9,658 research outputs found
Exact stabilization of entangled states in finite time by dissipative quantum circuits
Open quantum systems evolving according to discrete-time dynamics are
capable, unlike continuous-time counterparts, to converge to a stable
equilibrium in finite time with zero error. We consider dissipative quantum
circuits consisting of sequences of quantum channels subject to specified
quasi-locality constraints, and determine conditions under which stabilization
of a pure multipartite entangled state of interest may be exactly achieved in
finite time. Special emphasis is devoted to characterizing scenarios where
finite-time stabilization may be achieved robustly with respect to the order of
the applied quantum maps, as suitable for unsupervised control architectures.
We show that if a decomposition of the physical Hilbert space into virtual
subsystems is found, which is compatible with the locality constraint and
relative to which the target state factorizes, then robust stabilization may be
achieved by independently cooling each component. We further show that if the
same condition holds for a scalable class of pure states, a continuous-time
quasi-local Markov semigroup ensuring rapid mixing can be obtained. Somewhat
surprisingly, we find that the commutativity of the canonical parent
Hamiltonian one may associate to the target state does not directly relate to
its finite-time stabilizability properties, although in all cases where we can
guarantee robust stabilization, a (possibly non-canonical) commuting parent
Hamiltonian may be found. Beside graph states, quantum states amenable to
finite-time robust stabilization include a class of universal resource states
displaying two-dimensional symmetry-protected topological order, along with
tensor network states obtained by generalizing a construction due to Bravyi and
Vyalyi. Extensions to representative classes of mixed graph-product and thermal
states are also discussed.Comment: 20 + 9 pages, 9 figure
General fixed points of quasi-local frustration-free quantum semigroups: from invariance to stabilization
We investigate under which conditions a mixed state on a finite-dimensional
multipartite quantum system may be the unique, globally stable fixed point of
frustration-free semigroup dynamics subject to specified quasi-locality
constraints. Our central result is a linear-algebraic necessary and sufficient
condition for a generic (full-rank) target state to be frustration-free
quasi-locally stabilizable, along with an explicit procedure for constructing
Markovian dynamics that achieve stabilization. If the target state is not
full-rank, we establish sufficiency under an additional condition, which is
naturally motivated by consistency with pure-state stabilization results yet
provably not necessary in general. Several applications are discussed, of
relevance to both dissipative quantum engineering and information processing,
and non-equilibrium quantum statistical mechanics. In particular, we show that
a large class of graph product states (including arbitrary thermal graph
states) as well as Gibbs states of commuting Hamiltonians are frustration-free
stabilizable relative to natural quasi-locality constraints. Likewise, we
provide explicit examples of non-commuting Gibbs states and non-trivially
entangled mixed states that are stabilizable despite the lack of an underlying
commuting structure, albeit scalability to arbitrary system size remains in
this case an open question.Comment: 44 pages, main results are improved, several proofs are more
streamlined, application section is refine
Distributed finite-time stabilization of entangled quantum states on tree-like hypergraphs
Preparation of pure states on networks of quantum systems by controlled
dissipative dynamics offers important advantages with respect to circuit-based
schemes. Unlike in continuous-time scenarios, when discrete-time dynamics are
considered, dead-beat stabilization becomes possible in principle. Here, we
focus on pure states that can be stabilized by distributed, unsupervised
dynamics in finite time on a network of quantum systems subject to realistic
quasi-locality constraints. In particular, we define a class of quasi-locality
notions, that we name "tree-like hypergraphs," and show that the states that
are robustly stabilizable in finite time are then unique ground states of a
frustration-free, commuting quasi-local Hamiltonian. A structural
characterization of such states is also provided, building on a simple yet
relevant example.Comment: 6 pages, 3 figure
The implementation and validation of improved landsurface hydrology in an atmospheric general circulation model
Landsurface hydrological parameterizations are implemented in the NASA Goddard Institute for Space Studies (GISS) General Circulation Model (GCM). These parameterizations are: (1) runoff and evapotranspiration functions that include the effects of subgrid scale spatial variability and use physically based equations of hydrologic flux at the soil surface, and (2) a realistic soil moisture diffusion scheme for the movement of water in the soil column. A one dimensional climate model with a complete hydrologic cycle is used to screen the basic sensitivities of the hydrological parameterizations before implementation into the full three dimensional GCM. Results of the final simulation with the GISS GCM and the new landsurface hydrology indicate that the runoff rate, especially in the tropics is significantly improved. As a result, the remaining components of the heat and moisture balance show comparable improvements when compared to observations. The validation of model results is carried from the large global (ocean and landsurface) scale, to the zonal, continental, and finally the finer river basin scales
Generic pure quantum states as steady states of quasi-local dissipative dynamics
We investigate whether a generic multipartite pure state can be the unique
asymptotic steady state of locality-constrained purely dissipative Markovian
dynamics. In the simplest tripartite setting, we show that the problem is
equivalent to characterizing the solution space of a set of linear equations
and establish that the set of pure states obeying the above property has either
measure zero or measure one, solely depending on the subsystems' dimension. A
complete analytical characterization is given when the central subsystem is a
qubit. In the N-partite case, we provide conditions on the subsystems' size and
the nature of the locality constraint, under which random pure states cannot be
quasi-locally stabilized generically. Beside allowing for the possibility to
approximately stabilize entangled pure states that cannot be exact steady
states in settings where stabilizability is generic, our results offer insights
into the extent to which random pure states may arise as unique ground states
of frustration free parent Hamiltonians. We further argue that, to high
probability, pure quantum states sampled from a t-design enjoy the same
stabilizability properties of Haar-random ones as long as suitable dimension
constraints are obeyed and t is sufficiently large. Lastly, we demonstrate a
connection between the tasks of quasi-local state stabilization and unique
state reconstruction from local tomographic information, and provide a
constructive procedure for determining a generic N-partite pure state based
only on knowledge of the support of any two of the reduced density matrices of
about half the parties, improving over existing results.Comment: 36 pages (including appendix), 2 figure
A Model Connecting Galaxy Masses, Star Formation Rates, and Dust Temperatures Across Cosmic Time
We investigate the evolution of dust content in galaxies from redshifts z=0
to z=9.5. Using empirically motivated prescriptions, we model galactic-scale
properties -- including halo mass, stellar mass, star formation rate, gas mass,
and metallicity -- to make predictions for the galactic evolution of dust mass
and dust temperature in main sequence galaxies. Our simple analytic model,
which predicts that galaxies in the early Universe had greater quantities of
dust than their low-redshift counterparts, does a good job at reproducing
observed trends between galaxy dust and stellar mass out to z~6. We find that
for fixed galaxy stellar mass, the dust temperature increases from z=0 to z=6.
Our model forecasts a population of low-mass, high-redshift galaxies with
interstellar dust as hot as, or hotter than, their more massive counterparts;
but this prediction needs to be constrained by observations. Finally, we make
predictions for observing 1.1-mm flux density arising from interstellar dust
emission with the Atacama Large Millimeter Array.Comment: Accepted for publication in Ap
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