scholarly journals Bosonic entanglement renormalization circuits from wavelet theory

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Freek Witteveen ◽  
Michael Walter
Keyword(s):  
Design Problem ◽  
Filter Design ◽  
Real Space ◽  
Quantum Systems ◽  
Renormalization Scheme ◽  
Quantum Circuits ◽  
Quantum Field ◽  
Wavelet Theory ◽  
Tensor Networks ◽  
The Continuum

Entanglement renormalization is a unitary real-space renormalization scheme. The corresponding quantum circuits or tensor networks are known as MERA, and they are particularly well-suited to describing quantum systems at criticality. In this work we show how to construct Gaussian bosonic quantum circuits that implement entanglement renormalization for ground states of arbitrary free bosonic chains. The construction is based on wavelet theory, and the dispersion relation of the Hamiltonian is translated into a filter design problem. We give a general algorithm that approximately solves this design problem and provide an approximation theory that relates the properties of the filters to the accuracy of the corresponding quantum circuits. Finally, we explain how the continuum limit (a free bosonic quantum field) emerges naturally from the wavelet construction.

scholarly journals Formulation of 2D Graphene Deformation Based on Chiral-Tube Base Vectors

2010 ◽  
Vol 2010 ◽  
pp. 1-7
Author(s):  
Bohua Sun
Keyword(s):  
Molecular Dynamics ◽  
Shell Model ◽  
Continuum Model ◽  
Real Space ◽  
Honeycomb Lattice ◽  
Mechanical Behaviors ◽  
Future Studies ◽  
Physical Components ◽  
Intrinsic Feature ◽  
The Continuum

The intrinsic feature of graphene honeycomb lattice is defined by its chiral index (n,m), which can be taken into account when using molecular dynamics. However, how to introduce the index into the continuum model of graphene is still an open problem. The present manuscript adopts the continuum shell model with single director to describe the mechanical behaviors of graphene. In order to consider the intrinsic features of the graphene honeycomb lattice—chiral index (n,m), the chiral-tube vectors of graphene in real space have been used for construction of reference unit base vectors of the shell model; therefore, the formulations will contain the chiral index automatically, or in an explicit form in physical components. The results are quite useful for future studies of graphene mechanics.

scholarly journals Local Spin and Open Quantum Systems: Clarifying Misconceptions, Unifying Approaches

2020 ◽  
Author(s):  
Angel Martín Pendás ◽  
Evelio Francisco
Keyword(s):  
Quantum Control ◽  
Open Systems ◽  
Open Quantum Systems ◽  
Real Space ◽  
Quantum Systems ◽  
Spin Coupling ◽  
Molecular Systems ◽  
Open Quantum ◽  
Local Spin

<p>We now show that Clark and Davidson local spins operators are perfectly defined subsystem operators if a fragment is taken as an <i>open quantum system</i> (OQS). Open systems have become essential in quantum control and quantum computation, but have not received much attention in Chemistry. We have already shown (<i>J. Chem. Theory Comput</i>. <b>2018</b>, <i>15</i>, 1079) how real space OQSs can be defined in molecular systems and how they offer new insights relating quantum mechanical entaglement and chemical bonding. The OQS account of local spin that we offer yields a rigorous, yet easily accessible way to rationalize local spin values. A fragment is found in a mixed state direct sum of sectors characterized by different number of electrons that occur with different probabilities. The local spin is then a weighted sum of otherwise standard <i>S</i>(<i>S</i>+1) values. With OQS glasses, it is obvious that atomic or fragment spins should not vanish. Our approach thus casts doubts on any procedure used to annihilate them, like those used by Mayer and coworkers. OQS local spins allow for a fruitful use of models. One can propose easily sector probabilities for localized, covalent, ionic, zwitterionic, etc. situations, and examine their ideal local spins. We have mapped all 2c-2e cases, and shown how to do that in general multielectron cases. The role of electron correlation is also studied by tuning the Hubbard U/t parameter for H chains. Correlation induced localization changes the spin-coupling patterns even qualitatively, and show how the limiting antiferromagnet arises.</p>

scholarly journals Tensor networks for complex quantum systems

2019 ◽  
Vol 1 (9) ◽  
pp. 538-550 ◽  
Author(s):  
Román Orús
Keyword(s):  
Quantum Systems ◽  
Tensor Networks

scholarly journals Advanced exact synthesis of Clifford+T circuits

2020 ◽  
Vol 19 (9) ◽  
Author(s):  
Philipp Niemann ◽  
Robert Wille ◽  
Rolf Drechsler
Keyword(s):  
Large Scale ◽  
Fault Tolerant ◽  
Logic Synthesis ◽  
Research Problem ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Research Attention ◽  
Small Quantum ◽  
Significant Research ◽  
Important Research Problem

