38 research outputs found
One-dimensional many-body entangled open quantum systems with tensor network methods
We present a collection of methods to simulate entangled dynamics of open
quantum systems governed by the Lindblad equation with tensor network methods.
Tensor network methods using matrix product states have been proven very useful
to simulate many-body quantum systems and have driven many innovations in
research. Since the matrix product state design is tailored for closed
one-dimensional systems governed by the Schr\"odinger equation, the next step
for many-body quantum dynamics is the simulation of open quantum systems. We
review the three dominant approaches to the simulation of open quantum systems
via the Lindblad master equation: quantum trajectories, matrix product density
operators, and locally purified tensor networks. Selected examples guide
possible applications of the methods and serve moreover as a benchmark between
the techniques. These examples include the finite temperature states of the
transverse quantum Ising model, the dynamics of an exciton traveling under the
influence of spontaneous emission and dephasing, and a double-well potential
simulated with the Bose-Hubbard model including dephasing. We analyze which
approach is favorable leading to the conclusion that a complete set of all
three methods is most beneficial, push- ing the limits of different scenarios.
The convergence studies using analytical results for macroscopic variables and
exact diagonalization methods as comparison, show, for example, that matrix
product density operators are favorable for the exciton problem in our study.
All three methods access the same library, i.e., the software package Open
Source Matrix Product States, allowing us to have a meaningful comparison
between the approaches based on the selected examples. For example, tensor
operations are accessed from the same subroutines and with the same
optimization eliminating one possible bias in a comparison of such numerical
methods.Comment: 24 pages, 8 figures. Small extension of time evolution section and
moving quantum simulators to introduction in comparison to v
The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
We present a compendium of numerical simulation techniques, based on tensor
network methods, aiming to address problems of many-body quantum mechanics on a
classical computer. The core setting of this anthology are lattice problems in
low spatial dimension at finite size, a physical scenario where tensor network
methods, both Density Matrix Renormalization Group and beyond, have long proven
to be winning strategies. Here we explore in detail the numerical frameworks
and methods employed to deal with low-dimension physical setups, from a
computational physics perspective. We focus on symmetries and closed-system
simulations in arbitrary boundary conditions, while discussing the numerical
data structures and linear algebra manipulation routines involved, which form
the core libraries of any tensor network code. At a higher level, we put the
spotlight on loop-free network geometries, discussing their advantages, and
presenting in detail algorithms to simulate low-energy equilibrium states.
Accompanied by discussions of data structures, numerical techniques and
performance, this anthology serves as a programmer's companion, as well as a
self-contained introduction and review of the basic and selected advanced
concepts in tensor networks, including examples of their applications.Comment: 115 pages, 56 figure
Optimal sampling of tensor networks targeting wave function's fast decaying tails
We introduce an optimal strategy to sample quantum outcomes of local
measurement strings for isometric tensor network states. Our method generates
samples based on an exact cumulative bounding function, without prior
knowledge, in the minimal amount of tensor network contractions. The algorithm
avoids sample repetition and, thus, is efficient at sampling distribution with
exponentially decaying tails. We illustrate the computational advantage
provided by our optimal sampling method through various numerical examples,
involving condensed matter, optimization problems, and quantum circuit
scenarios. Theory predicts up to an exponential speedup reducing the scaling
for sampling the space up to an accumulated unknown probability from
to for a
decaying probability distribution. We confirm this in practice with over one
order of magnitude speedup or multiple orders improvement in the error
depending on the application. Our sampling strategy extends beyond local
observables, e.g., to quantum magic.Comment: 17 pages, 11 figures. All figures are available on figshare at
http://dx.doi.org/10.6084/m9.figshare.c.7023201. The code to reproduce the
results is available on zenodo at http://dx.doi.org/10.5281/zenodo.10499025.
The initial states to reproduce the results are available on zenodo at
http://dx.doi.org/10.5281/zenodo.1051100
Ab-initio two-dimensional digital twin for quantum computer benchmarking
Large-scale numerical simulations of the Hamiltonian dynamics of a Noisy
Intermediate Scale Quantum (NISQ) computer - a digital twin - could play a
major role in developing efficient and scalable strategies for tuning quantum
algorithms for specific hardware. Via a two-dimensional tensor network digital
twin of a Rydberg atom quantum computer, we demonstrate the feasibility of such
a program. In particular, we quantify the effects of gate crosstalks induced by
the van der Waals interaction between Rydberg atoms: according to an 8x8
digital twin simulation based on the current state-of-the-art experimental
setups, the initial state of a five-qubit repetition code can be prepared with
a high fidelity, a first indicator for a compatibility with fault-tolerant
quantum computing. The preparation of a 64-qubit Greenberger-Horne-Zeilinger
(GHZ) state with about 700 gates yields a 99.9% fidelity in a closed system
while achieving a speedup of 35% via parallelization.Comment: 15 pages, 6 figures, 2 table
Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures
We use tensor network methods - Matrix Product States, Tree Tensor Networks,
and Locally Purified Tensor Networks - to simulate the one dimensional
Bose-Hubbard model for zero and finite temperatures in experimentally
accessible regimes. We first explore the effect of thermal fluctuations on the
system ground state by characterizing its Mott and superfluid features. Then,
we study the behavior of the out-of-equilibrium dynamics induced by quenches of
the hopping parameter. We confirm a Kibble-Zurek scaling for zero temperature
and characterize the finite temperature behavior, which we explain by means of
a simple argument.Comment: 13 pages, 12 figure