scholarly journals Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states

2019 ◽  
Vol 99 (5) ◽  
Author(s):  
A. Elben ◽  
B. Vermersch ◽  
C. F. Roos ◽  
P. Zoller
Keyword(s):  
Quantum States ◽  
Many Body ◽  
Statistical Correlations

scholarly journals Probing Rényi entanglement entropy via randomized measurements

Science ◽  
2019 ◽  
Vol 364 (6437) ◽  
pp. 260-263 ◽  
Author(s):  
Tiff Brydges ◽  
Andreas Elben ◽  
Petar Jurcevic ◽  
Benoît Vermersch ◽  
Christine Maier ◽  
...  
Keyword(s):  
Quantum System ◽  
Entanglement Entropy ◽  
Quantum Systems ◽  
Quantum States ◽  
Many Body ◽  
Trapped Ion ◽  
Statistical Correlations ◽  
Quantum Simulator ◽  
Entanglement Structure ◽  
Arbitrary Quantum

Entanglement is a key feature of many-body quantum systems. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a protocol for measuring the second-order Rényi entropy based on statistical correlations between randomized measurements. Our experiments, carried out with a trapped-ion quantum simulator with partition sizes of up to 10 qubits, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts, in both the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, which is applicable to arbitrary quantum states of up to several tens of qubits.

scholarly journals Many-Body Chern Number from Statistical Correlations of Randomized Measurements

2021 ◽  
Vol 126 (5) ◽  
Author(s):  
Ze-Pei Cian ◽  
Hossein Dehghani ◽  
Andreas Elben ◽  
Benoît Vermersch ◽  
Guanyu Zhu ◽  
...  
Keyword(s):  
Chern Number ◽  
Many Body ◽  
Statistical Correlations

scholarly journals Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information

Science ◽  
2013 ◽  
Vol 340 (6137) ◽  
pp. 1205-1208 ◽  
Author(s):  
Michael Walter ◽  
Brent Doran ◽  
David Gross ◽  
Matthias Christandl
Keyword(s):  
Quantum Computing ◽  
Single Particle ◽  
Local Information ◽  
Geometric Object ◽  
Quantum States ◽  
Many Body ◽  
Arbitrary Size ◽  
Global Entanglement ◽  
Low Levels ◽  
Essential Resource

Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case of pure, multiparticle quantum states, features of the global entanglement can already be extracted from local information alone. This is achieved by associating any given class of entanglement with an entanglement polytope—a geometric object that characterizes the single-particle states compatible with that class. Our results, applicable to systems of arbitrary size and statistics, give rise to local witnesses for global pure-state entanglement and can be generalized to states affected by low levels of noise.

scholarly journals Neural network operations and Susuki–Trotter evolution of neural network states

2018 ◽  
Vol 16 (08) ◽  
pp. 1840008 ◽  
Author(s):  
Nahuel Freitas ◽  
Giovanna Morigi ◽  
Vedran Dunjko
Keyword(s):  
Neural Network ◽  
Optimization Techniques ◽  
Quantum States ◽  
Stochastic Methods ◽  
Many Body ◽  
Boltzmann Machines ◽  
Quantum Operations ◽  
Model Complex ◽  
Network States ◽  
Hidden Nodes

It was recently proposed to leverage the representational power of artificial neural networks, in particular Restricted Boltzmann Machines, in order to model complex quantum states of many-body systems [G. Carleo and M. Troyer, Science 355(6325) (2017) 602.]. States represented in this way, called Neural Network States (NNSs), were shown to display interesting properties like the ability to efficiently capture long-range quantum correlations. However, identifying an optimal neural network representation of a given state might be challenging, and so far this problem has been addressed with stöchastic optimization techniques. In this work, we explore a different direction. We study how the action of elementary quantum operations modifies NNSs. We parametrize a family of many body quantum operations that can be directly applied to states represented by Unrestricted Boltzmann Machines, by just adding hidden nodes and updating the network parameters. We show that this parametrization contains a set of universal quantum gates, from which it follows that the state prepared by any quantum circuit can be expressed as a Neural Network State with a number of hidden nodes that grows linearly with the number of elementary operations in the circuit. This is a powerful representation theorem (which was recently obtained with different methods) but that is not directly useful, since there is no general and efficient way to extract information from this unrestricted description of quantum states. To circumvent this problem, we propose a step-wise procedure based on the projection of Unrestricted quantum states to Restricted quantum states. In turn, two approximate methods to perform this projection are discussed. In this way, we show that it is in principle possible to approximately optimize or evolve Neural Network States without relying on stochastic methods such as Variational Monte Carlo, which are computationally expensive.

scholarly journals Decoherence in elastic and polaronic transport via discrete quantum states

Open Physics ◽  
2006 ◽  
Vol 4 (2) ◽  
Author(s):  
Kamil Walczak
Keyword(s):  
Scattering Problem ◽  
Electrical Current ◽  
Quantum States ◽  
Relaxation Processes ◽  
Nonlinear Transport ◽  
Many Body ◽  
Electron Phonon Interaction ◽  
The Many ◽  
Polaronic Transport ◽  
Interaction Problem

AbstractIn this work we study the effect of decoherence on elastic and polaronic transport via discrete quantum states. Calculations are performed with the help of a nonperturbative computational scheme, based on Green’s function theory within the framework of polaron transformation (GFT-PT), where the many-body electron-phonon interaction problem is mapped exactly into a single-electron multi-channel scattering problem. In particular, the influence of dephasing and relaxation processes on the shape of the electrical current and shot noise curves is discussed in detail under linear and nonlinear transport conditions.

scholarly journals Static and Dynamic Statistical Correlations in Water: Comparison of Classical Ab Initio Molecular Dynamics at Elevated Temperature With Path Integral Simulations at Ambient Temperature

2022 ◽  
Author(s):  
Chenghan Li ◽  
Francesco Paesani ◽  
Gregory A. Voth
Keyword(s):  
Molecular Dynamics ◽  
Elevated Temperature ◽  
Ambient Temperature ◽  
Ab Initio ◽  
Density Functional ◽  
Ab Initio Molecular Dynamics ◽  
Many Body ◽  
Statistical Correlations ◽  
Higher Temperature ◽  
The Many

It is a common practice in ab initio molecular dynamics (AIMD) simulations of water to use an elevated temperature to overcome the over-structuring and slow diffusion predicted by most current density functional theory (DFT) models. The simulation results obtained in this distinct thermodynamic state are then compared with experimental data at ambient temperature based on the rationale that a higher temperature effectively recovers nuclear quantum effects (NQEs) that are missing in the classical AIMD simulations. In this work, we systematically examine the foundation of this assumption for several DFT models as well as for the many-body MB-pol model. We find for the cases studied that a higher temperature does not correctly mimic NQEs at room temperature, which is especially manifest in significantly different three-molecule correlations as well as hydrogen bond dynamics. In many of these cases, the effects of NQEs are the opposite of the effects of carrying out the simulations at an elevated temperature.

Sign in / Sign up

Export Citation Format

Share Document