Exponential Quantum Speed-ups are Generic

A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any sufficiently long quantum circuit one can construct a black-box problem which is solved by the circuit with a constant number of quantum queries, but which requires exponentially many classical queries, even if the classical machine has the ability to postselect. We prove the result in two steps. In the first, we show that almost any element of an approximate unitary 3-design is useful to solve a certain black-box problem efficiently. The problem is based on a recent oracle construction of Aaronson and gives an exponential separation between quantum and classical bounded-error with postselection query complexities. In the second step, which may be of independent interest, we prove that linear-sized random quantum circuits give an approximate unitary 3-design. The key ingredient in the proof is a technique from quantum many-body theory to lower bound the spectral gap of local quantum Hamiltonians.Comment: 24 pages. v2 minor correction

Study of the Coleman - de Luccia instanton of the second order

We study the second order Coleman - de Luccia instanton which appears as the curvature of the effective potential reaches a sufficiently large value. We show how one can find the approximative formula for this instanton by perturbative expansion in the case when the second derivative of the effective potential divided by the Hubble parameter squared is close to -10, and we perform a numerical study of this instanton in the case of quasi-exponential potential.Comment: three pages, one figur

Quark and lepton masses and mixing in SO(10) with a GUT-scale vector matter

We explore in detail the effective matter fermion mass sum-rules in a class of renormalizable SUSY SO(10) grand unified models where the quark and lepton mass and mixing patterns originate from non-decoupling effects of an extra vector matter multiplet living around the unification scale. If the renormalizable type-II contribution governed by the SU(2)_L-triplet in 54_H dominates the seesaw formula, we obtain an interesting correlation between the maximality of the atmospheric neutrino mixing and the proximity of y_s/y_b to V_cb in the quark sector.Comment: 13 pages, 1 figure, 2 tables; v2: major update, references adde

Efficient Quantum Pseudorandomness

Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum systems, but in many case pseudorandom operations can emulate certain properties of truly random ones. Indeed in the classical realm there is by now a well-developed theory of such pseudorandom operations. However the construction of such objects turns out to be much harder in the quantum case. Here we show that random quantum circuits are a powerful source of quantum pseudorandomness. This gives the for the first time a polynomialtime construction of quantum unitary designs, which can replace fully random operations in most applications, and shows that generic quantum dynamics cannot be distinguished from truly random processes. We discuss applications of our result to quantum information science, cryptography and to understanding self-equilibration of closed quantum dynamics.Comment: 6 pages, 1 figure. Short version of http://arxiv.org/abs/1208.069

Investigation of mediastinitis due to coagulase-negative staphylococci after cardiothoracic surgery.

Six cases of coagulase-negative staphylococcal mediastinitis were identified in the latter half of 1999. A new preoperative cleansing solution was suspected by hospital staff to be a factor in the outbreak. We evaluated this possible risk factor along with other known and suspected surgical site infection risk factors in this case-control study

Synchronization of Micromechanical Oscillators Using Light

Synchronization, the emergence of spontaneous order in coupled systems, is of fundamental importance in both physical and biological systems. We demonstrate the synchronization of two dissimilar silicon nitride micromechanical oscillators, that are spaced apart by a few hundred nanometers and are coupled through optical radiation field. The tunability of the optical coupling between the oscillators enables one to externally control the dynamics and switch between coupled and individual oscillation states. These results pave a path towards reconfigurable massive synchronized oscillator networks

Will Short Peptides Revolutionize Chelation Therapy?

It will soon be twenty years since the last chelating agent was clinically approved to be used against toxic metals. Even though metal poisoning has been known to humankind for centuries, only about a dozen compounds, all of which are small molecules, compose the pharmaceutical toolbox to expel intrinsically toxic or essential but misregulated metals. These compounds widely suffer from various drawbacks, most critically, poor metal selectivity. Can medicinal inorganic chemistry offer modern solutions to these old challenges? In this perspective, the opportunities and advantages of harnessing short peptides for chelation therapy are described. While broadly aiming to address various toxic metals, achievements in targeting lead (Pb) with peptides reveal the unexplored potential hidden in this chemical space and raise the possibility that peptides may reform chelation therapy.       &nbsp