1,323 research outputs found
Implementation of Fault-tolerant Quantum Logic Gates via Optimal Control
The implementation of fault-tolerant quantum gates on encoded logic qubits is
considered. It is shown that transversal implementation of logic gates based on
simple geometric control ideas is problematic for realistic physical systems
suffering from imperfections such as qubit inhomogeneity or uncontrollable
interactions between qubits. However, this problem can be overcome by
formulating the task as an optimal control problem and designing efficient
algorithms to solve it. In particular, we can find solutions that implement all
of the elementary logic gates in a fixed amount of time with limited control
resources for the five-qubit stabilizer code. Most importantly, logic gates
that are extremely difficult to implement using conventional techniques even
for ideal systems, such as the T-gate for the five-qubit stabilizer code, do
not appear to pose a problem for optimal control.Comment: 18 pages, ioptex, many figure
Optimal Control of One-Qubit Gates
We consider the problem of carrying an initial Bloch vector to a final Bloch
vector in a specified amount of time under the action of three control fields
(a vector control field). We show that this control problem is solvable and
therefore it is possible to optimize the control. We choose the physically
motivated criteria of minimum energy spent in the control, minimum magnitude of
the rate of change of the control and a combination of both. We find exact
analytical solutions.Comment: 5 page
Complete controllability of quantum systems
Sufficient conditions for complete controllability of -level quantum
systems subject to a single control pulse that addresses multiple allowed
transitions concurrently are established. The results are applied in particular
to Morse and harmonic-oscillator systems, as well as some systems with
degenerate energy levels. Morse and harmonic oscillators serve as models for
molecular bonds, and the standard control approach of using a sequence of
frequency-selective pulses to address a single transition at a time is either
not applicable or only of limited utility for such systems.Comment: 8 pages, expanded and revised versio
Efficient Algorithms for Optimal Control of Quantum Dynamics: The "Krotov'' Method unencumbered
Efficient algorithms for the discovery of optimal control designs for
coherent control of quantum processes are of fundamental importance. One
important class of algorithms are sequential update algorithms generally
attributed to Krotov. Although widely and often successfully used, the
associated theory is often involved and leaves many crucial questions
unanswered, from the monotonicity and convergence of the algorithm to
discretization effects, leading to the introduction of ad-hoc penalty terms and
suboptimal update schemes detrimental to the performance of the algorithm. We
present a general framework for sequential update algorithms including specific
prescriptions for efficient update rules with inexpensive dynamic search length
control, taking into account discretization effects and eliminating the need
for ad-hoc penalty terms. The latter, while necessary to regularize the problem
in the limit of infinite time resolution, i.e., the continuum limit, are shown
to be undesirable and unnecessary in the practically relevant case of finite
time resolution. Numerical examples show that the ideas underlying many of
these results extend even beyond what can be rigorously proved.Comment: 19 pages, many figure
The star formation rate history in the FORS Deep and GOODS South Fields
We measure the star formation rate (SFR) as a function of redshift z up to z
\~4.5, based on B, I and (I+B) selected galaxy catalogues from the FORS Deep
Field (FDF) and the K-selected catalogue from the GOODS-South field. Distances
are computed from spectroscopically calibrated photometric redshifts accurate
to (Delta_z / (z_spec+1)) ~0.03 for the FDF and ~0.056 for the GOODS-South
field. The SFRs are derived from the luminosities at 1500 Angstroem. We find
that the total SFR estimates derived from B, I and I+B catalogues agree very
well (\lsim 0.1 dex) while the SFR from the K catalogue is lower by ~0.2 dex.
We show that the latter is solely due to the lower star-forming activity of
K-selected intermediate and low luminosity (L<L_*) galaxies. The SFR of bright
(L>L_*) galaxies is independent of the selection band, i.e. the same for B, I,
(I+B), and K-selected galaxy samples. At all redshifts, luminous galaxies
(L>L_*) contribute only ~1/3 to the total SFR. There is no evidence for
significant cosmic variance between the SFRs in the FDF and GOODs-South field,
~0.1 dex, consistent with theoretical expectations. The SFRs derived here are
in excellent agreement with previous measurements provided we assume the same
faint-end slope of the luminosity function as previous works (alpha ~ -1.6).
