24 research outputs found
Decoherence and Quantum Walks: anomalous diffusion and ballistic tails
The common perception is that strong coupling to the environment will always
render the evolution of the system density matrix quasi-classical (in fact,
diffusive) in the long time limit. We present here a counter-example, in which
a particle makes quantum transitions between the sites of a d-dimensional
hypercubic lattice whilst strongly coupled to a bath of two-level systems which
'record' the transitions. The long-time evolution of an initial wave packet
is found to be most unusual: the mean square displacement of the particle
density matrix shows long-range ballitic behaviour, but simultaneously a kind
of weakly-localised behaviour near the origin. This result may have important
implications for the design of quantum computing algorithms, since it describes
a class of quantum walks.Comment: 4 pages, 1 figur
Nuclear magnetic resonance spectrum of 31P donors in silicon quantum computer
The influence of the electric field created by a gate potential of the
silicon quantum computer on the hyperfine interaction constant (HIC) is
obtained. The errors due to technological inaccuracy of location of donor atoms
under a gate are evaluated. The energy spectra of electron-nuclear spin system
of two interacting donor atoms with various values of HIC are calculated. The
presence of two pairs of anticrossing levels in the ground electronic state is
shown. Parameters of the structure at which errors rate can be greatly
minimized are found.Comment: 12 pages,, 3 figure
Quantitative Treatment of Decoherence
We outline different approaches to define and quantify decoherence. We argue
that a measure based on a properly defined norm of deviation of the density
matrix is appropriate for quantifying decoherence in quantum registers. For a
semiconductor double quantum dot qubit, evaluation of this measure is reviewed.
For a general class of decoherence processes, including those occurring in
semiconductor qubits, we argue that this measure is additive: It scales
linearly with the number of qubits.Comment: Revised version, 26 pages, in LaTeX, 3 EPS figure
Auxiliary-level-assisted operations with charge qubits in semiconductors
We present a new scheme for rotations of a charge qubit associated with a
singly ionized pair of donor atoms in a semiconductor host. The logical states
of such a qubit proposed recently by Hollenberg et al. are defined by the
lowest two energy states of the remaining valence electron localized around one
or another donor. We show that an electron located initially at one donor site
can be transferred to another donor site via an auxiliary molecular level
formed upon the hybridization of the excited states of two donors. The electron
transfer is driven by a single resonant microwave pulse in the case that the
energies of the lowest donor states coincide or two resonant pulses in the case
that they differ from each other. Depending on the pulse parameters, various
one-qubit operations, including the phase gate, the NOT gate, and the Hadamard
gate, can be realized in short times. Decoherence of an electron due to the
interaction with acoustic phonons is analyzed and shown to be weak enough for
coherent qubit manipulation being possible, at least in the proof-of-principle
experiments on one-qubit devices.Comment: Extended version of cond-mat/0411605 with detailed discussion of
phonon-induced decoherence including dephasing and relaxation; to be
published in JET
On analog quantum algorithms for the mixing of Markov chains
The problem of sampling from the stationary distribution of a Markov chain
finds widespread applications in a variety of fields. The time required for a
Markov chain to converge to its stationary distribution is known as the
classical mixing time. In this article, we deal with analog quantum algorithms
for mixing. First, we provide an analog quantum algorithm that given a Markov
chain, allows us to sample from its stationary distribution in a time that
scales as the sum of the square root of the classical mixing time and the
square root of the classical hitting time. Our algorithm makes use of the
framework of interpolated quantum walks and relies on Hamiltonian evolution in
conjunction with von Neumann measurements.
