A Quantum Description of Physical Systems with Non-real Energies

2021 ◽  
Vol 1 ◽  
Keyword(s):  
Quantum Systems ◽  
Physical Systems ◽  
Quantum Description ◽  
Time Symmetry

While quantum systems are traditionally described by Hermitian Hamiltonians, the formalism is extendable to a non-Hermitian description for systems that are dissipative or obey parity-time symmetry.

Constructing physical systems with dynamical symmetry

2014 ◽  
Vol 92 (4) ◽  
pp. 335-340
Author(s):  
Yan Li ◽  
Fu-Lin Zhang ◽  
Rui-Juan Gu ◽  
Jing-Ling Chen ◽  
L.C. Kwek
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Dynamical Symmetry ◽  
Algebraic Method ◽  
Quantum Systems ◽  
Physical Systems ◽  
Generalized Systems ◽  
Dependent Mass ◽  
Position Dependent Mass

An approach to constructing quantum systems with dynamical symmetry is proposed. As examples, we construct generalized systems of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with position-dependent mass. They have symmetries that are similar to the corresponding ones, and can be solved by using the algebraic method. We also exhibit an example of the method applied to the noncentral field.

scholarly journals Photonic implementation of Majorana-based Berry phases

2018 ◽  
Vol 4 (10) ◽  
pp. eaat6533 ◽  
Author(s):  
Jin-Shi Xu ◽  
Kai Sun ◽  
Jiannis K. Pachos ◽  
Yong-Jian Han ◽  
Chuan-Feng Li ◽  
...  
Keyword(s):  
Quantum Systems ◽  
Majorana Fermions ◽  
Topological Characteristic ◽  
Fundamental Physics ◽  
Geometric Phases ◽  
Physical Systems ◽  
All Optical ◽  
Topological Version ◽  
Berry Phases ◽  
Statistical Evolution

Geometric phases, generated by cyclic evolutions of quantum systems, offer an inspiring playground for advancing fundamental physics and technologies alike. The exotic statistics of anyons realized in physical systems can be interpreted as a topological version of geometric phases. However, non-Abelian statistics has not yet been demonstrated in the laboratory. Here, we use an all-optical quantum system that simulates the statistical evolution of Majorana fermions. As a result, we experimentally realize non-Abelian Berry phases with the topological characteristic that they are invariant under continuous deformations of their control parameters. We implement a universal set of Majorana-inspired gates by performing topological and nontopological evolutions and investigate their resilience against perturbative errors. Our photonic experiment, though not scalable, suggests the intriguing possibility of experimentally simulating Majorana statistics with scalable technologies.

scholarly journals Experimentally Accessible Witnesses of Many-Body Localization

2019 ◽  
Vol 1 (1) ◽  
pp. 50-62 ◽  
Author(s):  
Marcel Goihl ◽  
Mathis Friesdorf ◽  
Albert H. Werner ◽  
Winton Brown ◽  
Jens Eisert
Keyword(s):  
Statistical Physics ◽  
Optical Lattices ◽  
Cold Atoms ◽  
Quantum Statistical Mechanics ◽  
Quantum Systems ◽  
Many Body ◽  
Physical Systems ◽  
Tensor Network ◽  
Distinct Features ◽  
Flight Measurements

The phenomenon of many-body localized (MBL) systems has attracted significant interest in recent years, for its intriguing implications from a perspective of both condensed-matter and statistical physics: they are insulators even at non-zero temperature and fail to thermalize, violating expectations from quantum statistical mechanics. What is more, recent seminal experimental developments with ultra-cold atoms in optical lattices constituting analog quantum simulators have pushed many-body localized systems into the realm of physical systems that can be measured with high accuracy. In this work, we introduce experimentally accessible witnesses that directly probe distinct features of MBL, distinguishing it from its Anderson counterpart. We insist on building our toolbox from techniques available in the laboratory, including on-site addressing, super-lattices, and time-of-flight measurements, identifying witnesses based on fluctuations, density–density correlators, densities, and entanglement. We build upon the theory of out of equilibrium quantum systems, in conjunction with tensor network and exact simulations, showing the effectiveness of the tools for realistic models.

scholarly journals Emergence of PT-symmetry breaking in open quantum systems

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Julian Huber ◽  
Peter Kirton ◽  
Stefan Rotter ◽  
Peter Rabl
Keyword(s):  
Symmetry Breaking ◽  
Open Quantum Systems ◽  
Symmetry Transformation ◽  
Quantum Systems ◽  
Coupled Systems ◽  
Physical Systems ◽  
Open Quantum ◽  
Parity Symmetry ◽  
Classical Correspondence ◽  
Liouville Operators