However, our deep FDF data indicate a shallower slope of alpha=-1.07, implying
a SFR lower by ~0.3 dex. We find the SFR to be roughly constant up to z ~4 and
then to decline slowly beyond, if dust extinctions are assumed to be constant
with redshift.Comment: 6 pages, 2 figures, Accepted for publication in ApJ
Entanglement Dissipation: Unitary and Non-unitary Processes
Dissipative processes in physics are usually associated with non-unitary
actions. However, the important resource of entanglement is not invariant under
general unitary transformations, and is thus susceptible to unitary
"dissipation". In this note we discuss both unitary and non-unitary dissipative
processes, showing that the former is ultimately of value, since reversible,
and enables the production of entanglement; while even in the presence of the
latter, more conventional non-unitary and non-reversible, process there exist
nonetheless invariant entangled states.Comment: 9 pages, 2 figures, Symmetries in Science XV (Bregenz Symposiun 2011
Constraints on relaxation rates for N-level quantum systems
We study the constraints imposed on the population and phase relaxation rates
by the physical requirement of completely positive evolution for open N-level
systems. The Lindblad operators that govern the evolution of the system are
expressed in terms of observable relaxation rates, explicit formulas for the
decoherence rates due to population relaxation are derived, and it is shown
that there are additional, non-trivial constraints on the pure dephasing rates
for N>2. Explicit experimentally testable inequality constraints for the
decoherence rates are derived for three and four-level systems, and the
implications of the results are discussed for generic ladder-, Lambda- and
V-systems, and transitions between degenerate energy levels.Comment: 10 pages, RevTeX, 4 figures (eps/pdf
Review of biorthogonal coupled cluster representations for electronic excitation
Single reference coupled-cluster (CC) methods for electronic excitation are
based on a biorthogonal representation (bCC) of the (shifted) Hamiltonian in
terms of excited CC states, also referred to as correlated excited (CE) states,
and an associated set of states biorthogonal to the CE states, the latter being
essentially configuration interaction (CI) configurations. The bCC
representation generates a non-hermitian secular matrix, the eigenvalues
representing excitation energies, while the corresponding spectral intensities
are to be derived from both the left and right eigenvectors. Using the
perspective of the bCC representation, a systematic and comprehensive analysis
of the excited-state CC methods is given, extending and generalizing previous
such studies. Here, the essential topics are the truncation error
characteristics and the separability properties, the latter being crucial for
designing size-consistent approximation schemes. Based on the general order
relations for the bCC secular matrix and the (left and right) eigenvector
matrices, formulas for the perturbation-theoretical (PT) order of the
truncation errors (TEO) are derived for energies, transition moments, and
property matrix elements of arbitrary excitation classes and truncation levels.
In the analysis of the separability properties of the transition moments, the
decisive role of the so-called dual ground state is revealed. Due to the use of
CE states the bCC approach can be compared to so-called intermediate state
representation (ISR) methods based exclusively on suitably orthonormalized CE
states. As the present analysis shows, the bCC approach has decisive advantages
over the conventional CI treatment, but also distinctly weaker TEO and
separability properties in comparison with a full (and hermitian) ISR method
Physics-based mathematical models for quantum devices via experimental system identification
We consider the task of intrinsic control system identification for quantum
devices. The problem of experimental determination of subspace confinement is
considered, and simple general strategies for full Hamiltonian identification
and decoherence characterization of a controlled two-level system are
presented.Comment: 15 pages, 8 figures, published in proceedings of workshop on
Physics-based mathematical models of low-dimensional semi-conductor
nanostructures (18-23 November, 2007, Banff International Research Station,
Alberta, Canada
Physics-based mathematical models for quantum devices via experimental system identification
We consider the task of intrinsic control system identification for quantum
devices. The problem of experimental determination of subspace confinement is
considered, and simple general strategies for full Hamiltonian identification
and decoherence characterization of a controlled two-level system are
presented.Comment: 15 pages, 8 figures, published in proceedings of workshop on
Physics-based mathematical models of low-dimensional semi-conductor
nanostructures (18-23 November, 2007, Banff International Research Station,
Alberta, Canada
- …