scholarly journals Mapping graph state orbits under local complementation

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 305
Author(s):  
Jeremy C. Adcock ◽  
Sam Morley-Short ◽  
Axel Dahlberg ◽  
Joshua W. Silverstone
Keyword(s):  
Quantum Computing ◽  
Graph Theory ◽  
Quantum Entanglement ◽  
Graph State ◽  
Graph States ◽  
Potential Applications ◽  
Graph Operation ◽  
Local Complementation ◽  
Equivalent Graph ◽  
Component Graph

Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation – the graph operation that links all local-Clifford equivalent graph states – allows us to classify all stabiliser states by their entanglement. Here, we study the structure of the orbits generated by local complementation, mapping them up to 9 qubits and revealing a rich hidden structure. We provide programs to compute these orbits, along with our data for each of the 587 orbits up to 9 qubits and a means to visualise them. We find direct links between the connectivity of certain orbits with the entanglement properties of their component graph states. Furthermore, we observe the correlations between graph-theoretical orbit properties, such as diameter and colourability, with Schmidt measure and preparation complexity and suggest potential applications. It is well known that graph theory and quantum entanglement have strong interplay – our exploration deepens this relationship, providing new tools with which to probe the nature of entanglement.

scholarly journals ESTIMATING PURITY AND ENTROPY IN STABILIZER STATE EXPERIMENTS

2010 ◽  
Vol 08 (01n02) ◽  
pp. 325-335 ◽  
Author(s):  
HARALD WUNDERLICH ◽  
MARTIN B. PLENIO
Keyword(s):  
Quantum Information ◽  
Measurement Data ◽  
Simulated Data ◽  
The State ◽  
Graph State ◽  
Graph States ◽  
Underlying Graph ◽  
Moderate Number ◽  
Full State ◽  
State Tomography

Many experiments in quantum information aim at creating graph states. Quantifying the purity of an experimentally achieved graph state could in principle be accomplished using full-state tomography. This method requires a number of measurement settings growing exponentially with the number of constituents involved. Thus, full-state tomography becomes experimentally infeasible even for a moderate number of qubits. In this paper, we present a method to estimate the purity of experimentally achieved graph states with simple measurements. The observables we consider are the stabilizers of the underlying graph. Then, we formulate the problem as: "What is the state with the least purity that is compatible with the measurement data?" We solve this problem analytically and compare the obtained bounds with results from full-state tomography for simulated data.

scholarly journals On the relation between a graph code and a graph state

2016 ◽  
Vol 16 (3&4) ◽  
pp. 237-250
Author(s):  
Yongsoo Hwang ◽  
Jun Heo
Keyword(s):  
Simple Graph ◽  
Graph State ◽  
Stabilizer Codes ◽  
Logical Qubits ◽  
Related Graph ◽  
Local Complementation ◽  
Stabilizer Group

A graph state and a graph code respectively are defined based on a mathematical simple graph. In this work, we examine a relation between a graph state and a graph code both obtained from the same graph, and show that a graph state is a superposition of logical qubits of the related graph code. By using the relation, we first discuss that a local complementation which has been used for a graph state can be useful for searching locally equivalent stabilizer codes, and second provide a method to find a stabilizer group of a graph code.

scholarly journals Quantum Computing and Complexity in Art

Leonardo ◽  
2019 ◽  
Vol 52 (3) ◽  
pp. 230-235
Author(s):  
Libby Heaney
Keyword(s):  
Quantum Computing ◽  
Quantum Entanglement ◽  
Quantum Measurement ◽  
Research Experience ◽  
Quantum Superposition ◽  
Interactive Installation

The author draws on her research experience in quantum computing to discuss the conception and form of an interactive installation, CLOUD. CLOUD explores complexity in the postdigital by referencing the principles of quantum superposition, quantum entanglement and quantum measurement.

Implementation of molecular spin quantum computing by pulsed ENDOR technique: Direct observation of quantum entanglement and spinor

2007 ◽  
Vol 40 (2) ◽  
pp. 363-366 ◽  
Author(s):  
Kazunobu Sato ◽  
Robabeh Rahimi ◽  
Nobuyuki Mori ◽  
Shinsuke Nishida ◽  
Kazuo Toyota ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Quantum Entanglement ◽  
Direct Observation ◽  
Spin Quantum ◽  
Molecular Spin

scholarly journals Qubit, Quantum Entanglement and all that: Quantum Computing Made Simple

