328 research outputs found
Anderson localization casts clouds over adiabatic quantum optimization
Understanding NP-complete problems is a central topic in computer science.
This is why adiabatic quantum optimization has attracted so much attention, as
it provided a new approach to tackle NP-complete problems using a quantum
computer. The efficiency of this approach is limited by small spectral gaps
between the ground and excited states of the quantum computer's Hamiltonian. We
show that the statistics of the gaps can be analyzed in a novel way, borrowed
from the study of quantum disordered systems in statistical mechanics. It turns
out that due to a phenomenon similar to Anderson localization, exponentially
small gaps appear close to the end of the adiabatic algorithm for large random
instances of NP-complete problems. This implies that unfortunately, adiabatic
quantum optimization fails: the system gets trapped in one of the numerous
local minima.Comment: 14 pages, 4 figure
Continuous-variable entanglement distillation over a pure loss channel with multiple quantum scissors
Entanglement distillation is a key primitive for distributing high-quality
entanglement between remote locations. Probabilistic noiseless linear
amplification based on the quantum scissors is a candidate for entanglement
distillation from noisy continuous-variable (CV) entangled states. Being a
non-Gaussian operation, quantum scissors is challenging to analyze. We present
a derivation of the non-Gaussian state heralded by multiple quantum scissors in
a pure loss channel with two-mode squeezed vacuum input. We choose the reverse
coherent information (RCI)---a proven lower bound on the distillable
entanglement of a quantum state under one-way local operations and classical
communication (LOCC), as our figure of merit. We evaluate a Gaussian lower
bound on the RCI of the heralded state. We show that it can exceed the
unlimited two-way LOCCassisted direct transmission entanglement distillation
capacity of the pure loss channel. The optimal heralded Gaussian RCI with two
quantum scissors is found to be significantly more than that with a single
quantum scissors, albeit at the cost of decreased success probability. Our
results fortify the possibility of a quantum repeater scheme for CV quantum
states using the quantum scissors.Comment: accepted for publication in Physical Review
Coherent Communication with Continuous Quantum Variables
The coherent bit (cobit) channel is a resource intermediate between classical
and quantum communication. It produces coherent versions of teleportation and
superdense coding. We extend the cobit channel to continuous variables by
providing a definition of the coherent nat (conat) channel. We construct
several coherent protocols that use both a position-quadrature and a
momentum-quadrature conat channel with finite squeezing. Finally, we show that
the quality of squeezing diminishes through successive compositions of coherent
teleportation and superdense coding.Comment: 4 pages, 3 figure
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