The effect of \mathcal{PT}𝒫𝒯-symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. However, it is still an unsolved problem how to generalize the concept of \mathcal{PT}𝒫𝒯 symmetry to the quantum domain, where the conventional definition in terms of non-Hermitian Hamiltonians is not applicable. Here we introduce a symmetry relation for Liouville operators that describe the dissipative evolution of arbitrary open quantum systems. Specifically, we show that the invariance of the Liouvillian under this symmetry transformation implies the existence of stationary states with preserved and broken parity symmetry. As the dimension of the Hilbert space grows, the transition between these two limiting phases becomes increasingly sharp and the classically expected \mathcal{PT}𝒫𝒯-symmetry breaking transition is recovered. This quantum-to-classical correspondence allows us to establish a common theoretical framework to identify and accurately describe \mathcal{PT}𝒫𝒯-symmetry breaking effects in a large variety of physical systems, operated both in the classical and quantum regimes.

scholarly journals Nearly tight Trotterization of interacting electrons

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 495
Author(s):  
Yuan Su ◽  
Hsin-Yuan Huang ◽  
Earl T. Campbell
Keyword(s):  
Electronic Structure ◽  
Plane Wave ◽  
Hubbard Model ◽  
Transition Amplitude ◽  
Quantum Systems ◽  
Quantum Computers ◽  
Initial State ◽  
Physical Systems ◽  
Interacting Electrons ◽  
Simulation Error

We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting commutativity of the target Hamiltonian, sparsity of interactions, and prior knowledge of the initial state. We achieve this using Trotterization for a class of interacting electrons that encompasses various physical systems, including the plane-wave-basis electronic structure and the Fermi-Hubbard model. We estimate the simulation error by taking the transition amplitude of nested commutators of the Hamiltonian terms within the η-electron manifold. We develop multiple techniques for bounding the transition amplitude and expectation of general fermionic operators, which may be of independent interest. We show that it suffices to use (n5/3η2/3+n4/3η2/3)no(1) gates to simulate electronic structure in the plane-wave basis with n spin orbitals and η electrons, improving the best previous result in second quantization up to a negligible factor while outperforming the first-quantized simulation when n=η2−o(1). We also obtain an improvement for simulating the Fermi-Hubbard model. We construct concrete examples for which our bounds are almost saturated, giving a nearly tight Trotterization of interacting electrons.

scholarly journals Holism and Time Symmetry

Quanta ◽  
2016 ◽  
Vol 5 (1) ◽  
pp. 85 ◽  
Author(s):  
Peter J. Lewis
Keyword(s):  
Quantum Mechanics ◽  
Quantum Systems ◽  
Many Worlds ◽  
Variable Theory ◽  
General Argument ◽  
Hidden Variable ◽  
Time Symmetry ◽  
General Quantum ◽  
Einstein Podolsky Rosen

<p>Quantum mechanics is often taken to entail holism. I examine the arguments for this claim, and find that although there is no general argument from the structure of quantum mechanics to holism, there are specific arguments for holism available within the three main realist interpretations (Bohm, Ghirardi-Rimini-Weber and many-worlds). However, Evans, Price and Wharton's sideways Einstein-Podolsky-Rosen-Bell example challenges the holistic conclusion. I show how the symmetry between the sideways and standard Einstein-Podolsky-Rosen-Bell set-ups can be used to argue against holism. I evaluate the prospects for extending this insight to more general quantum systems, with a view to producing a genuinely time-symmetric hidden variable theory. I conclude that, although this extension undermines the analogy between the sideways and standard cases, quantum mechanics without holism remains a live possibility.</p><p>Quanta 2016; 5: 85–92.</p>

scholarly journals HIDDEN UNITY IN THE QUANTUM DESCRIPTION OF MATTER

2003 ◽  
Vol 17 (28) ◽  
pp. 5413-5423 ◽  
Author(s):  
G. ORTIZ ◽  
C. D. BATISTA
Keyword(s):  
General Concept ◽  
Quantum Systems ◽  
Fundamental Concept ◽  
Critical Behaviour ◽  
Broken Symmetry ◽  
Quantum Description ◽  
Algebraic Framework ◽  
Complex Phenomena ◽  
Physical Phenomena

We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterised by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity behind seemingly unrelated physical phenomena, thus establishing exact connections between them. This leads to the fundamental concept of universality of physical phenomena, a general concept not restricted to the domain of critical behaviour. Key to our framework is the concept of languages and the construction of dictionaries relating them.

