
Quantum Computer ◽  
Imaginary Time ◽  
Thermal States

scholarly journals Thermal bosons in 3d optical lattices via tensor networks

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Saeed S. Jahromi ◽  
Román Orús
Keyword(s):  
Optical Lattice ◽  
Optical Lattices ◽  
Numerical Algorithms ◽  
Hard Core ◽  
Strongly Correlated ◽  
Cubic Lattices ◽  
Tensor Networks ◽  
Tensor Network ◽  
Ideal Tool ◽  
Thermal States

Abstract Ultracold atoms in optical lattices are one of the most promising experimental setups to simulate strongly correlated systems. However, efficient numerical algorithms able to benchmark experiments at low-temperatures in interesting 3d lattices are lacking. To this aim, here we introduce an efficient tensor network algorithm to accurately simulate thermal states of local Hamiltonians in any infinite lattice, and in any dimension. We apply the method to simulate thermal bosons in optical lattices. In particular, we study the physics of the (soft-core and hard-core) Bose–Hubbard model on the infinite pyrochlore and cubic lattices with unprecedented accuracy. Our technique is therefore an ideal tool to benchmark realistic and interesting optical-lattice experiments.

scholarly journals Complexity growth of operators in the SYK model and in JT gravity

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Shao-Kai Jian ◽  
Brian Swingle ◽  
Zhuo-Yu Xian
Keyword(s):  
Black Hole ◽  
Computational Complexity ◽  
Time Evolution ◽  
Quantum Chaos ◽  
Linear Growth ◽  
Quantum Systems ◽  
Growth Behavior ◽  
Definition Of ◽  
Heisenberg Operators ◽  
Thermal States

Abstract The concepts of operator size and computational complexity play important roles in the study of quantum chaos and holographic duality because they help characterize the structure of time-evolving Heisenberg operators. It is particularly important to understand how these microscopically defined measures of complexity are related to notions of complexity defined in terms of a dual holographic geometry, such as complexity-volume (CV) duality. Here we study partially entangled thermal states in the Sachdev-Ye-Kitaev (SYK) model and their dual description in terms of operators inserted in the interior of a black hole in Jackiw-Teitelboim (JT) gravity. We compare a microscopic definition of complexity in the SYK model known as K-complexity to calculations using CV duality in JT gravity and find that both quantities show an exponential-to-linear growth behavior. We also calculate the growth of operator size under time evolution and find connections between size and complexity. While the notion of operator size saturates at the scrambling time, our study suggests that complexity, which is well defined in both quantum systems and gravity theories, can serve as a useful measure of operator evolution at both early and late times.

scholarly journals Publisher Correction: Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution

2019 ◽  
Vol 16 (2) ◽  
pp. 231-231 ◽  
Author(s):  
Mario Motta ◽  
Chong Sun ◽  
Adrian T. K. Tan ◽  
Matthew J. O’Rourke ◽  
Erika Ye ◽  
...  
Keyword(s):  
Time Evolution ◽  
Quantum Computer ◽  
Imaginary Time ◽  
Thermal States

Nonclassicality revival of photon-added displaced thermal states in the amplitude decay channel

2020 ◽  
Vol 98 (5) ◽  
pp. 458-463 ◽  
Author(s):  
Ran Zhang ◽  
Xiang-Guo Meng ◽  
Jian-Meng Sun ◽  
Ji-Suo Wang
Keyword(s):  
Time Evolution ◽  
Wigner Function ◽  
Thermal State ◽  
Decay Channel ◽  
Product Representation ◽  
Normal Product ◽  
Decoherence Rate ◽  
Thermal States

In this paper, the decoherence features of the photon-added displaced thermal state (PADTS) in the amplitude decay channel were studied by analytically and numerically investigating the time evolution of the Wigner function. The normal product representation of density for the PADTS is presented. The results indicate that the nonclassicality of PADTS can revive after disappearing with time. This kind of revival can maintain for a period of time and inevitably disappear eventually. However, we find that the operation of adding photons has the effect of reducing the decoherence rate of PADTS in the amplitude decay channel, although it also can decrease the PADTS’s nonclassicality markedly.

scholarly journals Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution

2019 ◽  
Vol 16 (2) ◽  
pp. 205-210 ◽  
Author(s):  
Mario Motta ◽  
Chong Sun ◽  
Adrian T. K. Tan ◽  
Matthew J. O’Rourke ◽  
Erika Ye ◽  
...  
Keyword(s):  
Time Evolution ◽  
Quantum Computer ◽  
Imaginary Time ◽  
Thermal States
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