Abstract Quantum systems provide a new way of conducting computations based on the so-called qubits. Due to the potential for significant speed-ups, this field received significant research attention in recent years. The Clifford+T library is a very promising and popular gate library for these kinds of computations. Unlike other libraries considered so far, it consists of only a small number of gates for all of which robust, fault-tolerant realizations are known for many technologies that seem to be promising for large-scale quantum computing. As a consequence, (logic) synthesis of Clifford+T quantum circuits became an important research problem. However, previous work in this area has several drawbacks: Corresponding approaches are either only applicable to very small quantum systems or lead to circuits that are far from being optimal. The latter is mainly caused by the fact that current synthesis realizes the desired circuit by a local, i.e., column-wise, consideration of the underlying unitary transformation matrix to be synthesized. In this paper, we analyze the conceptual drawbacks of this approach and propose to overcome them by taking a global view of the matrices and perform a separation of concerns regarding individual synthesis steps. We precisely describe a corresponding algorithm as well as its efficient implementation on top of decision diagrams. Experimental results confirm the resulting benefits and show improvements of up to several orders of magnitudes in costs compared to previous work.

scholarly journals New numerical methods for quantum field theories on the continuum

2000 ◽  
Vol 83-84 ◽  
pp. 938-940 ◽  
Author(s):  
P. Emirdaǧ ◽  
R. Easther ◽  
G.S. Guralnik ◽  
S.C. Hahn
Keyword(s):  
Numerical Methods ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
The Continuum

scholarly journals Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems

2013 ◽  
Vol 85 (2) ◽  
pp. 623-653 ◽  
Author(s):  
Ze-Liang Xiang ◽  
Sahel Ashhab ◽  
J. Q. You ◽  
Franco Nori
Keyword(s):  
Quantum Systems ◽  
Quantum Circuits ◽  
Superconducting Circuits

scholarly journals SYSTEMS OF CLASSICAL PARTICLES IN THE GRAND CANONICAL ENSEMBLE, SCALING LIMITS AND QUANTUM FIELD THEORY

2005 ◽  
Vol 17 (02) ◽  
pp. 175-226 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
HANNO GOTTSCHALK ◽  
MINORU W. YOSHIDA
Keyword(s):  
Canonical Ensemble ◽  
Grand Canonical Ensemble ◽  
Infinite Volume ◽  
Quantum Field ◽  
Quantum Fields ◽  
Local Interactions ◽  
Related Field ◽  
Potts Models ◽  
Grand Canonical ◽  
The Continuum

Euclidean quantum fields obtained as solutions of stochastic partial pseudo differential equations driven by a Poisson white noise have paths given by locally integrable functions. This makes it possible to define a class of ultra-violet finite local interactions for these models (in any space-time dimension). The corresponding interacting Euclidean quantum fields can be identified with systems of classical "charged" particles in the grand canonical ensemble with an interaction given by a nonlinear energy density of the "static field" generated by the particles' charges via a "generalized Poisson equation". A new definition of some well-known systems of statistical mechanics is given by formulating the related field theoretic local interactions. The infinite volume limit of such systems is discussed for models with trigonometric interactions using a representation of such models as Widom–Rowlinson models associated with (formal) Potts models at imaginary temperature. The infinite volume correlation functional of such Potts models can be constructed by a cluster expansion. This leads to the construction of extremal Gibbs measures with trigonometric interactions in the low-density high-temperature (LD-HT) regime. For Poissonian models with certain trigonometric interactions an extension of the well-known relation between the (massive) sine-Gordon model and the Yukawa particle gas connecting characteristic and correlation functionals is given and used to derive infinite volume measures for interacting Poisson quantum field models through an alternative route. The continuum limit of the particle systems under consideration is also investigated and the formal analogy with the scaling limit of renormalization group theory is pointed out. In some simple cases the question of (non-) triviality of the continuum limits is clarified.

scholarly journals Quantum circuits for strongly correlated quantum systems

2009 ◽  
Vol 79 (3) ◽  
Author(s):  
Frank Verstraete ◽  
J. Ignacio Cirac ◽  
José I. Latorre
Keyword(s):  
Quantum Systems ◽  
Quantum Circuits ◽  
Strongly Correlated ◽  
Correlated Quantum Systems
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