scholarly journals Perfect state transfer on graphs with a potential

2017 ◽  
Vol 17 (3&4) ◽  
pp. 303-327
Author(s):  
Mark Kempton ◽  
Gabor Lippner ◽  
Shing-Tung Yau
Keyword(s):  
Potential Function ◽  
Quantum State ◽  
Quantum Tunneling ◽  
Perfect State ◽  
Graph Products ◽  
Quantum State Transfer ◽  
State Transfer ◽  
Vertex Set ◽  
Perfect State Transfer

In this paper we study quantum state transfer (also called quantum tunneling) on graphs when there is a potential function on the vertex set. We present two main results. First, we show that for paths of length greater than three, there is no potential on the vertices of the path for which perfect state transfer between the endpoints can occur. In particular, this answers a question raised by Godsil in Section 20 of [1]. Second, we show that if a graph has two vertices that share a common neighborhood, then there is a potential on the vertex set for which perfect state transfer will occur between those two vertices. This gives numerous examples where perfect state transfer does not occur without the potential, but adding a potential makes perfect state transfer possible. In addition, we investigate perfect state transfer on graph products, which gives further examples where perfect state transfer can occur.

scholarly journals Pretty good state transfer on 1-sum of star graphs

2018 ◽  
Vol 16 (1) ◽  
pp. 1483-1489
Author(s):  
Hailong Hou ◽  
Rui Gu ◽  
Mengdi Tong
Keyword(s):  
Quantum State ◽  
Complex Number ◽  
Adjacency Matrix ◽  
Perfect State ◽  
Quantum State Transfer ◽  
Positive Real ◽  
Star Graphs ◽  
State Transfer ◽  
Good State ◽  
Perfect State Transfer

AbstractLetAbe the adjacency matrix of a graphGand supposeU(t) = exp(itA). We say that we have perfect state transfer inGfrom the vertexuto the vertexvat timetif there is a scalarγof unit modulus such thatU(t)eu=γ ev. It is known that perfect state transfer is rare. So C.Godsil gave a relaxation of this definition: we say that we have pretty good state transfer fromutovif there exists a complex numberγof unit modulus and, for each positive realϵthere is a timetsuch that ‖U(t)eu–γ ev‖ <ϵ. In this paper, the quantum state transfer on 1-sum of star graphsFk,lis explored. We show that there is no perfect state transfer onFk,l, but there is pretty good state transfer onFk,lif and only ifk=l.

scholarly journals PERFECT STATE TRANSFER IN XX CHAINS INDUCED BY BOUNDARY MAGNETIC FIELDS

2012 ◽  
Vol 10 (03) ◽  
pp. 1250029 ◽  
Author(s):  
THORBEN LINNEWEBER ◽  
JOACHIM STOLZE ◽  
GÖTZ S. UHRIG
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Strong Magnetic Field ◽  
Quantum State ◽  
Numerical Study ◽  
Perfect State ◽  
Quantum State Transfer ◽  
State Transfer ◽  
Perfect State Transfer

A recent numerical study of short chains found near-perfect quantum state transfer between the boundary sites of a spin-1/2 XX chain if a sufficiently strong magnetic field acts on these sites. We show that the phenomenon is based on a pair of states strongly localized at the boundaries of the system and provide a simple quantitative analytical explanation.

scholarly journals PERFECT STATE TRANSFER, GRAPH PRODUCTS AND EQUITABLE PARTITIONS

2011 ◽  
Vol 09 (03) ◽  
pp. 823-842 ◽  
Author(s):  
YANG GE ◽  
BENJAMIN GREENBERG ◽  
OSCAR PEREZ ◽  
CHRISTINO TAMON
Keyword(s):  
Continuous Time ◽  
Quantum Walks ◽  
Perfect State ◽  
Graph Products ◽  
State Transfer ◽  
Time Quantum ◽  
Perfect State Transfer

We describe new constructions of graphs which exhibit perfect state transfer on continuous-time quantum walks. Our constructions are based on generalizations of the double cones and variants of the Cartesian graph products (which include the hypercube). We also describe a generalization of the path collapsing argument (which reduces questions about perfect state transfer to simpler weighted multigraphs) for graphs with equitable distance partitions.