scholarly journals QUANTUM FIELD THEORY FROM FIRST PRINCIPLES

2020 ◽  
Author(s):  
Paolo Perinotti
Keyword(s):  
Quantum Theory ◽  
Cellular Automata ◽  
Hilbert Spaces ◽  
First Principles ◽  
Relativistic Quantum ◽  
Quantum Systems ◽  
Space Time ◽  
Physical Systems ◽  
Minkowski Space Time ◽  
Physical Laws

The mathematical description of quantum systems univocally identies their nature. In other words we treat a system as quantum if we describe its behaviour adopting Hilbert spaces and structures thereof, as prescribed by the postulates of quantum theory. The choice of using quantum systems as the elementary systems of physics can be justied in terms of informational principles, thanks to results of the last decade. Such results come as the conclusion of a research program that lasted almost one century, with the aim of reformulating quantum theory in terms of operational principles. This achievement now poses a new challenge, that we face here. If the systems of quantum theory are thought of as elementary information carriers in the rst place, rather than elementary constituents of matter, and their connections are logical connections within a given algorithm, rather than space-time relations, then we need to nd the origin of mechanical concepts—that characterise quantum mechanics as a theory of physical systems. To this end,we will illustrate howphysical laws can be viewed as algorithms for the update of memory registers that make a physical system. Imposing the characteristic properties of physical laws to such an algorithm, i.e. homogeneity, reversibility and isotropy, we will show that the physical laws thus selected are particular algorithms known as cellular automata. Further assumptions regarding maximal simplicity of the algorithm lead to two cellular automata only, that in a suitable regime can be described by Weyl’s dierential equations, lying at the basis of the dynamics of relativistic quantum elds. We will nally discuss how the same cellular automaton can give rise to both Fermionic eld dynamics and to Maxwell’s equations, that rule the dynamics of the electromagnetic eld. We will conclude reviewing the discussion of the relativity principle, that must be suitably adapted to the scenario where space-time is not an elementary notion, through the denition of a change of inertial reference frame, and whose formulation leads to the recovery of the symmetry of Minkowski space-time, identied with Poincar´e’s group. Space-time thus emerges as one of the manifestations of physical laws, rather than the background where they occur, and its features are determined by the dynamics of systems, necessarily equipped with dierential equations that express it. In brief, there is no space-time unless an evolution rule requires it.

scholarly journals Experimental comparison of two quantum computing architectures

2017 ◽  
Vol 114 (13) ◽  
pp. 3305-3310 ◽  
Author(s):  
Norbert M. Linke ◽  
Dmitri Maslov ◽  
Martin Roetteler ◽  
Shantanu Debnath ◽  
Caroline Figgatt ◽  
...  
Keyword(s):  
State Of The Art ◽  
Quantum Algorithms ◽  
Quantum Systems ◽  
Experimental Comparison ◽  
Quantum Computers ◽  
Physical Systems ◽  
Technology Platforms ◽  
Fully Connected ◽  
Identical Quantum ◽  
Selection Of

We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device (www.research.ibm.com/ibm-q) with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programed in a way that is blind to the underlying hardware, thus allowing a comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that use more connectivity clearly benefit from a better-connected system of qubits. Although the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that codesigning particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future.

scholarly journals Observation of parity-time symmetry breaking in a single-spin system

Science ◽  
2019 ◽  
Vol 364 (6443) ◽  
pp. 878-880 ◽  
Author(s):  
Yang Wu ◽  
Wenquan Liu ◽  
Jianpei Geng ◽  
Xingrui Song ◽  
Xiangyu Ye ◽  
...  
Keyword(s):  
Quantum Systems ◽  
Spin Systems ◽  
Nitrogen Vacancy ◽  
Single Quantum ◽  
Single Spin ◽  
Classical Systems ◽  
Time Symmetry ◽  
Nitrogen Vacancy Center ◽  
Quantum Sensing ◽  
Vacancy Center

Steering the evolution of single spin systems is crucial for quantum computing and quantum sensing. The dynamics of quantum systems has been theoretically investigated with parity-time–symmetric Hamiltonians exhibiting exotic properties. Although parity-time symmetry has been explored in classical systems, its observation in a single quantum system remains elusive. We developed a method to dilate a general parity-time–symmetric Hamiltonian into a Hermitian one. The quantum state evolutions ranging from regions of unbroken to broken PT symmetry have been observed with a single nitrogen-vacancy center in diamond. Owing to the universality of the dilation method, our result provides a route for further exploiting and understanding the exotic properties of parity-time symmetric Hamiltonian in quantum systems.

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