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 Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)

2018 ◽  
Author(s):  
Johannes Hauschild ◽  
Frank Pollmann
Keyword(s):  
Matrix Product ◽  
Many Body ◽  
Density Matrix Renormalization ◽  
Tensor Networks ◽  
Condensed Matter Theory ◽  
Tensor Network ◽  
Matter Theory ◽  
Particle Number Conservation ◽  
Many Body Systems ◽  
The One

Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in condensed matter theory and quantum chemistry. In these lecture notes, we combine a compact review of basic TPS concepts with the introduction of a versatile tensor library for Python (TeNPy) [1]. As concrete examples, we consider the MPS based time-evolving block decimation and the density matrix renormalization group algorithm. Moreover, we provide a practical guide on how to implement abelian symmetries (e.g., a particle number conservation) to accelerate tensor operations.

scholarly journals Mutual Information Scaling for Tensor Network Machine Learning

2021 ◽  
Author(s):  
Ian Convy ◽  
William Huggins ◽  
Haoran Liao ◽  
K Birgitta Whaley
Keyword(s):  
Machine Learning ◽  
Mutual Information ◽  
Many Body ◽  
Learning Tasks ◽  
Tensor Networks ◽  
Tensor Network ◽  
Logistic Regression Algorithm ◽  
Entanglement Structure ◽  
Insight Into ◽  
Specific Learning

Abstract Tensor networks have emerged as promising tools for machine learning, inspired by their widespread use as variational ansatze in quantum many-body physics. It is well known that the success of a given tensor network ansatz depends in part on how well it can reproduce the underlying entanglement structure of the target state, with different network designs favoring different scaling patterns. We demonstrate here how a related correlation analysis can be applied to tensor network machine learning, and explore whether classical data possess correlation scaling patterns similar to those found in quantum states which might indicate the best network to use for a given dataset. We utilize mutual information as measure of correlations in classical data, and show that it can serve as a lower-bound on the entanglement needed for a probabilistic tensor network classifier. We then develop a logistic regression algorithm to estimate the mutual information between bipartitions of data features, and verify its accuracy on a set of Gaussian distributions designed to mimic different correlation patterns. Using this algorithm, we characterize the scaling patterns in the MNIST and Tiny Images datasets, and find clear evidence of boundary-law scaling in the latter. This quantum-inspired classical analysis offers insight into the design of tensor networks which are best suited for specific learning tasks.

scholarly journals Cooling and entangling ultracold atoms in optical lattices

Science ◽  
2020 ◽  
Vol 369 (6503) ◽  
pp. 550-553 ◽  
Author(s):  
Bing Yang ◽  
Hui Sun ◽  
Chun-Jiong Huang ◽  
Han-Yi Wang ◽  
Youjin Deng ◽  
...  
Keyword(s):  
Large Scale ◽  
Thermal Fluctuations ◽  
Two Dimensional ◽  
Many Body ◽  
Quantum Phases ◽  
Atom Pairs ◽  
Speed Up ◽  
Quantum Simulator ◽  
Many Body Systems ◽  
Qubit Gate

Scalable, coherent many-body systems can enable the realization of previously unexplored quantum phases and have the potential to exponentially speed up information processing. Thermal fluctuations are negligible and quantum effects govern the behavior of such systems with extremely low temperature. We report the cooling of a quantum simulator with 10,000 atoms and mass production of high-fidelity entangled pairs. In a two-dimensional plane, we cool Mott insulator samples by immersing them into removable superfluid reservoirs, achieving an entropy per particle of 1.9−0.4+1.7×10−3kB. The atoms are then rearranged into a two-dimensional lattice free of defects. We further demonstrate a two-qubit gate with a fidelity of 0.993 ± 0.001 for entangling 1250 atom pairs. Our results offer a setting for exploring low-energy many-body phases and may enable the creation of large-scale entanglement.

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 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 Quantum advantage from energy measurements of many-body quantum systems

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 465
Author(s):  
Leonardo Novo ◽  
Juani Bermejo-Vega ◽  
Raúl García-Patrón
Keyword(s):  
High Resolution ◽  
Measurement Errors ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Polynomial Hierarchy ◽  
Many Body ◽  
Classical Simulation ◽  
Measurement Resolution ◽  
New Perspective ◽  
Sampling Problems

The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage demonstrations can be achieved for more physically-motivated sampling problems, related to measurements of physical observables. We focus on the problem of sampling the outcomes of an energy measurement, performed on a simple-to-prepare product quantum state – a problem we refer to as energy sampling. For different regimes of measurement resolution and measurement errors, we provide complexity theoretic arguments showing that the existence of efficient classical algorithms for energy sampling is unlikely. In particular, we describe a family of Hamiltonians with nearest-neighbour interactions on a 2D lattice that can be efficiently measured with high resolution using a quantum circuit of commuting gates (IQP circuit), whereas an efficient classical simulation of this process should be impossible. In this high resolution regime, which can only be achieved for Hamiltonians that can be exponentially fast-forwarded, it is possible to use current theoretical tools tying quantum advantage statements to a polynomial-hierarchy collapse whereas for lower resolution measurements such arguments fail. Nevertheless, we show that efficient classical algorithms for low-resolution energy sampling can still be ruled out if we assume that quantum computers are strictly more powerful than classical ones. We believe our work brings a new perspective to the problem of demonstrating quantum advantage and leads to interesting new questions in Hamiltonian complexity.

Prospective Merger Between Car-Parrinello and Lattice Boltzmann Methods for Quantum Many-Body Simulations

2011 ◽  
Vol 9 (5) ◽  
pp. 1137-1151 ◽  
Author(s):  
Sauro Succi ◽  
Silvia Palpacelli
Keyword(s):  
Molecular Dynamics ◽  
Computational Efficiency ◽  
Lattice Boltzmann ◽  
Quantum Fluids ◽  
Ab Initio Molecular Dynamics ◽  
Many Body ◽  
Lattice Boltzmann Methods ◽  
Quantum Simulations ◽  
Speed Up ◽  
Many Body Systems

AbstractFormal analogies between the Car-Parrinello (CP) ab-initio molecular dynamics for quantum many-body systems, and the Lattice Boltzmann (LB) method for classical and quantum fluids, are pointed out. A theoretical scenario, whereby the quantum LB would be coupled to the CP framework to speed-up many-body quantum simulations, is also discussed, together with accompanying considerations on the computational efficiency of the prospective CP-LB scheme.

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
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