scholarly journals Size consistency of tensor network methods for quantum many-body systems

2013 ◽  
Vol 88 (12) ◽  
Author(s):  
Zhen Wang ◽  
Yongjian Han ◽  
Guang-Can Guo ◽  
Lixin He
Keyword(s):  
Many Body ◽  
Size Consistency ◽  
Tensor Network ◽  
Network Methods ◽  
Many Body Systems

scholarly journals Hyper-optimized tensor network contraction

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 410
Author(s):  
Johnnie Gray ◽  
Stefanos Kourtis
Keyword(s):  
Computation Time ◽  
Quantum Circuit ◽  
Optimization Approach ◽  
Many Body ◽  
Tensor Networks ◽  
Randomized Protocols ◽  
Classical Simulation ◽  
Tensor Network ◽  
Speed Up ◽  
Many Body Systems

Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to tensor networks with irregular geometries. Finding the best possible contraction path for such networks is a central problem, with an exponential effect on computation time and memory footprint. In this work, we implement new randomized protocols that find very high quality contraction paths for arbitrary and large tensor networks. We test our methods on a variety of benchmarks, including the random quantum circuit instances recently implemented on Google quantum chips. We find that the paths obtained can be very close to optimal, and often many orders or magnitude better than the most established approaches. As different underlying geometries suit different methods, we also introduce a hyper-optimization approach, where both the method applied and its algorithmic parameters are tuned during the path finding. The increase in quality of contraction schemes found has significant practical implications for the simulation of quantum many-body systems and particularly for the benchmarking of new quantum chips. Concretely, we estimate a speed-up of over 10,000× compared to the original expectation for the classical simulation of the Sycamore `supremacy' circuits.

scholarly journals Automatic differentiation applied to excitations with projected entangled pair states

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Boris Ponsioen ◽  
Fakher Assaad ◽  
Philippe Corboz
Keyword(s):  
Automatic Differentiation ◽  
Optimization Methods ◽  
Two Dimensions ◽  
Strongly Correlated ◽  
Many Body ◽  
Tensor Networks ◽  
Tensor Network ◽  
New Ideas ◽  
Half Filling ◽  
Many Body Systems

The excitation ansatz for tensor networks is a powerful tool for simulating the low-lying quasiparticle excitations above ground states of strongly correlated quantum many-body systems. Recently, the two-dimensional tensor network class of infinite projected entangled-pair states gained new ground state optimization methods based on automatic differentiation, which are at the same time highly accurate and simple to implement. Naturally, the question arises whether these new ideas can also be used to optimize the excitation ansatz, which has recently been implemented in two dimensions as well. In this paper, we describe a straightforward way to reimplement the framework for excitations using automatic differentiation, and demonstrate its performance for the Hubbard model at half filling.

scholarly journals The seniority quantum number in Tensor Network States

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Klaas Gunst ◽  
Dimitri Van Neck ◽  
Peter Andreas Limacher ◽  
Stijn De Baerdemacker
Keyword(s):  
Quantum Number ◽  
Body Wave ◽  
Many Body ◽  
Dynamical Correlation ◽  
Molecular Systems ◽  
Tensor Network ◽  
Network Methods ◽  
Unpaired Electrons ◽  
Network States ◽  
Tensor Network States

We employ tensor network methods for the study of the seniority quantum number – defined as the number of unpaired electrons in a many-body wave function – in molecular systems. Seniority-zero methods recently emerged as promising candidates to treat strong static correlations in molecular systems, but are prone to deficiencies related to dynamical correlation and dispersion. We systematically resolve these deficiencies by increasing the allowed seniority number using tensor network methods. In particular, we investigate the number of unpaired electrons needed to correctly describe the binding of the neon and nitrogen dimer and the \mathbf{D_{6h}}D6h symmetry of benzene.

scholarly journals Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems

2016 ◽  
Vol 116 (23) ◽  
Author(s):  
A. H. Werner ◽  
D. Jaschke ◽  
P. Silvi ◽  
M. Kliesch ◽  
T. Calarco ◽  
...  
Keyword(s):  
Network Approach ◽  
Many Body ◽  
Open Quantum ◽  
Tensor Network ◽  
Many Body Systems

scholarly journals Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Qi Zhang ◽  
Wen-Tao Xu ◽  
Zi-Qi Wang ◽  
Guang-Ming Zhang
Keyword(s):  
Partition Function ◽  
Ground State ◽  
Local Transformation ◽  
Many Body ◽  
Ground State Wavefunction ◽  
Conformal Field ◽  
Time Symmetry ◽  
Tensor Network ◽  
Network Methods ◽  
Global Phase Diagram

AbstractNegative signs in many-body wavefunctions play an important role in quantum mechanics because interference relies on cancellation between amplitudes of opposite signs. The ground-state wavefunction of double semion model contains negative signs that cannot be removed by any local transformation. Here we study the quantum effects of these intrinsic negative signs. By proposing a generic double semion wavefunction in tensor network representation, we show that its norm can be mapped to the partition function of a triangular lattice Ashkin-Teller model with imaginary interactions. We use numerical tensor-network methods to solve this non-Hermitian model with parity-time symmetry and determine a global phase diagram. In particular, we find a dense loop phase described by non-unitary conformal field theory and a parity-time-symmetry breaking phase characterized by the zeros of the partition function. Therefore, our work establishes a connection between the intrinsic signs in the topological wavefunction and non-unitary phases in the parity-time-symmetric non-Hermitian statistical model.

scholarly journals Tensor network approach to thermalization in open quantum many-body systems

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
Hayate Nakano ◽  
Tatsuhiko Shirai ◽  
Takashi Mori
Keyword(s):  
Network Approach ◽  
Many Body ◽  
Open Quantum ◽  
Tensor Network ◽  
Many Body Systems

scholarly journals Quantum Machine Learning Tensor Network States

2021 ◽  
Vol 8 ◽  
Author(s):  
Andrey Kardashin ◽  
Alexey Uvarov ◽  
Jacob Biamonte
Keyword(s):  
Machine Learning ◽  
Quantum Algorithm ◽  
Unitary Matrix ◽  
Many Body ◽  
Network Algorithms ◽  
Tensor Networks ◽  
Tensor Network ◽  
Network Methods ◽  
Network States ◽  
Tensor Network States

Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools—called tensor network methods—form the backbone of modern numerical methods used to simulate many-body physics and have a further range of applications in machine learning. Finding and contracting tensor network states is a computational task, which may be accelerated by quantum computing. We present a quantum algorithm that returns a classical description of a rank-r tensor network state satisfying an area law and approximating an eigenvector given black-box access to a unitary matrix. Our work creates a bridge between several contemporary approaches, including tensor networks, the variational quantum eigensolver (VQE), quantum approximate optimization algorithm (QAOA), and quantum computation.

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