scholarly journals A scalable realization of local U(1) gauge invariance in cold atomic mixtures

Science ◽  
2020 ◽  
Vol 367 (6482) ◽  
pp. 1128-1130 ◽  
Author(s):  
Alexander Mil ◽  
Torsten V. Zache ◽  
Apoorva Hegde ◽  
Andy Xia ◽  
Rohit P. Bhatt ◽  
...  
Keyword(s):  
Large Scale ◽  
Gauge Theories ◽  
Spatial Dimension ◽  
Gauge Fields ◽  
Quantum Computers ◽  
Computational Techniques ◽  
Quantum Devices ◽  
Gauge Invariant ◽  
Quantum Simulator ◽  
Elementary Building

In the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is the quantum theory of electrons interacting with the electromagnetic field, based on U(1) gauge symmetry. Solving such gauge theories is in general a hard problem for classical computational techniques. Although quantum computers suggest a way forward, large-scale digital quantum devices for complex simulations are difficult to build. We propose a scalable analog quantum simulator of a U(1) gauge theory in one spatial dimension. Using interspecies spin-changing collisions in an atomic mixture, we achieve gauge-invariant interactions between matter and gauge fields with spin- and species-independent trapping potentials. We experimentally realize the elementary building block as a key step toward a platform for quantum simulations of continuous gauge theories.

GAUGE-INVARIANT QUANTISATION OF CHIRAL GAUGE THEORIES

1990 ◽  
Vol 05 (03) ◽  
pp. 175-182 ◽  
Author(s):  
T. D. KIEU
Keyword(s):  
Path Integral ◽  
Gauge Theories ◽  
Berry Phase ◽  
Integral Functional ◽  
Gauge Fields ◽  
Quantum Mechanical ◽  
Gauge Invariant ◽  
Normal Ordering ◽  
Schwinger Model ◽  
Holomorphic Representation

The path-integral functional of chiral gauge theories with background gauge potentials are derived in the holomorphic representation. Justification is provided, from first quantum mechanical principles, for the appearance of a functional phase factor of the gauge fields in order to maintain the gauge invariance. This term is shown to originate either from the Berry phase of the first-quantized hamiltonians or from the normal ordering of the second-quantized hamiltonian with respect to the Dirac in-vacuum. The quantization of the chiral Schwinger model is taken as an example.

scholarly journals NEURAL MULTIGRID METHODS FOR GAUGE THEORIES AND OTHER DISORDERED SYSTEMS

1993 ◽  
Vol 04 (02) ◽  
pp. 239-247 ◽  
Author(s):  
M. BÄKER ◽  
T. KALKREUTER ◽  
G. MACK ◽  
M. SPEH
Keyword(s):  
Monte Carlo ◽  
Disordered Systems ◽  
Large Scale ◽  
Wave Equations ◽  
Gauge Theories ◽  
Point Of View ◽  
Gauge Fields ◽  
Present Evidence ◽  
Neural Computations ◽  
Large Scale Simulations

We present evidence that multigrid works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder, but one needs to introduce a "neural computations" point of view into large scale simulations: First, the system must learn how to do the simulations efficiently, then do the simulation (fast). The method can also be used to provide smooth interpolation kernels which are needed in multigrid Monte Carlo updates.

scholarly journals Overview and Comparison of Gate Level Quantum Software Platforms

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 130 ◽  
Author(s):  
Ryan LaRose
Keyword(s):  
Quantum Computing ◽  
Quantum Computer ◽  
Quantum Computers ◽  
Quantum Devices ◽  
Software Packages ◽  
Software Platforms ◽  
Library Support ◽  
Quantum Simulator ◽  
Computing Landscape ◽  
A Current

