2,317 research outputs found
Quantum Isomorphic Simulation
A new type of quantum simulator is proposed which can simulate any quantum
many-body system in an isomorphic manner. It can actually synthesize a
duplicate of the system to be simulated. The isomorphic simulation has the
great advantage that the inevitable coupling of the simulator to the
environment can be fully exploited in simulating thermodynamic processes.Comment: 3 page
Single Molecule Magnetic Resonance and Quantum Computation
It is proposed that nuclear (or electron) spins in a trapped molecule would
be well isolated from the environment and the state of each spin can be
measured by means of mechanical detection of magnetic resonance. Therefore
molecular traps make an entirely new approach possible for spin-resonance
quantum computation which can be conveniently scaled up. In the context of
magnetic resonance spectroscopy, a molecular trap promises the ultimate
sensitivity for single spin detection and an unprecedented spectral resolution
as well
Static Quantum Computation
Tailoring many-body interactions among a proper quantum system endows it with
computing ability by means of static quantum computation in the sense that some
of the physical degrees of freedom can be used to store binary information and
the corresponding binary variables satisfy some given logic relations if and
only if the system is in the ground state. Two theorems are proved showing that
the universal static quantum computer can encode the solutions for any P and NP
problem into its ground state using only polynomial number (in the problem
input size) of logic gates. The second step is to read out the solutions by
relaxing the system. The time complexity is relevant when one tries to read out
the solution by relaxing the system, therefore our model of static quantum
computation provides a new connection between the computational complexity and
the dynamics of a complex system.Comment: 8 pages, 3 ps figure
Tailoring Many-Body Interactions to Solve Hard Combinatorial Problems
A quantum machine consisting of interacting linear clusters of atoms is
proposed for the 3SAT problem. Each cluster with two relevant states of
collective motion can be used to register a Boolean variable. Given any 3SAT
Boolean formula the interactions among the clusters can be so tailored that the
ground state(s) (possibly degenerate) of the whole system encodes the
satisfying truth assignment(s) for it. This relates the 3SAT problem to the
dynamics of the properly designed glass system.Comment: Latex 7 pages, 3 ps figure
Emergence of grid-like representations by training recurrent neural networks to perform spatial localization
Decades of research on the neural code underlying spatial navigation have
revealed a diverse set of neural response properties. The Entorhinal Cortex
(EC) of the mammalian brain contains a rich set of spatial correlates,
including grid cells which encode space using tessellating patterns. However,
the mechanisms and functional significance of these spatial representations
remain largely mysterious. As a new way to understand these neural
representations, we trained recurrent neural networks (RNNs) to perform
navigation tasks in 2D arenas based on velocity inputs. Surprisingly, we find
that grid-like spatial response patterns emerge in trained networks, along with
units that exhibit other spatial correlates, including border cells and
band-like cells. All these different functional types of neurons have been
observed experimentally. The order of the emergence of grid-like and border
cells is also consistent with observations from developmental studies.
Together, our results suggest that grid cells, border cells and others as
observed in EC may be a natural solution for representing space efficiently
given the predominant recurrent connections in the neural circuits
Trapping Quantum Coherence in Local Energy Minima
Clusters of solid-state quantum devices have long-living metastable states of
local energy minima which may be used to store quantum information. The low to
vanishing rate of dissipation fulfils the prerequisite to maintain quantum
coherence. Then physical symmetrization of the devices could minimize the
couplings of the clusters to environmental degrees of freedom so to reduce the
rate of decoherence. Combined with various other error correction mechanisms
and methods, such designs and optimizations could render solid-state devices
useful for quantum information processing, which have the advantages of
flexibility in state manipulation and system scaling.Comment: Latex fil
NMR Quantum Automata in Doped Crystals
In a lattice of nuclear spins with ABCABCABC... type periodic
structure embedded in a single-crystal solid, each ABC-unit can be used to
store quantum information and the information can be moved around via some
cellular shifting mechanism. Impurity doping marks a special site
D which together with the local spin lattice constitute a
quantum automaton where the D site serves as the input/output port and
universal quantum logic is done through two-body interactions between two spins
at D and a nearby site. The novel NMR quantum computer can be easily scaled up
and may work at low temperature to overcome the problem of exponential decay in
signal-to-noise ratio in room temperature NMR.Comment: Latex file, one eps figur
Superconductive Static Quantum Logic
Superconducting rings with exactly magnetic flux threading are
analogous of Ising spins having two degenerate states which can be used to
store binary information. When brought close these rings interact by means of
magnetic coupling. If the interactions are properly tailored, a system of such
superconducting rings can accomplish static quantum logic in the sense that the
states of the rings interpreted as Boolean variables satisfy the desired logic
relations when and only when the whole system is in the ground state. Such
static logic is essential to carry out the static quantum computation [1,2].Comment: Latex 4 pages, 4 ps figure
Dynamic self-organized error-correction of grid cells by border cells
Grid cells in the entorhinal cortex are believed to establish their regular,
spatially correlated firing patterns by path integration of the animal's
motion. Mechanisms for path integration, e.g. in attractor network models,
predict stochastic drift of grid responses, which is not observed
experimentally. We demonstrate a biologically plausible mechanism of dynamic
self-organization by which border cells, which fire at environmental
boundaries, can correct such drift in grid cells. In our model,
experience-dependent Hebbian plasticity during exploration allows border cells
to learn connectivity to grid cells. Border cells in this learned network reset
the phase of drifting grids. This error-correction mechanism is robust to
environmental shape and complexity, including enclosures with interior
barriers, and makes distinctive predictions for environmental deformation
experiments. Our work demonstrates how diverse cell types in the entorhinal
cortex could interact dynamically and adaptively to achieve robust path
integration.Comment: 6 pages, 4 figure
Learning identifiable and interpretable latent models of high-dimensional neural activity using pi-VAE
The ability to record activities from hundreds of neurons simultaneously in
the brain has placed an increasing demand for developing appropriate
statistical techniques to analyze such data. Recently, deep generative models
have been proposed to fit neural population responses. While these methods are
flexible and expressive, the downside is that they can be difficult to
interpret and identify. To address this problem, we propose a method that
integrates key ingredients from latent models and traditional neural encoding
models. Our method, pi-VAE, is inspired by recent progress on identifiable
variational auto-encoder, which we adapt to make appropriate for neuroscience
applications. Specifically, we propose to construct latent variable models of
neural activity while simultaneously modeling the relation between the latent
and task variables (non-neural variables, e.g. sensory, motor, and other
externally observable states). The incorporation of task variables results in
models that are not only more constrained, but also show qualitative
improvements in interpretability and identifiability. We validate pi-VAE using
synthetic data, and apply it to analyze neurophysiological datasets from rat
hippocampus and macaque motor cortex. We demonstrate that pi-VAE not only fits
the data better, but also provides unexpected novel insights into the structure
of the neural codes
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