1,453 research outputs found
Proof of finite surface code threshold for matching
The field of quantum computation currently lacks a formal proof of
experimental feasibility. Qubits are fragile and sophisticated quantum error
correction is required to achieve reliable quantum computation. The surface
code is a promising quantum error correction code, requiring only a physically
reasonable 2-D lattice of qubits with nearest neighbor interactions. However,
existing proofs that reliable quantum computation is possible using this code
assume the ability to measure four-body operators and, despite making this
difficult to realize assumption, require that the error rate of these operator
measurements is less than 10^-9, an unphysically low target. High error rates
have been proved tolerable only when assuming tunable interactions of strength
and error rate independent of distance, which is also unphysical. In this work,
given a 2-D lattice of qubits with only nearest neighbor two-qubit gates, and
single-qubit measurement, initialization, and unitary gates, all of which have
error rate p, we prove that arbitrarily reliable quantum computation is
possible provided p<7.4x10^-4, a target that many experiments have already
achieved. This closes a long-standing open problem, formally proving the
experimental feasibility of quantum computation under physically reasonable
assumptions.Comment: 5 pages, 4 figures, published versio
Limiting absorption principle and perfectly matched layer method for Dirichlet Laplacians in quasi-cylindrical domains
We establish a limiting absorption principle for Dirichlet Laplacians in
quasi-cylindrical domains. Outside a bounded set these domains can be
transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet
Laplacians model quantum or acoustically-soft waveguides associated with
quasi-cylindrical domains. We construct a uniquely solvable problem with
perfectly matched layers of finite length. We prove that solutions of the
latter problem approximate outgoing or incoming solutions with an error that
exponentially tends to zero as the length of layers tends to infinity. Outgoing
and incoming solutions are characterized by means of the limiting absorption
principle.Comment: to appear in SIAM Journal on Mathematical Analysi
Topologically non-trivial quantum layers
Given a complete non-compact surface embedded in R^3, we consider the
Dirichlet Laplacian in a layer of constant width about the surface. Using an
intrinsic approach to the layer geometry, we generalise the spectral results of
an original paper by Duclos et al. to the situation when the surface does not
possess poles. This enables us to consider topologically more complicated
layers and state new spectral results. In particular, we are interested in
layers built over surfaces with handles or several cylindrically symmetric
ends. We also discuss more general regions obtained by compact deformations of
certain layers.Comment: 15 pages, 6 figure
Weakly regular Floquet Hamiltonians with pure point spectrum
We study the Floquet Hamiltonian: -i omega d/dt + H + V(t) as depending on
the parameter omega. We assume that the spectrum of H is discrete, {h_m (m =
1..infinity)}, with h_m of multiplicity M_m. and that V is an Hermitian
operator, 2pi-periodic in t. Let J > 0 and set Omega_0 = [8J/9,9J/8]. Suppose
that for some sigma > 0: sum_{m,n such that h_m > h_n} mu_{mn}(h_m -
h_n)^(-sigma) < infinity where mu_{mn} = sqrt(min{M_m,M_n)) M_m M_n. We show
that in that case there exist a suitable norm to measure the regularity of V,
denoted epsilon, and positive constants, epsilon_* & delta_*, such that: if
epsilon
|Omega_0| - delta_* epsilon and the Floquet Hamiltonian has a pure point
spectrum for all omega in Omega_infinity.Comment: 35 pages, Latex with AmsAr
Tissue fusion over non-adhering surfaces
Tissue fusion eliminates physical voids in a tissue to form a continuous
structure and is central to many processes in development and repair. Fusion
events in vivo, particularly in embryonic development, often involve the
purse-string contraction of a pluricellular actomyosin cable at the free edge.
However in vitro, adhesion of the cells to their substrate favors a closure
mechanism mediated by lamellipodial protrusions, which has prevented a
systematic study of the purse-string mechanism. Here, we show that monolayers
can cover well-controlled mesoscopic non-adherent areas much larger than a cell
size by purse-string closure and that active epithelial fluctuations are
required for this process. We have formulated a simple stochastic model that
includes purse-string contractility, tissue fluctuations and effective friction
to qualitatively and quantitatively account for the dynamics of closure. Our
data suggest that, in vivo, tissue fusion adapts to the local environment by
coordinating lamellipodial protrusions and purse-string contractions
Adiabatically switched-on electrical bias in continuous systems, and the Landauer-Buttiker formula
Consider a three dimensional system which looks like a cross-connected pipe
system, i.e. a small sample coupled to a finite number of leads. We investigate
the current running through this system, in the linear response regime, when we
adiabatically turn on an electrical bias between leads. The main technical tool
is the use of a finite volume regularization, which allows us to define the
current coming out of a lead as the time derivative of its charge. We finally
prove that in virtually all physically interesting situations, the conductivity
tensor is given by a Landauer-B{\"u}ttiker type formula.Comment: 20 pages, submitte
Topological code Autotune
Many quantum systems are being investigated in the hope of building a
large-scale quantum computer. All of these systems suffer from decoherence,
resulting in errors during the execution of quantum gates. Quantum error
correction enables reliable quantum computation given unreliable hardware.
Unoptimized topological quantum error correction (TQEC), while still effective,
performs very suboptimally, especially at low error rates. Hand optimizing the
classical processing associated with a TQEC scheme for a specific system to
achieve better error tolerance can be extremely laborious. We describe a tool
Autotune capable of performing this optimization automatically, and give two
highly distinct examples of its use and extreme outperformance of unoptimized
TQEC. Autotune is designed to facilitate the precise study of real hardware
running TQEC with every quantum gate having a realistic, physics-based error
model.Comment: 13 pages, 17 figures, version accepted for publicatio
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