Quantum computers are available to use over the cloud, but the recent explosion of quantum software platforms can be overwhelming for those deciding on which to use. In this paper, we provide a current picture of the rapidly evolving quantum computing landscape by comparing four software platforms - Forest (pyQuil), Qiskit, ProjectQ, and the Quantum Developer Kit (Q#) - that enable researchers to use real and simulated quantum devices. Our analysis covers requirements and installation, language syntax through example programs, library support, and quantum simulator capabilities for each platform. For platforms that have quantum computer support, we compare hardware, quantum assembly languages, and quantum compilers. We conclude by covering features of each and briefly mentioning other quantum computing software packages.

scholarly journals Efficiently measuring a quantum device using machine learning

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
D. T. Lennon ◽  
H. Moon ◽  
L. C. Camenzind ◽  
Liuqi Yu ◽  
D. M. Zumbühl ◽  
...  
Keyword(s):  
Machine Learning ◽  
Large Scale ◽  
Learning Algorithm ◽  
Quantum Computers ◽  
Quantum Devices ◽  
Full Resolution ◽  
Large Numbers ◽  
Quantum Device ◽  
On Chip ◽  
Combining Information

Abstract Scalable quantum technologies such as quantum computers will require very large numbers of quantum devices to be characterised and tuned. As the number of devices on chip increases, this task becomes ever more time-consuming, and will be intractable on a large scale without efficient automation. We present measurements on a quantum dot device performed by a machine learning algorithm in real time. The algorithm selects the most informative measurements to perform next by combining information theory with a probabilistic deep-generative model that can generate full-resolution reconstructions from scattered partial measurements. We demonstrate, for two different current map configurations that the algorithm outperforms standard grid scan techniques, reducing the number of measurements required by up to 4 times and the measurement time by 3.7 times. Our contribution goes beyond the use of machine learning for data search and analysis, and instead demonstrates the use of algorithms to automate measurements. This works lays the foundation for learning-based automated measurement of quantum devices.

scholarly journals On classical and quantum deformations of gauge theories

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
I. L. Buchbinder ◽  
P. M. Lavrov
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Gauge Fields ◽  
Exact Relation ◽  
Gauge Invariant ◽  
Gauge Algebra ◽  
Local Functions ◽  
Quantum Deformations ◽  
Non Local ◽  
The Given

AbstractWe elaborate the generalizations of the approach to gauge-invariant deformations of the gauge theories developed in our previous work (Buchbinder and Lavrov in JHEP 06:097, 2021). In the given paper we construct the exact transformations defying the gauge-invariant deformed theory on the base of initial gauge theory with irreducible open gauge algebra. Like in [1], for the theories with open gauge algebras these transformations are the shifts of the initial gauge fields $$A \rightarrow A+h(A)$$ A → A + h ( A ) , with the help of the arbitrary and in general non-local functions h(A). The results are applied to study the quantum aspects of the deformed theories. We derive the exact relation between the quantum effective actions for the above classical theories, where one is obtained from another with the help of the deformation.

scholarly journals AN EQUIVALENCE OF TWO MASS GENERATION MECHANISMS FOR GAUGE FIELDS

2008 ◽  
Vol 23 (13) ◽  
pp. 1973-1993
Author(s):  
ALEXEY SEVOSTYANOV
Keyword(s):  
Gauge Theories ◽  
Generation Mechanism ◽  
Gauge Fields ◽  
Quantum Field ◽  
Mass Generation ◽  
Gauge Invariant ◽  
Massive Vector ◽  
Abelian Case ◽  
Generation Mechanisms ◽  
Topological Mass

Two mass generation mechanisms for gauge theories are studied. It is proved that in the Abelian case the topological mass generation mechanism introduced in Refs. 4, 12 and 15 is equivalent to the mass generation mechanism defined in Refs. 5 and 20 with the help of "localization" of a nonlocal gauge invariant action. In the non-Abelian case the former mechanism is known to generate a unitary renormalizable quantum field theory, describing a massive vector field.

