14,601 research outputs found
Range of (1,2) random walk in random environment
Consider random walk in random environment In each
step, the walk jumps at most a distance to the right or a distance to
the left. For the walk transient to the right, it is proved that almost surely
for some The result shows that the range of the walk covers only
a linear proportion of the lattice of the positive half line. For the nearest
neighbor random walk in random or non-random environment, this phenomenon could
not appear in any circumstance.Comment: 14 page
Birth and death process with one-side bounded jumps in random environment
Let , which serves as the
environment, be a sequence of i.i.d. random nonnegative vectors, with a
positive integer. We study birth and death process which, given the
environment waits at a state an exponentially distributed time
with parameter and then jumps to with
probability or to
with probability A
sufficient condition for the existence, a criterion for recurrence, and a law
of large numbers of the process are presented. We show that the first
passage time where
is an -type branching process in random
environment and, given are mutually independent random variables such that
This fact enables us to give an explicit velocity of the law of large numbers.Comment: 9 page
Law of large numbers for random walk with unbounded jumps and BDP with bounded jumps in random environment
We study random walk with unbounded jumps in random environment. The
environment is stationary and ergodic, uniformly elliptic and decays
polynomially with speed for some small
and proper We prove a law of large number with
positive velocity under the condition that the annealed mean of the hitting
time of the positive half lattice is finite. Secondly, we consider birth and
death process with bounded jumps in stationary and ergodic environment. Under
the uniformly elliptic condition, we prove a law of large number and give the
explicit formula of its velocity.Comment: 25 page
Stationary distribution for birth and death process with one-side bounded jumps
In this paper, we study a birth and death process on
positive half lattice, which at each discontinuity jumps at most a distance
to the right or exactly a distance to the left. The transitional
probabilities at each site are nonhomogeneous. Firstly, sufficient conditions
for the recurrence and positive recurrence are presented. Then by the branching
structure within random walk with one-side bounded jumps set up in Hong and
Wang (2013), the explicit form of the stationary distribution of the process
is formulated.Comment: 6 page
Fast universal quantum gates on microwave photons with all-resonance operations in circuit QED
Stark shift on a superconducting qubit in circuit quantum electrodynamics
(QED) has been used to construct universal quantum entangling gates on
superconducting resonators in previous works. It is a second-order coupling
effect between the resonator and the qubit in the dispersive regime, which
leads to a slow state-selective rotation on the qubit. Here, we present two
proposals to construct the fast universal quantum gates on superconducting
resonators in a microwave-photon quantum processor composed of multiple
superconducting resonators coupled to a superconducting transmon qutrit, that
is, the controlled-phase (c-phase) gate on two microwave-photon resonators and
the controlled-controlled phase (cc-phase) gates on three resonators, resorting
to quantum resonance operations, without any drive field. Compared with
previous works, our universal quantum gates have the higher fidelities and
shorter operation times in theory. The numerical simulation shows that the
fidelity of our c-phase gate is 99.57% within about 38.1 ns and that of our
cc-phase gate is 99.25% within about 73.3 ns.Comment: 12 pages, 6 figures, 2 table
NOON state generation with phonons in acoustic wave resonators assisted by a nitrogen-vacancy-center ensemble
Since the quality factor of an acoustic wave resonator (AWR) reached
, AWRs have been regarded as a good carrier of quantum information. In
this paper, we propose a scheme to construct a NOON state with two AWRs
assisted by a nitrogen-vacancy-center ensemble (NVE). The two AWRs cross each
other vertically, and the NVE is located at the center of the crossing. By
considering the decoherence of the system and using resonant interactions
between the AWRs and the NVE, and the single-qubit operation of the NVE, a NOON
state can be achieved with a fidelity higher than when the number of
phonons in the AWR is
Quantum state transfer and controlled-phase gate on one-dimensional superconducting resonators assisted by a quantum bus
We propose a quantum processor for the scalable quantum computation on
microwave photons in distant one-dimensional superconducting resonators. It is
composed of a common resonator R acting as a quantum bus and some distant
resonators coupled to the bus in different positions assisted by
superconducting quantum interferometer devices (SQUID), different from previous
processors. R is coupled to one transmon qutrit, and the coupling strengths
between and R can be fully tuned by the external flux through the SQUID.
To show the processor can be used to achieve universal quantum computation
effectively, we present a scheme to complete the high-fidelity quantum state
transfer between two distant microwave-photon resonators and another one for
the high-fidelity controlled-phase gate on them. By using the technique for
catching and releasing the microwave photons from resonators, our processor may
play an important role in quantum communication as well.Comment: 11 pages, 4 figures, one colum
Universal quantum gates on microwave photons assisted by circuit quantum electrodynamics
Based on a microwave-photon quantum processor with two superconducting
resonators coupled to one transmon qutrit, we construct the controlled-phase
(c-phase) gate on microwave-photon-resonator qudits, by combination of the
photon-number-dependent frequency-shift effect on the transmon qutrit by the
first resonator and the resonant operation between the qutrit and the second
resonator. This distinct feature provides us a useful way to achieve the
c-phase gate on the two resonator qudits with a higher fidelity and a shorter
operation time, compared with the previous proposals. The fidelity of our
c-phase gate can reach 99.51% within 93 ns. Moreover, our device can be
extended easily to construct the three-qudit gates on three resonator qudits,
far different from the existing proposals. Our controlled-controlled-phase gate
on three resonator qudits is accomplished with the assistance of a transmon
qutrit and its fidelity can reach 92.92% within 124.64 ns.Comment: 9 pages, 5 figure
One-step implementation of entanglement generation on microwave photons in distant 1D superconducting resonators
We present a scalable quantum-bus-based device for generating the
entanglement on microwave photons (MPs) in distant superconducting resonators
(SRs). Different from the processors in previous works with some resonators
coupled to a superconducting qubit (SQ), our device is composed of some 1D SRs
which are coupled to the quantum bus (another common resonator ) in
its different positions simply, assisted by superconducting quantum
interferometer devices. By using the technique for catching and releasing a MP
state in a 1D SR, it can work as an entanglement generator or a node in quantum
communication. To demonstrate the performance of this device, we propose a
one-step scheme to generate high-fidelity Bell states on MPs in two distant
SRs. It works in the dispersive regime of and , which enables us to
extend it to generate high-fidelity multi-Bell states on different resonator
pairs simultaneously.Comment: 5 pages, 3 figure
Asymptotics of product of nonnegative 2-by-2 matrices with applications to random walks with asymptotically zero drifts
Let be product of some nonnegative 2-by-2 matrices. In
general, its elements are hard to evaluate. Under some conditions, we show that
as
where is the spectral radius of the matrix and
is some constant, so that the elements of can be estimated. As applications, consider the maxima of certain
excursions of (2,1) and (1,2) random walks with asymptotically zero drifts.
We get some delicate limit theories which are quite different from the ones
of simple random walks. Limit theories of both the tail and critical tail
sequences of continued fractions play important roles in our studies.Comment: 30 pages;In the second version, we add the result of (1,2) random
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