Vol.19 No.7&8, June 1, 2019

Switching and partially switching the hypercube while maintaining perfect state transfer (pp0541-0554)
          Steve Kirkland, Sarah Plosker, and Xiaohong Zhang
A graph is said to exhibit perfect state transfer (PST) if one of its corresponding Hamiltonian matrices, which are based on the vertex-edge structure of  the graph, gives rise to PST in a quantum information-theoretic context, namely with respect to inter-qubit interactions of a quantum  system. We perform various perturbations to the hypercube graph---a graph that is known to exhibit PST---to create graphs that maintain many of the same properties of the hypercube, including PST as well as the distance for which PST occurs. We show that the sensitivity with respect to readout time errors remains unaffected for the vertices involved in PST. We give motivation for when these perturbations may be physically desirable or even necessary.

Improving quantum spatial search in two dimensions (pp0555-0574)
          Abhijith J. and Apoorva Patel
The question of whether quantum spatial search in two dimensions can be made optimal has long been an open problem. We report progress towards its resolution by showing that the oracle complexity for target location can be made optimal, by increasing the number of calls to the walk operator that incorporates the graph structure by a logarithmic factor. Our algorithm does not require amplitude amplification. An important ingredient of our algorithm is the implementation of multi-step quantum walks by graph powering, using a coin space of walk-length dependent dimension, which may be of independent interest. Finally, we demonstrate how to implement quantum walks arising from powers of symmetric Markov chains using our methods.

Cohering power and decohering power of Gaussian unitary operations (pp0575-0586)
          Yangyang Wang, Xiaofei Qi, Jinchuan Hou, and Rufen Ma
Having a suitable measure to quantify the coherence of quantum states, a natural task is to evaluate the power of  quantum channels for creating or destroying the coherence of  input quantum states. In the present paper, by introducing the maximal coherent Gaussian states based on the relative entropy measure of coherence, we propose  the (generalized) cohering power and the (generalized) decohering power of Gaussian unitary operations for continuous-variable systems. Some basic properties are obtained and the cohering power and decohering power of two special kinds of Gaussian unitary operations are calculated.

Eavesdropping on quantum secret sharing protocols based on ring topology (pp0587-0600)
          Dong Jiang, Yongkai Yang, Qisheng Guang, Chaohui Gao, and Lijun Chen
Quantum secret sharing (QSS) is the process of splitting a secret message into multiple parts such that no subset of parts is sufficient to reconstruct the secret message, but the entire set is. Ever since the first protocol was proposed, QSS has attracted intensive study, and many protocols have been proposed and implemented over recent years. However, we discover that several ring-topology based QSS protocols cannot resist Trojan-horse attacks. In this paper, we first give a modified Trojan-horse attack strategy and show that the eavesdropper can obtain any player's private data and the dealer's secret message without leaving any trace. Then we show that existing defense strategies cannot resist our attack. To defeat such attacks, we design a defense strategy based on quantum memory and evaluate its performance. The evaluation results indicate that the eavesdropper's attack significantly increases the quantum bit error rate and can thus be detected.

A complete characterization of pretty good state transfer on paths (pp0601-0608)
          Christopher M. van Bommel
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 of the path, and the vertices are indexed by the positive integers from 1 to $n$, with adjacent vertices having consecutive indices, then the necessary and sufficient conditions for pretty good state transfer between vertices $a$ and $b$ are that (a) $a + b = n + 1$, (b) $n + 1$ has at most one positive odd non-trivial divisor, and (c) if $n = 2^t r - 1$, for $r$ odd and $r \neq 1$, then $a$ is a multiple of $2^{t - 1}$.

Quantum speedup of training radial basis function networks (pp0609-0625)
          Changpeng Shao
Radial basis function (RBF) network is a simple but useful neural network model that contains wide applications in machine learning. The training of an RBF network reduces to solve a linear system, which is time consuming classically. Based on HHL algorithm, we propose two quantum algorithms to train RBF networks. To apply the HHL algorithm, we choose using the Hamiltonian simulation algorithm proposed in [P. Rebentrost, A. Steffens, I. Marvian and S. Lloyd, Phys. Rev. A 97, 012327, 2018]. However, to use this result, an oracle to query the entries of the matrix of the network should be constructed. We apply the amplitude estimation technique to build this oracle. The final results indicate that if the centers of the RBF network are the training samples, then the quantum computer achieves exponential speedup at the number and the dimension of training samples over the classical computer; if the centers are determined by the $K$-means algorithm, then the quantum computer achieves quadratic speedup at the number of samples and exponential speedup at the dimension of samples.

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