scholarly journals Probing quantum walks through coherent control of high-dimensionally entangled photons

2020 ◽  
Vol 6 (29) ◽  
pp. eaba8066 ◽  
Author(s):  
Poolad Imany ◽  
Navin B. Lingaraju ◽  
Mohammed S. Alshaykh ◽  
Daniel E. Leaird ◽  
Andrew M. Weiner
Keyword(s):  
Bound States ◽  
Coherent Control ◽  
Ballistic Transport ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Full Potential ◽  
Many Body ◽  
Frequency Combs ◽  
System A ◽  
Electro Optic

Control over the duration of a quantum walk is critical to unlocking its full potential for quantum search and the simulation of many-body physics. Here we report quantum walks of biphoton frequency combs where the duration of the walk, or circuit depth, is tunable over a continuous range without any change to the physical footprint of the system—a feature absent from previous photonic implementations. In our platform, entangled photon pairs hop between discrete frequency modes with the coupling between these modes mediated by electro-optic modulation of the waveguide refractive index. Through control of the phase across different modes, we demonstrate a rich variety of behavior: from walks exhibiting enhanced ballistic transport or strong energy confinement, to subspaces featuring scattering centers or local traps. We also explore the role of entanglement dimensionality in the creation of energy bound states, which illustrates the potential for these walks to quantify high-dimensional entanglement.

scholarly journals Borromean states in discrete-time quantum walks

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 523
Author(s):  
Marcin Markiewicz ◽  
Marcin Karczewski ◽  
Pawel Kurzynski
Keyword(s):  
Discrete Time ◽  
Bound States ◽  
Quantum Walk ◽  
Bound State ◽  
Quantum Walks ◽  
Interacting Particles ◽  
Time Quantum ◽  
The Right ◽  
Efimov States ◽  
Peculiar Behavior

In the right conditions, removing one particle from a multipartite bound state can make it fall apart. This feature, known as the "Borromean property", has been recently demonstrated experimentally in Efimov states. One could expect that such peculiar behavior should be linked with the presence of strong inter-particle correlations. However, any exploration of this connection is hindered by the complexity of the physical systems exhibiting the Borromean property. To overcome this problem, we introduce a simple dynamical toy model based on a discrete-time quantum walk of many interacting particles. We show that the particles described by it need to exhibit the Greenberger-Horne-Zeillinger (GHZ) entanglement to form Borromean bound states. As this type of entanglement is very prone to particle losses, our work demonstrates an intuitive link between correlations and Borromean properties of the system. Moreover, we discuss our findings in the context of the formation of composite particles.

Quantum walks and synthetic tight-binding crystals in on-chip electro-optic frequency combs

2019 ◽  
Author(s):  
Christian Reimer ◽  
Yaowen Hu ◽  
Mian Zhang ◽  
Amirhassan Shams-Ansari ◽  
Marko Loncar
Keyword(s):  
Tight Binding ◽  
Quantum Walks ◽  
Frequency Combs ◽  
Electro Optic ◽  
On Chip

High-bandwidth readout of optomechanical cavity sensors with electro-optic frequency combs

2020 ◽  
Author(s):  
Benjamin J. Reschovsky ◽  
David. A. Long ◽  
Yiliang Bao ◽  
Feng Zhou ◽  
Richard A. Allen ◽  
...  
Keyword(s):  
Frequency Combs ◽  
Electro Optic ◽  
High Bandwidth ◽  
Optomechanical Cavity

Global Optimization With Quantum Walk Enhanced Grover Search

2014 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Early Stage ◽  
Hybrid Approach ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Tunneling Effect ◽  
Grover’S Algorithm ◽  
Grover's Algorithm ◽  
Grover Search

One of the significant breakthroughs in quantum computation is Grover’s algorithm for unsorted database search. Recently, the applications of Grover’s algorithm to solve global optimization problems have been demonstrated, where unknown optimum solutions are found by iteratively improving the threshold value for the selective phase shift operator in Grover rotation. In this paper, a hybrid approach that combines continuous-time quantum walks with Grover search is proposed. By taking advantage of quantum tunneling effect, local barriers are overcome and better threshold values can be found at the early stage of search process. The new algorithm based on the formalism is demonstrated with benchmark examples of global optimization. The results between the new algorithm and the Grover search method are also compared.

Higher-dimensional open quantum walk in environment of quantum Bernoulli noises

2021 ◽  
pp. 2250001
Author(s):  
Ce Wang
Keyword(s):  
Quantum Walk ◽  
Quantum Walks ◽  
Initial State ◽  
Quantum Random Walks ◽  
Open Quantum ◽  
Higher Dimensional ◽  
Gauss Type ◽  
Open Quantum Random Walks ◽  
Limit Probability ◽  
Creation Operators

Open quantum walks (OQWs) (also known as open quantum random walks) are quantum analogs of classical Markov chains in probability theory, and have potential application in quantum information and quantum computation. Quantum Bernoulli noises (QBNs) are annihilation and creation operators acting on Bernoulli functionals, and can be used as the environment of an open quantum system. In this paper, by using QBNs as the environment, we introduce an OQW on a general higher-dimensional integer lattice. We obtain a quantum channel representation of the walk, which shows that the walk is indeed an OQW. We prove that all the states of the walk are separable provided its initial state is separable. We also prove that, for some initial states, the walk has a limit probability distribution of higher-dimensional Gauss type. Finally, we show links between the walk and a unitary quantum walk recently introduced in terms of QBNs.

