scholarly journals Computable Rényi mutual information: Area laws and correlations

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 541
Author(s):  
Samuel O. Scalet ◽  
Álvaro M. Alhambra ◽  
Georgios Styliaris ◽  
J. Ignacio Cirac
Keyword(s):  
Mutual Information ◽  
Correlation Functions ◽  
Quantum Correlations ◽  
Matrix Product ◽  
Many Body ◽  
Von Neumann ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States ◽  
Area Law

The mutual information is a measure of classical and quantum correlations of great interest in quantum information. It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all correlation functions. However, calculating it exactly or approximately is often challenging in practice. Here, we consider alternative definitions based on Rényi divergences. Their main advantage over their von Neumann counterpart is that they can be expressed as a variational problem whose cost function can be efficiently evaluated for families of states like matrix product operators while preserving all desirable properties of a measure of correlations. In particular, we show that they obey a thermal area law in great generality, and that they upper bound all correlation functions. We also investigate their behavior on certain tensor network states and on classical thermal distributions.

scholarly journals Universal photonic quantum computation via time-delayed feedback

2017 ◽  
Vol 114 (43) ◽  
pp. 11362-11367 ◽  
Author(s):  
Hannes Pichler ◽  
Soonwon Choi ◽  
Peter Zoller ◽  
Mikhail D. Lukin
Keyword(s):  
Single Atom ◽  
Many Body ◽  
Cluster States ◽  
Quantum Emitter ◽  
Tensor Network ◽  
Quantum Feedback ◽  
Network States ◽  
Tensor Network States ◽  
Photonic Quantum Computation ◽  
Time Delayed Feedback

We propose and analyze a deterministic protocol to generate two-dimensional photonic cluster states using a single quantum emitter via time-delayed quantum feedback. As a physical implementation, we consider a single atom or atom-like system coupled to a 1D waveguide with a distant mirror, where guided photons represent the qubits, while the mirror allows the implementation of feedback. We identify the class of many-body quantum states that can be produced using this approach and characterize them in terms of 2D tensor network states.

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 Studying dynamics in two-dimensional quantum lattices using tree tensor network states

2020 ◽  
Vol 9 (5) ◽  
Author(s):  
Benedikt Kloss ◽  
David Reichman ◽  
Yevgeny Bar Lev
Keyword(s):  
Exact Algorithm ◽  
Matrix Product ◽  
Two Dimensional ◽  
Convergence Properties ◽  
Lattice Systems ◽  
Matrix Product State ◽  
Tensor Network ◽  
Network States ◽  
Quantum Lattices ◽  
Tensor Network States

We analyze and discuss convergence properties of a numerically exact algorithm tailored to study the dynamics of interacting two-dimensional lattice systems. The method is based on the application of the time-dependent variational principle in a manifold of binary and quaternary Tree Tensor Network States. The approach is found to be competitive with existing matrix product state approaches. We discuss issues related to the convergence of the method, which could be relevant to a broader set of numerical techniques used for the study of two-dimensional systems.

scholarly journals A local model of quantum Turing machines

2020 ◽  
Vol 20 (3&4) ◽  
pp. 213-229
Author(s):  
Dong-Sheng Wang
Keyword(s):  
Information Processing ◽  
Turing Machine ◽  
Matrix Product ◽  
Simulation Methods ◽  
Turing Machines ◽  
Matrix Product States ◽  
Tensor Network ◽  
Standard Models ◽  
Network States ◽  
Tensor Network States

The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have definite locations. The local Turing machines are shown to be equivalent to the corresponding circuit models and standard models of Turing machines by simulation methods. This work reveals the fundamental connection between tensor-network states and information processing.

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.

scholarly journals Plaquette renormalization scheme for tensor network states

2011 ◽  
Vol 83 (5) ◽  
Author(s):  
Ling Wang ◽  
Ying-Jer Kao ◽  
Anders W. Sandvik
Keyword(s):  
Renormalization Scheme ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States

scholarly journals Matrix Product State–Based Quantum Classifier

2019 ◽  
Vol 31 (7) ◽  
pp. 1499-1517 ◽  
Author(s):  
Amandeep Singh Bhatia ◽  
Mandeep Kaur Saggi ◽  
Ajay Kumar ◽  
Sushma Jain
Keyword(s):  
Performance Metrics ◽  
Quantum Computer ◽  
Binary Classification ◽  
Learning Ability ◽  
Matrix Product ◽  
Product State ◽  
Data Set ◽  
Matrix Product State ◽  
Tensor Network ◽  
Network States

Interest in quantum computing has increased significantly. Tensor network theory has become increasingly popular and widely used to simulate strongly entangled correlated systems. Matrix product state (MPS) is a well-designed class of tensor network states that plays an important role in processing quantum information. In this letter, we show that MPS, as a one-dimensional array of tensors, can be used to classify classical and quantum data. We have performed binary classification of the classical machine learning data set Iris encoded in a quantum state. We have also investigated its performance by considering different parameters on the ibmqx4 quantum computer and proved that MPS circuits can be used to attain better accuracy. Furthermore the learning ability of an MPS quantum classifier is tested to classify evapotranspiration (ET[Formula: see text]) for the Patiala meteorological station located in northern Punjab (India), using three years of a historical data set (Agri). We have used different performance metrics of classification to measure its capability. Finally, the results are plotted and the degree of correspondence among values of each sample is shown.

scholarly journals Fermionic Orbital Optimization in Tensor Network States

2016 ◽  
Vol 117 (21) ◽  
Author(s):  
C. Krumnow ◽  
L. Veis ◽  
Ö. Legeza ◽  
J. Eisert
Keyword(s):  
Orbital Optimization ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States

scholarly journals Proposal for Quantum Simulation via All-Optically-Generated Tensor Network States

2018 ◽  
Vol 120 (13) ◽  
Author(s):  
I. Dhand ◽  
M. Engelkemeier ◽  
L. Sansoni ◽  
S. Barkhofen ◽  
C. Silberhorn ◽  
...  
Keyword(s):  
Quantum Simulation ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States
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