scholarly journals EFFICIENT AND PERFECT STATE TRANSFER IN QUANTUM CHAINS

2006 ◽  
Vol 04 (03) ◽  
pp. 405-414 ◽  
Author(s):  
DANIEL BURGARTH ◽  
SOUGATO BOSE ◽  
VITTORIO GIOVANNETTI
Keyword(s):  
Quantum Wires ◽  
Perfect State ◽  
Heisenberg Chain ◽  
Quantum State Transfer ◽  
General Hypothesis ◽  
Heisenberg Spin ◽  
State Transfer ◽  
Perfect State Transfer ◽  
Heisenberg Spin Chains ◽  
Identical Quantum

We present a communication protocol for chains of permanently coupled qubits which achieves perfect quantum state transfer and which is efficient with respect to the number of chains employed in the scheme. The system consists of M uncoupled identical quantum chains. Local control (gates, measurements) is only allowed at the sending/receiving end of the chains. Under a quite general hypothesis on the interaction Hamiltonian of the qubits, a theorem can be proved which shows that the receiver is able to asymptotically recover the messages by repetitive monitoring of his qubits. We show how two parallel Heisenberg spin chains can be used as quantum wires. Perfect state transfer with a probability of failure lower than P in a Heisenberg chain of N spin-1/2 particles can be achieved in a time scale of the order of [Formula: see text].

scholarly journals PERFECT, EFFICIENT, STATE TRANSFER AND ITS APPLICATION AS A CONSTRUCTIVE TOOL

2010 ◽  
Vol 08 (04) ◽  
pp. 641-676 ◽  
Author(s):  
ALASTAIR KAY
Keyword(s):  
Quantum State ◽  
Signal Amplification ◽  
Fixed Time ◽  
Perfect State ◽  
Entanglement Generation ◽  
State Transfer ◽  
Universal Quantum ◽  
The Subject ◽  
Perfect State Transfer ◽  
A Chain

We review the subject of perfect state transfer — how one designs the (fixed) interactions of a chain of spins so that a quantum state, initially inserted on one end of the chain, is perfectly transferred to the opposite end in a fixed time. The perfect state transfer systems are then used as a constructive tool to design Hamiltonian implementations of other primitive protocols such as entanglement generation and signal amplification in measurements, before showing that, in fact, universal quantum computation can be implemented in this way.

Quantum state transfer on unsymmetrical graphs via discrete-time quantum walk

2019 ◽  
Vol 34 (38) ◽  
pp. 1950317
Author(s):  
Wei-Feng Cao ◽  
Yu-Guang Yang ◽  
Dan Li ◽  
Jing-Ru Dong ◽  
Yi-Hua Zhou ◽  
...  
Keyword(s):  
Quantum State ◽  
Discrete Time ◽  
Complete Bipartite Graph ◽  
Quantum Walk ◽  
Star Graph ◽  
Perfect State ◽  
Quantum State Transfer ◽  
State Transfer ◽  
Butterfly Network ◽  
Time Quantum

Perfect state transfer can be achieved between two marked vertices of graphs like a star graph, a complete graph with self-loops and a complete bipartite graph, and two-dimensional Lattice by means of discrete-time quantum walk. In this paper, we investigate the quality of quantum state transfer between two marked vertices of an unsymmetrical graph like the butterfly network. Our numerical results support the conjecture that the fidelity of state transfer depends on the quantum state to be transferred dynamically. The butterfly network is a typical example studied in networking coding. Therefore, these results can provide a clue to the construction of quantum network coding schemes.

scholarly journals Spectrally Extremal Vertices, Strong Cospectrality, and State Transfer

10.37236/5031 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Gabriel Coutinho
Keyword(s):  
Extremal Property ◽  
Maximum Distance ◽  
Perfect State ◽  
Trade Off ◽  
Simple Graphs ◽  
Underlying Graph ◽  
State Transfer ◽  
Vertex Set ◽  
Perfect State Transfer

In order to obtain perfect state transfer between two sites in a network of interacting qubits, their corresponding vertices in the underlying graph must satisfy a property called strong cospectrality. Here we determine the structure of graphs containing pairs of vertices which are strongly cospectral and satisfy a certain extremal property related to the spectrum of the graph. If the graph satisfies this property globally and is regular, we also show that the existence of a partition of the vertex set into pairs of vertices at maximum distance admitting perfect state transfer forces the graph to be distance-regular. Finally, we present some new examples of perfect state transfer in simple graphs constructed with our technology. In particular, for odd distances, we improve the known trade-off between the distance perfect state transfer occurs in simple graphs and the size of the graph.

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