2021 ◽  
Vol 7 (1) ◽  
pp. 1-9
Author(s):  
Zion Elani
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Popular Culture ◽  
Quantum Entanglement ◽  
High Tech ◽  
Quantum Computers ◽  
The World ◽  
Media Hype ◽  
The Impact ◽  
Fully Functioning

Quantum computing, a fancy word resting on equally fancy fundamentals in quantum mechanics, has become a media hype, a mainstream topic in popular culture and an eye candy for high-tech company researchers and investors alike. Quantum computing has the power to provide faster, more efficient, secure and accurate computing solutions for emerging future innovations. Governments the world over, in collaboration with high-tech companies, pour in billions of dollars for the advancement of computing solutions quantum-based and for the development of fully functioning quantum computers that may one day aid in or even replace classical computers. Despite much hype and publicity, most people do not understand what quantum computing is, nor do they comprehend the significance of the developments required in this field, and the impact it may have on the future. Through these lecture notes, we embark on a pedagogic journey of understanding quantum computing, gradually revealing the concepts that form its basis, later diving in a vast pool of future possibilities that lie ahead, concluding with understanding and acknowledging some major hindrance and speed breaking bumpers in their path.

scholarly journals Superconductor Electronics Research: National Competitiveness and Funding Activity

2021 ◽  
Author(s):  
Karson Elmgren ◽  
Ashwin Acharya ◽  
Will Hunt
Keyword(s):  
Artificial Intelligence ◽  
Energy Efficiency ◽  
Signal Processing ◽  
Quantum Computing ◽  
Research Output ◽  
National Competitiveness ◽  
Potential Applications ◽  
Superconductor Electronics

Devices based on superconductor electronics can achieve much higher energy efficiency than standard electronics. Research in superconductor electronics could advance a range of commercial and defense priorities, with potential applications for supercomputing, artificial intelligence, sensors, signal processing, and quantum computing. This brief identifies the countries most actively contributing to superconductor electronics research and assesses their relative competitiveness in terms of both research output and funding.

Connections between Weyl geometry, quantum potential and quantum entanglement

2021 ◽  
Author(s):  
Shi-Dong Liang ◽  
Wenjing Huang
Keyword(s):  
Quantum Mechanics ◽  
Scalar Curvature ◽  
Quantum Entanglement ◽  
Quantum Potential ◽  
Entangled State ◽  
Dimensional System ◽  
Weyl Geometry ◽  
3D Space ◽  
Potential Applications ◽  
Weyl Scalar

The Weyl geometry promises potential applications in gravity and quantum mechanics. We study the relationships between the Weyl geometry, quantum entropy and quantum entanglement based on the Weyl geometry endowing the Euclidean metric. We give the formulation of the Weyl Ricci curvature and Weyl scalar curvature in the n-dimensional system. The Weyl scalar field plays a bridge role to connect the Weyl scalar curvature, quantum potential and quantum entanglement. We also give the Einstein–Weyl tensor and the generalized field equation in 3D vacuum case, which reveals the relationship between Weyl geometry and quantum potential. Particularly, we find that the correspondence between the Weyl scalar curvature and quantum potential is dimension-dependent and works only for the 3D space, which reveals a clue to quantize gravity and an understanding why our space must be 3D if quantum gravity is compatible with quantum mechanics. We analyze numerically a typical example of two orthogonal oscillators to reveal the relationships between the Weyl scalar curvature, quantum potential and quantum entanglement based on this formulation. We find that the Weyl scalar curvature shows a negative dip peak for separate state but becomes a positive peak for the entangled state near original point region, which can be regarded as a geometric signal to detect quantum entanglement.

Quantum Computing II

2020 ◽  
pp. 245-262
Author(s):  
M. Suhail Zubairy
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Quantum Entanglement ◽  
Arbitrary Number ◽  
Quantum Fourier Transform ◽  
Grover’S Algorithm ◽  
Computing Algorithm ◽  
Shor's Algorithm ◽  
Grover's Algorithm

This chapter deals with some of the most prominent successes of quantum computing. The most well-known quantum computing algorithm, Shor’s algorithm for factoring a number in its prime factors, is discussed in details. The key to Shor’s algorithm is the quantum Fourier transform that is explained with the help of simple examples. The role of quantum entanglement is also discussed. The next important quantum computing algorithm is Grover’s algorithm that helps in searching an item in an unsorted database. This algorithm is motivated by first discussing a quantum shell game in which a pea hidden under one of the four shells is found in one measurement with certainty each time. This amazing result is then generalized to an arbitrary number of objects and Grover’s algorithm.

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