scholarly journals A divide-and-conquer algorithm for quantum state preparation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Israel F. Araujo ◽  
Daniel K. Park ◽  
Francesco Petruccione ◽  
Adenilton J. da Silva
Keyword(s):  
Computational Cost ◽  
Quantum Circuit ◽  
Divide And Conquer ◽  
Computational Time ◽  
Quantum Computers ◽  
Dimensional Vector ◽  
Quantum Devices ◽  
Divide And Conquer Algorithm ◽  
Quantum State Preparation ◽  
Quantum Device

AbstractAdvantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with exponential time advantage using a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a real quantum device and present two applications for quantum machine learning. We expect that this new loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices.

scholarly journals Renormalization group theory of molecular dynamics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Daiji Ichishima ◽  
Yuya Matsumura
Keyword(s):  
Molecular Dynamics ◽  
Renormalization Group ◽  
Critical Exponent ◽  
Computational Efficiency ◽  
Large Scale ◽  
Dissipative Particle Dynamics ◽  
Computational Cost ◽  
Coarse Graining ◽  
Spatial Dimension ◽  
Deborah Number

AbstractLarge scale computation by molecular dynamics (MD) method is often challenging or even impractical due to its computational cost, in spite of its wide applications in a variety of fields. Although the recent advancement in parallel computing and introduction of coarse-graining methods have enabled large scale calculations, macroscopic analyses are still not realizable. Here, we present renormalized molecular dynamics (RMD), a renormalization group of MD in thermal equilibrium derived by using the Migdal–Kadanoff approximation. The RMD method improves the computational efficiency drastically while retaining the advantage of MD. The computational efficiency is improved by a factor of $$2^{n(D+1)}$$ 2 n ( D + 1 ) over conventional MD where D is the spatial dimension and n is the number of applied renormalization transforms. We verify RMD by conducting two simulations; melting of an aluminum slab and collision of aluminum spheres. Both problems show that the expectation values of physical quantities are in good agreement after the renormalization, whereas the consumption time is reduced as expected. To observe behavior of RMD near the critical point, the critical exponent of the Lennard-Jones potential is extracted by calculating specific heat on the mesoscale. The critical exponent is obtained as $$\nu =0.63\pm 0.01$$ ν = 0.63 ± 0.01 . In addition, the renormalization group of dissipative particle dynamics (DPD) is derived. Renormalized DPD is equivalent to RMD in isothermal systems under the condition such that Deborah number $$De\ll 1$$ D e ≪ 1 .

scholarly journals QUBO formulations for training machine learning models

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Prasanna Date ◽  
Davis Arthur ◽  
Lauren Pusey-Nazzaro
Keyword(s):  
Machine Learning ◽  
Linear Regression ◽  
Large Scale ◽  
Support Vector ◽  
Quantum Computers ◽  
Np Hard ◽  
Learning Models ◽  
Moore’S Law ◽  
Moore's Law ◽  
Machine Learning Models

AbstractTraining machine learning models on classical computers is usually a time and compute intensive process. With Moore’s law nearing its inevitable end and an ever-increasing demand for large-scale data analysis using machine learning, we must leverage non-conventional computing paradigms like quantum computing to train machine learning models efficiently. Adiabatic quantum computers can approximately solve NP-hard problems, such as the quadratic unconstrained binary optimization (QUBO), faster than classical computers. Since many machine learning problems are also NP-hard, we believe adiabatic quantum computers might be instrumental in training machine learning models efficiently in the post Moore’s law era. In order to solve problems on adiabatic quantum computers, they must be formulated as QUBO problems, which is very challenging. In this paper, we formulate the training problems of three machine learning models—linear regression, support vector machine (SVM) and balanced k-means clustering—as QUBO problems, making them conducive to be trained on adiabatic quantum computers. We also analyze the computational complexities of our formulations and compare them to corresponding state-of-the-art classical approaches. We show that the time and space complexities of our formulations are better (in case of SVM and balanced k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.

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