There also exists a different notion for quantum mixing: the problem of
sampling from the limiting distribution of quantum walks, defined in a
time-averaged sense. In this scenario, the quantum mixing time is defined as
the time required to sample from a distribution that is close to this limiting
distribution. Recently we provided an upper bound on the quantum mixing time
for Erd\"os-Renyi random graphs [Phys. Rev. Lett. 124, 050501 (2020)]. Here, we
also extend and expand upon our findings therein. Namely, we provide an
intuitive understanding of the state-of-the-art random matrix theory tools used
to derive our results. In particular, for our analysis we require information
about macroscopic, mesoscopic and microscopic statistics of eigenvalues of
random matrices which we highlight here. Furthermore, we provide numerical
simulations that corroborate our analytical findings and extend this notion of
mixing from simple graphs to any ergodic, reversible, Markov chain.Comment: The section concerning time-averaged mixing (Sec VIII) has been
updated: Now contains numerical plots and an intuitive discussion on the
random matrix theory results used to derive the results of arXiv:2001.0630
Charge-based quantum computing using single donors in semiconductors
Solid-state quantum computer architectures with qubits encoded using single
atoms are now feasible given recent advances in atomic doping of
semiconductors. Here we present a charge qubit consisting of two dopant atoms
in a semiconductor crystal, one of which is singly ionised. Surface electrodes
control the qubit and a radio-frequency single electron transistor provides
fast readout. The calculated single gate times, of order 50ps or less, are much
shorter than the expected decoherence time. We propose universal one- and
two-qubit gate operations for this system and discuss prospects for fabrication
and scale up.Comment: 5 pages, 4 figures, updated version submitted to Physical Review
Coherent quantum transport in narrow constrictions in the presence of a finite-range longitudinally polarized time-dependent field
We have studied the quantum transport in a narrow constriction acted upon by
a finite-range longitudinally polarized time-dependent electric field. The
electric field induces coherent inelastic scatterings which involve both
intra-subband and inter-sideband transitions. Subsequently, the dc conductance
G is found to exhibit suppressed features. These features are recognized as the
quasi-bound-state (QBS) features which are associated with electrons making
transitions to the vicinity of a subband bottom, of which the density of states
is singular. Having valley-like instead of dip-like structures, these QBS
features are different from the G characteristics for constrictions acted upon
by a finite-range time-modulated potential. In addition, the subband bottoms in
the time-dependent electric field region are shifted upward by an energy
proportional to the square of the electric field and inversely proportional to
the square of the frequency. This effective potential barrier is originated
from the square of the vector potential and it leads to the interesting
field-sensitive QBS features. An experimental set-up is proposed for the
observation of these features.Comment: 8 pages, 4 figure
Network Analysis of Biochemical Logic for Noise Reduction and Stability: A System of Three Coupled Enzymatic AND Gates
We develop an approach aimed at optimizing the parameters of a network of
biochemical logic gates for reduction of the "analog" noise buildup.
Experiments for three coupled enzymatic AND gates are reported, illustrating
our procedure. Specifically, starch - one of the controlled network inputs - is
converted to maltose by beta-amylase. With the use of phosphate (another
controlled input), maltose phosphorylase then produces glucose. Finally,
nicotinamide adenine dinucleotide (NAD+) - the third controlled input - is
reduced under the action of glucose dehydrogenase to yield the optically
detected signal. Network functioning is analyzed by varying selective inputs
and fitting standardized few-parameters "response-surface" functions assumed
for each gate. This allows a certain probe of the individual gate quality, but
primarily yields information on the relative contribution of the gates to noise
amplification. The derived information is then used to modify our experimental
system to put it in a regime of a less noisy operation.Comment: 31 pages, PD
Optimization of Enzymatic Biochemical Logic for Noise Reduction and Scalability: How Many Biocomputing Gates Can Be Interconnected in a Circuit?
We report an experimental evaluation of the "input-output surface" for a
biochemical AND gate. The obtained data are modeled within the rate-equation
approach, with the aim to map out the gate function and cast it in the language
of logic variables appropriate for analysis of Boolean logic for scalability.
In order to minimize "analog" noise, we consider a theoretical approach for
determining an optimal set for the process parameters to minimize "analog"
noise amplification for gate concatenation. We establish that under optimized
conditions, presently studied biochemical gates can be concatenated for up to
order 10 processing steps. Beyond that, new paradigms for avoiding noise
build-up will have to be developed. We offer a general discussion of the ideas
and possible future challenges for both experimental and theoretical research
for advancing scalable biochemical computing
Semiconductor Spintronics
Spintronics refers commonly to phenomena in which the spin of electrons in a
solid state environment plays the determining role. In a more narrow sense
spintronics is an emerging research field of electronics: spintronics devices
are based on a spin control of electronics, or on an electrical and optical
control of spin or magnetism. This review presents selected themes of
semiconductor spintronics, introducing important concepts in spin transport,
spin injection, Silsbee-Johnson spin-charge coupling, and spindependent
tunneling, as well as spin relaxation and spin dynamics. The most fundamental
spin-dependent nteraction in nonmagnetic semiconductors is spin-orbit coupling.
Depending on the crystal symmetries of the material, as well as on the
structural properties of semiconductor based heterostructures, the spin-orbit
coupling takes on different functional forms, giving a nice playground of
effective spin-orbit Hamiltonians. The effective Hamiltonians for the most
relevant classes of materials and heterostructures are derived here from
realistic electronic band structure descriptions. Most semiconductor device
systems are still theoretical concepts, waiting for experimental
demonstrations. A review of selected proposed, and a few demonstrated devices
is presented, with detailed description of two important classes: magnetic
resonant tunnel structures and bipolar magnetic diodes and transistors. In most
cases the presentation is of tutorial style, introducing the essential
theoretical formalism at an accessible level, with case-study-like
illustrations of actual experimental results, as well as with brief reviews of
relevant recent achievements in the field.Comment: tutorial review; 342 pages, 132 figure