243 research outputs found
Majorization in Quantum Adiabatic Algorithms
The majorization theory has been applied to analyze the mathematical
structure of quantum algorithms. An empirical conclusion by numerical
simulations obtained in the previous literature indicates that step-by-step
majorization seems to appear universally in quantum adiabatic algorithms. In
this paper, a rigorous analysis of the majorization arrow in a special class of
quantum adiabatic algorithms is carried out. In particular, we prove that for
any adiabatic algorithm of this class, step-by-step majorization of the ground
state holds exactly. For the actual state, we show that step-by-step
majorization holds approximately, and furthermore that the longer the running
time of the algorithm, the better the approximation.Comment: 7 pages;1 figur
The LU-LC conjecture is false
The LU-LC conjecture is an important open problem concerning the structure of
entanglement of states described in the stabilizer formalism. It states that
two local unitary equivalent stabilizer states are also local Clifford
equivalent. If this conjecture were true, the local equivalence of stabilizer
states would be extremely easy to characterize. Unfortunately, however, based
on the recent progress made by Gross and Van den Nest, we find that the
conjecture is false.Comment: Added a new part explaining how the counterexamples are foun
Multicell Edge Coverage Enhancement Using Mobile UAV-Relay
Unmanned aerial vehicle (UAV)-assisted communication is a promising technology in future wireless communication networks. UAVs can not only help offload data traffic from ground base stations (GBSs) but also improve the Quality of Service (QoS) of cell-edge users (CEUs). In this article, we consider the enhancement of cell-edge communications through a mobile relay, i.e., UAV, in multicell networks. During each transmission period, GBSs first send data to the UAV, and then the UAV forwards its received data to CEUs according to a certain association strategy. In order to maximize the sum rate of all CEUs, we jointly optimize the UAV mobility management, including trajectory, velocity, and acceleration, and association strategy of CEUs to the UAV, subject to minimum rate requirements of CEUs, mobility constraints of the UAV, and causal buffer constraints in practice. To address the mixed-integer nonconvex problem, we transform it into two convex subproblems by applying tight bounds and relaxations. An iterative algorithm is proposed to solve the two subproblems in an alternating manner. Numerical results show that the proposed algorithm achieves higher rates of CEUs as compared with the existing benchmark schemes
Electroosmotic Flow of Viscoelastic Fluid Through a Constriction Microchannel
Electroosmotic flow (EOF) has been widely used in various biochemical microfluidic applications, many of which use viscoelastic non-Newtonian fluid. This study numerically investigates the EOF of viscoelastic fluid through a 10:1 constriction microfluidic channel connecting two reservoirs on either side. The flow is modelled by the Oldroyd-B (OB) model coupled with the Poisson–Boltzmann model. EOF of polyacrylamide (PAA) solution is studied as a function of the PAA concentration and the applied electric field. In contrast to steady EOF of Newtonian fluid, the EOF of PAA solution becomes unstable when the applied electric field (PAA concentration) exceeds a critical value for a fixed PAA concentration (electric field), and vortices form at the upstream of the constriction. EOF velocity of viscoelastic fluid becomes spatially and temporally dependent, and the velocity at the exit of the constriction microchannel is much higher than that at its entrance, which is in qualitative agreement with experimental observation from the literature. Under the same apparent viscosity, the time-averaged velocity of the viscoelastic fluid is lower than that of the Newtonian fluid
Correlations in excited states of local Hamiltonians
Physical properties of the ground and excited states of a -local
Hamiltonian are largely determined by the -particle reduced density matrices
(-RDMs), or simply the -matrix for fermionic systems---they are at least
enough for the calculation of the ground state and excited state energies.
Moreover, for a non-degenerate ground state of a -local Hamiltonian, even
the state itself is completely determined by its -RDMs, and therefore
contains no genuine -particle correlations, as they can be inferred from
-particle correlation functions. It is natural to ask whether a similar
result holds for non-degenerate excited states. In fact, for fermionic systems,
it has been conjectured that any non-degenerate excited state of a 2-local
Hamiltonian is simultaneously a unique ground state of another 2-local
Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version
of this conjecture states that any non-degenerate excited state of a 2-local
Hamiltonian is uniquely determined by its 2-matrix among all the pure
-particle states. We construct explicit counterexamples to show that both
conjectures are false. It means that correlations in excited states of local
Hamiltonians could be dramatically different from those in ground states. We
further show that any non-degenerate excited state of a -local Hamiltonian
is a unique ground state of another -local Hamiltonian, hence is uniquely
determined by its -RDMs (or -matrix)
Complete Characterization of the Ground Space Structure of Two-Body Frustration-Free Hamiltonians for Qubits
The problem of finding the ground state of a frustration-free Hamiltonian
carrying only two-body interactions between qubits is known to be solvable in
polynomial time. It is also shown recently that, for any such Hamiltonian,
there is always a ground state that is a product of single- or two-qubit
states. However, it remains unclear whether the whole ground space is of any
succinct structure. Here, we give a complete characterization of the ground
space of any two-body frustration-free Hamiltonian of qubits. Namely, it is a
span of tree tensor network states of the same tree structure. This
characterization allows us to show that the problem of determining the ground
state degeneracy is as hard as, but no harder than, its classical analog.Comment: 5pages, 3 figure
Characterization of cell cycle and apoptosis using flow cytometry for bioprocess monitoring
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Capacity Limitation and Optimization Strategy for Flexible Point-to-Multi-Point Optical Networks
Point-to-multi-point (PtMP) optical networks become the main solutions for
network-edge applications such as passive optical networks and radio access
networks. Entropy-loading digital subcarrier multiplexing (DSCM) is the core
technology to achieve low latency and approach high capacity for flexible PtMP
optical networks. However, the high peak-to-average power ratio of the
entropy-loading DSCM signal limits the power budget and restricts the capacity,
which can be reduced effectively by clipping operation. In this paper, we
derive the theoretical capacity limitation of the flexible PtMP optical
networks based on the entropy-loading DSCM signal. Meanwhile, an optimal
clipping ratio for the clipping operation is acquired to approach the highest
capacity limitation. Based on an accurate clipping-noise model under the
optimal clipping ratio, we establish a three-dimensional look-up table for
bit-error ratio, spectral efficiency, and link loss. Based on the
three-dimensional look-up table, an optimization strategy is proposed to
acquire optimal spectral efficiencies for achieving a higher capacity of the
flexible PtMP optical networks.Comment: The paper has been submitted to the IEEE Transactions on
Communication
Ground-State Spaces of Frustration-Free Hamiltonians
We study the ground-state space properties for frustration-free Hamiltonians.
We introduce a concept of `reduced spaces' to characterize local structures of
ground-state spaces. For a many-body system, we characterize mathematical
structures for the set of all the -particle reduced spaces, which
with a binary operation called join forms a semilattice that can be interpreted
as an abstract convex structure. The smallest nonzero elements in ,
called atoms, are analogs of extreme points. We study the properties of atoms
in and discuss its relationship with ground states of -local
frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms
in are unique ground states of some 2-local frustration-free
Hamiltonians. Moreover, we show that the elements in may not be the
join of atoms, indicating a richer structure for beyond the convex
structure. Our study of deepens the understanding of ground-state
space properties for frustration-free Hamiltonians, from a new angle of reduced
spaces.Comment: 23 pages, no figur
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