QIC Abstracts

 Vol.18 No.3&4, March 1, 2018

Research Articles:

Properties of quantum stochastic walks from the asymptotic scaling exponent (pp0181-0197)
          
Krzysztof Domino, Adam Glos, Mateusz Ostaszewski, Lukasz Pawela, and Przemyslaw Sadowski
This work focuses on the study of quantum stochastic walks, which are a generalization of coherent, \ie{} unitary quantum walks. Our main goal is to present a measure of a coherence of the walk. To this end, we utilize the asymptotic scaling exponent of the second moment of the walk \ie{} of the mean squared distance covered by a walk. As the quantum stochastic walk model encompasses both classical random walks and quantum walks, we are interested how the continuous change from one regime to the other influences the asymptotic scaling exponent. Moreover this model allows for behavior which is not found in any of the previously mentioned model -- a model with global dissipation. We derive the probability distribution for the walker, and determine the asymptotic scaling exponent analytically, showing that ballistic regime of the walk is maintained even at large dissipation strength.

Adversary lower bounds for the collision and the set equality problems (pp0198-0222)
          
Aleksandrs Belovs and Ansis Rosmanis
We prove tight $\Omega(n^{1/3})$ lower bounds on the quantum query complexity of the \cpp and the \sep problems, provided that the size of the alphabet is large enough. We do this using the negative-weight adversary method. Thus, we reprove the result by Aaronson and Shi, as well as a more recent development by Zhandry.

Constructing new q-ary quantum MDS codes with distances bigger than q/2 from generator matrices (pp0223-0230)
          
Xianmang He
The construction of quantum error-correcting codes has been an active field of quantum information theory since the publication of \cite{Shor1995Scheme,Steane1998Enlargement,Laflamme1996Perfect}. It is becoming more and more difficult to construct some new  quantum MDS codes with large minimum distance. In this paper, based on the approach developed in the paper \cite{NewHeMDS2016}, we construct several new classes of quantum MDS codes. The quantum MDS codes exhibited here have not been constructed before and the distance parameters are bigger than $\frac{q}{2}$.

Quantum information transmission through a qubit chain with quasi-local dissipation (pp0231-0246)
          
Roya Radgohar, Laleh Memarzadeh, and Stefano Mancini
We study quantum information transmission in a Heisenberg-XY chain where qubits are affected by quasi-local environment action and compare it with the case of local action of the environment. We find that for open boundary conditions the former situation always improves quantum state transfer process, especially for short chains. In contrast, for closed boundary conditions quasi-local environment results advantageous in the strong noise regime. When the noise strength is comparable with the XY interaction strength, the state transfer fidelity through chain of odd/even number of qubits in presence of quasi-local environment results smaller/greater than that in presence of local environment.

Rapid and robust generation of Einstein-–Podolsky–-Rosen pairs with spin chains (pp0247-0264)
          
Kieran N. Wilkinson, Marta P. Estarellas, Timothy P. Spiller, and Irene D'Amico
We investigate the ability of dimerized spin chains with defects to generate EPR pairs to very high fidelity through their natural dynamics. We propose two protocols based on different initializations of the system, which yield the same maximally entangled Bell state after a characteristic time. This entangling time can be varied through engineering the weak/strong couplings' ratio of the chain, with larger values giving rise to an exponentially faster quantum entangling operation. We demonstrate that there is a set of characteristic values of the coupling, for which the entanglement generated remains extremely high. We investigate the robustness of both protocols to diagonal and off-diagonal disorder. Our results demonstrate extremely strong robustness to both perturbation types, up to strength of 50\% of the weak coupling. Robustness to disorder can be further enhanced by increasing the coupling ratio. The combination of these properties makes the use of our proposed device suitable for the rapid and robust generation of Bell states in quantum information processing applications.

Multi-qubit non-Markovian dynamics in photonic crystal with infinite cavity-array structure (pp0265-0282)
          
Heng-Na Xiong, Yi Li, Yixiao Huang, and Zichun Le
We study the exact non-Markovian dynamics of a multi-qubit system coupled to a photonic-crystal waveguide with infinite cavity-array structure. A general solution of the evolution state of the system is solved for a general initial state in the single-excitation subspace. With this solution, we find that the non-Markovian effect of the environment on the system could be enhanced not only by increasing the system-environment coupling strength but also by adding the qubit number in the system. The explicit non-Markovian dynamics are discussed under two initial states to see the non-Markovian effect on entanglement preservation and entanglement generation. We find that the non-Markovian effect tends to preserve the system in its initial state.

Space-efficient classical and quantum algorithms for the shortest vector problem (pp0283-0305)
          
Yanlin Chen, Kai-Min Chung, and Ching-Yi Lai
A lattice is the integer span of some linearly independent vectors. Lattice problems have many significant applications in coding theory and cryptographic systems for their conjectured hardness. The Shortest Vector Problem (SVP), which asks to find a shortest nonzero vector in a lattice, is one of the well-known problems that are believed to be hard to solve, even with a quantum computer.  In this paper we propose  space-efficient  classical  and  quantum algorithms for solving SVP. Currently the  best time-efficient algorithm for solving SVP takes $2^{n+o(n)}$ time and $2^{n+o(n)}$ space. Our classical algorithm takes $2^{2.05n+o(n)}$ time to solve SVP and it requires only $2^{0.5n+o(n)}$ space. We then adapt our classical algorithm to a quantum version, which can solve SVP in time $2^{1.2553n+o(n)}$  with $2^{0.5n+o(n)}$ classical space and only poly$(n)$ qubits.

Hyperbolic quantum color codes (pp0306-0318)
          
Waldir Silva Soares Jr. and Eduardo Brandani da Silva
Current work presents a new approach to quantum color codes on compact surfaces with genus $g \geq 2$ using the identification of these surfaces with hyperbolic polygons and  hyperbolic tessellations. We show that this method may give rise to color codes with a very good parameters and we present tables with several examples of these codes whose parameters had not been shown before. We also present a family of codes with minimum distance $d=4$ and the encoding rate asymptotically going to 1 while $n \rightarrow \infty$.

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