Vol.18 No.13&14, November 1, 2018

Non-local universal gates generated within a resonant magnetic cavity (pp1081-1094)
          Francisco Delgado
Quantum Information is a quantum resource being advised as a useful tool to set up information processing. Despite physical components being considered are normally two-level systems, still the combination of some of them together with their entangling interactions (another key property in the quantum information processing) become in a complex dynamics needing be addressed and modeled under precise control to set programmed quantum processing tasks. Universal quantum gates are simple controlled evolutions resembling some classical computation gates. Despite their simple forms, not always become easy fit the quantum evolution to them. $SU(2)$ decomposition is a mechanism to reduce the dynamics on $SU(2)$ operations in composed quantum processing systems. It lets an easier control of evolution into the structure required by those gates by the adequate election of the basis for the computation grammar. In this arena, $SU(2)$ decomposition has been studied under piecewise magnetic field pulses. Despite, it is completely applicable for time-dependent pulses, which are more affordable technologically, could be continuous and then possibly free of resonant effects. In this work, we combine the $SU(2)$ reduction with linear and quadratic numerical approaches in the solving of time-dependent Schr\"odinger equation to model and to solve the controlled dynamics for two-qubits, the basic block for composite quantum systems being analyzed under the $SU(2)$ reduction. A comparative benchmark of both approaches is presented together with some useful outcomes for the dynamics in the context of quantum information processing operations.

A method for synthesis and optimization for linear nearest neighbor quantum circuits by parallel processing (pp1095-1114)
          Zongyuan Zhang, Zhijin Guan, Hong Zhang, Haiying Ma, and Weiping Ding
In order to realize the linear nearest neighbor{(LNN)} of the quantum circuits and reduce the quantum cost of linear reversible quantum circuits, a method for synthesizing and optimizing linear reversible quantum circuits based on matrix multiplication of the structure of the quantum circuit is proposed. This method shows the matrix representation of linear quantum circuits by multiplying matrices of different parts of the whole circuit. The LNN realization by adding the SWAP gates is proposed and the equivalence of two ways of adding the SWAP gates is proved. The elimination rules of the SWAP gates between two overlapped adjacent quantum gates in different cases are proposed, which reduce the quantum cost of quantum circuits after realizing the LNN architecture. We propose an algorithm based on parallel processing in order to effectively reduce the time consumption for large-scale quantum circuits. Experiments show that the quantum cost can be improved by 34.31\% on average and the speed-up ratio of the GPU-based algorithm can reach 4 times compared with the CPU-based algorithm. The average time optimization ratio of the benchmark large-scale circuits in RevLib processed by the parallel algorithm is {95.57\%} comparing with the serial algorithm.

Super-activating quantum memory with entanglement (pp1115-1124)
          Ji Guan, Yuan Feng, and Mingsheng Ying
Noiseless subsystems were proved to be an efficient and faithful approach to preserve fragile information against decoherence in quantum information processing and quantum computation. They were employed to design a general (hybrid) quantum memory cell model that can store both quantum and classical information. In this paper, we find an interesting new phenomenon that the purely classical memory cell can be super-activated to preserve quantum states, whereas the null memory cell can only be super-activated to encode classical information. Furthermore, necessary and sufficient conditions for this phenomenon are discovered so that the super-activation can be easily checked by examining certain eigenvalues of the quantum memory cell without computing the noiseless subsystems explicitly. In particular, it is found that entangled and separable stationary states are responsible for the super-activation of storing quantum and classical information, respectively.

Proposal for dimensionality testing in QPQ (pp1125-1142)
          Arpita Maitra, Bibhas Adhikari, and Satyabrata Adhikari
Recently, dimensionality testing of a quantum state has received extensive attention (Ac{\'i}n et al. Phys. Rev. Letts. 2006, Scarani et al. Phys. Rev. Letts. 2006). Security proofs of existing quantum information processing protocols rely on the assumption about the dimension of quantum states in which logical bits are encoded. However, removing such assumption may cause security loophole. In the present paper, we show that this is indeed the case. We choose two players' quantum private query protocol by Yang et al. (Quant. Inf. Process. 2014) as an example and show how one player can gain an unfair advantage by changing the dimension of subsystem of a shared quantum system. To resist such attack we propose dimensionality testing in a different way. Our proposal is based on CHSH like game. As we exploit CHSH like game, it can be used to test if the states are product states for which the protocol becomes completely vulnerable.

A quantum primality test with order finding (pp1143-1151)
          Alvaro Donis-Vela and Juan Carlos Garcia-Escartin
Determining whether a given integer is prime or composite is a basic task in number theory. We present a primality test based on quantum order finding and the converse of Fermat's theorem. For an integer $N$, the test tries to find an element of the multiplicative group of integers modulo $N$ with order $N-1$. If one is found, the number is known to be prime. During the test, we can also show most of the times $N$ is composite  with certainty (and a witness) or, after $\log\log  N$ unsuccessful attempts to find an element of order $N-1$, declare it composite with high probability. The algorithm requires $O((\log n)^2 n^3)$ operations for a number $N$ with $n$ bits, which can be reduced to $O(\log\log n (\log n)^3 n^2)$ operations in the asymptotic limit if we use fast multiplication.

New bounds of Mutually unbiased maximally entangled bases in C^dxC^(kd) (pp1152-1164)
          Xiaoya Cheng and Yun Shang
Mutually unbiased bases which is also maximally entangled bases is called mutually unbiased maximally entangled bases (MUMEBs). We study the construction of MUMEBs in bipartite system. In detail, we construct $2(p^a-1)$ MUMEBs in $\cd$ by properties of Guss sums for arbitrary odd $d$. It improves the known lower bound $p^a-1$ for odd $d$. Certainly, it also generalizes the lower bound $2(p^a-1)$ for $d$ being a single prime power. Furthermore, we construct MUMEBs in $\ckd$ for general $k\geq 2$ and odd $d$. We get the similar lower bounds as $k,b$ are both single prime powers. Particularly, when $k$ is a square number, by using mutually orthogonal Latin squares, we can construct more MUMEBs in $\ckd$, and obtain greater lower bounds than reducing the problem into prime power dimension in some cases.

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