## References

SHOWING 1-10 OF 22 REFERENCES

Pretty good quantum fractional revival in paths and cycles

- MathematicsAlgebraic Combinatorics
- 2022

We initiate the study of pretty good quantum fractional revival in graphs, a generalization of pretty good quantum state transfer in graphs. We give a complete characterization of pretty good…

Laplacian Fractional Revival on Graphs

- MathematicsElectron. J. Comb.
- 2021

A spectral characterization of Laplacian fractional revival is given, which leads to a polynomial time algorithm to check this phenomenon and find the earliest time when it occurs, and the characterization theorem is applied to special families of graphs.

Approximate quantum fractional revival in paths and cycles

- Mathematics
- 2020

We initiate the study of approximate quantum fractional revival in graphs, a generalization of pretty good quantum state transfer in graphs. We give a complete characterization of approximate…

Pretty Good State Transfer in Qubit Chains - The Heisenberg Hamiltonian

- Physics
- 2016

Pretty good state transfer in networks of qubits occurs when a continuous-time quantum walk allows the transmission of a qubit state from one node of the network to another, with fidelity arbitrarily…

Universal computation by quantum walk.

- PhysicsPhysical review letters
- 2009

It is shown that quantum walk can be regarded as a universal computational primitive, with any quantum computation encoded in some graph, even if the Hamiltonian is restricted to be the adjacency matrix of a low-degree graph.

No Laplacian Perfect State Transfer in Trees

- MathematicsSIAM J. Discret. Math.
- 2015

It is conjecture that perfect state transfer does not happen in trees with more than three vertices, and the model based on the $XY$-Hamiltonian, whose action is equivalent to the action of the adjacency matrix of the graph, is considered.

Quantum Walks and Pretty Good State transfer on Paths

- Computer Science
- 2019

Techniques from algebraic graph theory and number theory are used to analyze the mathematical model for continuous time quantum walks on graphs and provide necessary and sufficient conditions for pretty good state transfer in a particular family of paths in terms of the eigenvalue support of the initial state.

Exponential algorithmic speedup by a quantum walk

- Computer ScienceSTOC '03
- 2003

A black box graph traversal problem that can be solved exponentially faster on a quantum computer than on a classical computer is constructed and it is proved that no classical algorithm can solve the problem in subexponential time.

A complete characterization of pretty good state transfer on paths

- MathematicsQuantum Inf. Comput.
- 2019

We give a complete characterization of pretty good state transfer on paths between any pair of vertices with respect to the quantum walk model determined by the XY-Hamiltonian. If $n$ is the length…

Almost perfect state transfer in quantum spin chains

- Physics
- 2012

The natural notion of almost perfect state transfer (APST) is examined. It is applied to the modelling of efficient quantum wires with the help of $XX$ spin chains. It is shown that APST occurs in…