25 research outputs found
Improved Simulation of Stabilizer Circuits
The Gottesman-Knill theorem says that a stabilizer circuit -- that is, a
quantum circuit consisting solely of CNOT, Hadamard, and phase gates -- can be
simulated efficiently on a classical computer. This paper improves that theorem
in several directions. First, by removing the need for Gaussian elimination, we
make the simulation algorithm much faster at the cost of a factor-2 increase in
the number of bits needed to represent a state. We have implemented the
improved algorithm in a freely-available program called CHP
(CNOT-Hadamard-Phase), which can handle thousands of qubits easily. Second, we
show that the problem of simulating stabilizer circuits is complete for the
classical complexity class ParityL, which means that stabilizer circuits are
probably not even universal for classical computation. Third, we give efficient
algorithms for computing the inner product between two stabilizer states,
putting any n-qubit stabilizer circuit into a "canonical form" that requires at
most O(n^2/log n) gates, and other useful tasks. Fourth, we extend our
simulation algorithm to circuits acting on mixed states, circuits containing a
limited number of non-stabilizer gates, and circuits acting on general
tensor-product initial states but containing only a limited number of
measurements.Comment: 15 pages. Final version with some minor updates and corrections.
Software at http://www.scottaaronson.com/ch
Kinetic pathways of the Nematic-Isotropic phase transition as studied by confocal microscopy on rod-like viruses
We investigate the kinetics of phase separation for a mixture of rodlike
viruses (fd) and polymer (dextran), which effectively constitutes a system of
attractive rods. This dispersion is quenched from a flow-induced fully nematic
state into the region where the nematic and the isotropic phase coexist. We
show experimental evidence that the kinetic pathway depends on the overall
concentration. When the quench is made at high concentrations, the system is
meta-stable and we observe typical nucleation-and-growth. For quenches at low
concentration the system is unstable and the system undergoes a spinodal
decomposition. At intermediate concentrations we see the transition between
both demixing processes, where we locate the spinodal point.Comment: 11 pages, 6 figures, accepted in J. Phys.: Condens. Matter as
symposium paper for the 6th Liquid Matter Conference in Utrech
Synthesis and Optimization of Reversible Circuits - A Survey
Reversible logic circuits have been historically motivated by theoretical
research in low-power electronics as well as practical improvement of
bit-manipulation transforms in cryptography and computer graphics. Recently,
reversible circuits have attracted interest as components of quantum
algorithms, as well as in photonic and nano-computing technologies where some
switching devices offer no signal gain. Research in generating reversible logic
distinguishes between circuit synthesis, post-synthesis optimization, and
technology mapping. In this survey, we review algorithmic paradigms ---
search-based, cycle-based, transformation-based, and BDD-based --- as well as
specific algorithms for reversible synthesis, both exact and heuristic. We
conclude the survey by outlining key open challenges in synthesis of reversible
and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table
Quantum walks: a comprehensive review
Quantum walks, the quantum mechanical counterpart of classical random walks,
is an advanced tool for building quantum algorithms that has been recently
shown to constitute a universal model of quantum computation. Quantum walks is
now a solid field of research of quantum computation full of exciting open
problems for physicists, computer scientists, mathematicians and engineers.
In this paper we review theoretical advances on the foundations of both
discrete- and continuous-time quantum walks, together with the role that
randomness plays in quantum walks, the connections between the mathematical
models of coined discrete quantum walks and continuous quantum walks, the
quantumness of quantum walks, a summary of papers published on discrete quantum
walks and entanglement as well as a succinct review of experimental proposals
and realizations of discrete-time quantum walks. Furthermore, we have reviewed
several algorithms based on both discrete- and continuous-time quantum walks as
well as a most important result: the computational universality of both
continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing
Journa
There is more than one way to turn a spherical cellular monolayer inside out: type B embryo inversion in Volvox globator
Höhn S, Hallmann A. There is more than one way to turn a spherical cellular monolayer inside out: type B embryo inversion in Volvox globator. BMC Biology. 2011;9(1): 89.Background:
Epithelial folding is a common morphogenetic process during the development of multicellular organisms. In metazoans, the biological and biomechanical processes that underlie such three-dimensional (3D) developmental events are usually complex and difficult to investigate. Spheroidal green algae of the genus Volvox are uniquely suited as model systems for studying the basic principles of epithelial folding. Volvox embryos begin life inside out and then must turn their spherical cell monolayer outside in to achieve their adult configuration; this process is called 'inversion.' There are two fundamentally different sequences of inversion processes in Volvocaceae: type A and type B. Type A inversion is well studied, but not much is known about type B inversion. How does the embryo of a typical type B inverter, V. globator, turn itself inside out?
Results:
In this study, we investigated the type B inversion of V. globator embryos and focused on the major movement patterns of the cellular monolayer, cell shape changes and changes in the localization of cytoplasmic bridges (CBs) connecting the cells. Isolated intact, sectioned and fragmented embryos were analyzed throughout the inversion process using light microscopy, confocal laser scanning microscopy, scanning electron microscopy and transmission electron microscopy techniques. We generated 3D models of the identified cell shapes, including the localizations of CBs. We show how concerted cell-shape changes and concerted changes in the position of cells relative to the CB system cause cell layer movements and turn the spherical cell monolayer inside out. The type B inversion of V. globator is compared to the type A inversion in V. carteri.
Conclusions:
Concerted, spatially and temporally coordinated changes in cellular shapes in conjunction with concerted migration of cells relative to the CB system are the causes of type B inversion in V. globator. Despite significant similarities between type A and type B inverters, differences exist in almost all details of the inversion process, suggesting analogous inversion processes that arose through parallel evolution. Based on our results and due to the cellular biomechanical implications of the involved tensile and compressive forces, we developed a global mechanistic scenario that predicts epithelial folding during embryonic inversion in V. globator