Exploring scalar quantum walks on Cayley graphs

2008 ◽  
Vol 8 (1&2) ◽  
pp. 68-81
Author(s):  
O.L. Acevedo ◽  
J. Roland ◽  
N.J. Cerf
Keyword(s):  
Evolution Operator ◽  
Cayley Graphs ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Constructive Method ◽  
Quantum Evolution ◽  
Necessary Condition ◽  
Internal Space ◽  
Special Cases ◽  
Scalar Quantum

A quantum walk, \emph{i.e.}, the quantum evolution of a particle on a graph, is termed \emph{scalar} if the internal space of the moving particle (often called the coin) has dimension one. Here, we study the existence of scalar quantum walks on Cayley graphs, which are built from the generators of a group. After deriving a necessary condition on these generators for the existence of a scalar quantum walk, we present a general method to express the evolution operator of the walk, assuming homogeneity of the evolution. We use this necessary condition and the subsequent constructive method to investigate the existence of scalar quantum walks on Cayley graphs of groups presented with two or three generators. In this restricted framework, we classify all groups -- in terms of relations between their generators -- that admit scalar quantum walks, and we also derive the form of the most general evolution operator. Finally, we point out some interesting special cases, and extend our study to a few examples of Cayley graphs built with more than three generators.

Transport through several four-quantum-dot topological structures

2021 ◽  
pp. 2150393
Author(s):  
Qingshuang Zhi ◽  
Kongfa Chen ◽  
Zelong He
Keyword(s):  
Quantum Dot ◽  
Coupling Strength ◽  
Bound States ◽  
Resonance Peak ◽  
Coulomb Interactions ◽  
Many Body ◽  
Body Effect ◽  
Topological Structures ◽  
Resonance Band ◽  
Interdot Coupling

In this paper, several four-quantum-dot topological structures are designed. The influence of the interdot coupling strength and intradot Coulomb interactions on the conductance is discussed. The location of the anti-resonance band can be manipulated by tuning the interdot coupling strength, which suggests a physical scheme of an effective quantum switch. The Fano anti-resonance peak may evolve into a resonance peak. For the particular value of the interdot coupling strength, two Fano anti-resonances collapse and bound states in the continuum are formed. Moreover, many-body effect makes the number of anti-resonance bands increase. This study provides a theoretical basis for the design of quantum computing devices.

scholarly journals Marking Vertices to Find Graph Isomorphism Mapping Based on Continuous-Time Quantum Walk

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 586 ◽  
Author(s):  
Xin Wang ◽  
Yi Zhang ◽  
Kai Lu ◽  
Xiaoping Wang ◽  
Kai Liu
Keyword(s):  
Polynomial Time ◽  
Continuous Time ◽  
Graph Isomorphism ◽  
Quantum Walk ◽  
Isomorphism Problem ◽  
Quantum Walks ◽  
Regular Graphs ◽  
Structure Preserving ◽  
Topological Structures ◽  
Time Quantum

The isomorphism problem involves judging whether two graphs are topologically the same and producing structure-preserving isomorphism mapping. It is widely used in various areas. Diverse algorithms have been proposed to solve this problem in polynomial time, with the help of quantum walks. Some of these algorithms, however, fail to find the isomorphism mapping. Moreover, most algorithms have very limited performance on regular graphs which are generally difficult to deal with due to their symmetry. We propose IsoMarking to discover an isomorphism mapping effectively, based on the quantum walk which is sensitive to topological structures. Firstly, IsoMarking marks vertices so that it can reduce the harmful influence of symmetry. Secondly, IsoMarking can ascertain whether the current candidate bijection is consistent with existing bijections and eventually obtains qualified mapping. Thirdly, our experiments on 1585 pairs of graphs demonstrate that our algorithm performs significantly better on both ordinary graphs and regular graphs.

scholarly journals Quantum walks and elliptic integrals

2010 ◽  
Vol 20 (6) ◽  
pp. 1091-1098 ◽  
Author(s):  
NORIO KONNO
Keyword(s):  
Random Walk ◽  
Generating Function ◽  
Elliptic Integral ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Elliptic Integrals ◽  
Two Dimensional ◽  
One Dimensional ◽  
Similar Expression ◽  
Return Probability

Pólya showed in his 1921 paper that the generating function of the return probability for a two-dimensional random walk can be written in terms of an elliptic integral. In this paper we present a similar expression for a one-dimensional quantum walk.

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