Deutsch, Toffoli, and CNOT Gates via Rydberg Blockade of Neutral Atoms

Universal quantum gates and quantum error correction~(QEC) lie in the heart of quantum information science. Large-scale quantum computing depends on a universal set of quantum gates, in which some gates may be easily carried out, while others are hard with a certain physical system. There is a unique three-qubit quantum gate called the Deutsch gate~[$\mathbb{D}(\theta)$], from which alone a circuit can be constructed so that any feasible quantum computing is attainable. As far as we know, however, $\mathbb{D}(\theta)$ has not been demonstrated. Here we design an easily realizable $\mathbb{D}(\theta)$ by using Rydberg blockade of neutral atoms, where $\theta$ can be tuned to any value in $[0,\pi]$ by adjusting the strengths of external control fields. Using similar protocols, we further show that both the Toffoli and CNOT gates can be achieved with only three laser pulses. The Toffoli gate, being universal for classical reversible computing, is also useful for QEC that plays an important role in quantum communication and fault-tolerant quantum computation. The possibility and briefness to realize these gates shed new light on the study of quantum information with neutral atoms.Comment: Letter & Editors' Suggestion; Including 8 pages (with Supplemental Material), 5 figure

Universal Barenco quantum gates via a tunable non-collinear interaction

The Barenco gate~($\mathbb{B}$) is a type of two-qubit quantum gate based on which alone universal quantum computation can be achieved. Each $\mathbb{B}$ is characterized by three angles ($\alpha,\theta$, and $\phi$) though it works in a two-qubit Hilbert space. Here we design $\mathbb{B}$ via a non-collinear interaction $V|r_1r_2\rangle\langle r_1r_3|+$H.c., where $|r_i\rangle$ is a state that can be excited from a qubit state and $V$ is adjustable. We present two protocols of $\mathbb{B}$. The first~(second) protocol consists of two~(six) pulses and one~(two) wait period(s), where the former causes rotations between the qubit states and excited states, and the latter induces gate transformation via the non-collinear interaction. In the first protocol, the variable $\phi$ can be tuned by varying phases of external controls, and the other two variables $\alpha$ and $\theta$, tunable via adjusting the wait duration, have a linear dependence upon each other. Meanwhile, the first protocol can give rise to the CNOT and Controlled-Y gates. In the second protocol, $\alpha,\theta$, and $\phi$ can be varied by changing the interaction amplitudes and wait durations, and the latter two are dependent on $\alpha$ non-linearly. Both protocols can also lead to another universal gate when $\{\alpha,\phi\}=\{1/4,1/2\}\pi$ with appropriate parameters. Implementation of these universal gates is analyzed based on the van der Waals interaction of neutral Rydberg atoms.Comment: 11 pages, 6 figure

Acute Triangulations of the Cuboctahedral Surface

In this paper we prove that the surface of the cuboctahedron can be triangulated into 8 non-obtuse triangles and 12 acute triangles. Furthermore, we show that both bounds are the best possible.Comment: 16 pages, 8 figures, presented on CGGA201

RMB Exchange Rate and Local Currency Price Stability : The Case of China and ASEAN+3

This paper uses Chinese and ASEAN+3 industry panel data to measure variations in mark-up adjustment behaviour that is associated with the exchange rate changes across export destination markets. Exports that are substitutes for local products exhibit a high degree of mark-up adjustment, which has the effect of stabilising prices in export destination countries. There is evidence of this behaviour in certain export products to China where the Chinese Government provides subsidies. When markup adjustment behaviour exists, the short-term dynamic mark-up adjustments are consistent with the long-term pricing behaviour in source countries.RMB Exchange Rate, Local Currency Price Stability, China, ASEAN, ASEAN+3

Comment on "Next-to-leading order forward hadron production in the small-x regime: rapidity factorization" arXiv:1403.5221 by Kang et al

In a recent paper (arXiv:1403.5221), Kang et al.proposed the so-called "rapidity factorization" for the single inclusive forward hadron production in pA collisions. We point out that the leading small-x logarithm was mis-identified in this paper, and hence the newly added next-to-leading order correction term is unjustified and should be absent in view of the small-x factorization.Comment: 3 page

Pre-management of Disentanglement

We define threshold disentanglement (TD) as the level above which entanglement must be maintained for later use and calculate the values of quantum system parameters at $t=0$ that will ensure that the threshold is not crossed in a specified time. An important issue is the possibility of non-smooth, typically non-exponential, decay of entanglement into the state of complete disentanglement (CD). Given a specified operation time $\tau$, we determine phase diagrams showing entanglement preservation during the evolution of a generic two-qubit mixed state as a function of selected initial parameters such as concurrence and excitation probabilities. In other words, disentanglement can be pre-managed through these parameters. Three common relaxation processes - amplitude, phase and depolarization - are considered.Comment: 14 page