1,912 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
Degrees of controllability for quantum systems and applications to atomic systems
Precise definitions for different degrees of controllability for quantum
systems are given, and necessary and sufficient conditions are discussed. The
results are applied to determine the degree of controllability for various
atomic systems with degenerate energy levels and transition frequencies.Comment: 20 pages, IoP LaTeX, revised and expanded versio
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
First Order Static Excitation Potential: Scheme for Excitation Energies and Transition Moments
We present an approximation scheme for the calculation of the principal
excitation energies and transition moments of finite many-body systems. The
scheme is derived from a first order approximation to the self energy of a
recently proposed extended particle-hole Green's function. A hermitian
eigenvalue problem is encountered of the same size as the well-known Random
Phase Approximation (RPA). We find that it yields a size consistent description
of the excitation properties and removes an inconsistent treatment of the
ground state correlation by the RPA. By presenting a hermitian eigenvalue
problem the new scheme avoids the instabilities of the RPA and should be well
suited for large scale numerical calculations. These and additional properties
of the new approximation scheme are illuminated by a very simple exactly
solvable model.Comment: 15 pages revtex, 1 eps figure included, corrections in Eq. (A1) and
Sec. II
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
Reinforcement Learning vs. Gradient-Based Optimisation for Robust Energy Landscape Control of Spin-1/2 Quantum Networks
We explore the use of policy gradient methods in reinforcement learning for
quantum control via energy landscape shaping of XX-Heisenberg spin chains in a
model agnostic fashion. Their performance is compared to finding controllers
using gradient-based L-BFGS optimisation with restarts, with full access to an
analytical model. Hamiltonian noise and coarse-graining of fidelity
measurements are considered. Reinforcement learning is able to tackle
challenging, noisy quantum control problems where L-BFGS optimization
algorithms struggle to perform well. Robustness analysis under different levels
of Hamiltonian noise indicates that controllers found by reinforcement learning
appear to be less affected by noise than those found with L-BFGS.Comment: 7 pages, 7 figure
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
Magnetotransport properties of iron microwires fabricated by focused electron beam induced autocatalytic growth
We have prepared iron microwires in a combination of focused electron beam
induced deposition (FEBID) and autocatalytic growth from the iron
pentacarbonyl, Fe(CO)5, precursor gas under UHV conditions. The electrical
transport properties of the microwires were investigated and it was found that
the temperature dependence of the longitudinal resistivity (rhoxx) shows a
typical metallic behaviour with a room temperature value of about 88
micro{\Omega} cm. In order to investigate the magnetotransport properties we
have measured the isothermal Hall-resistivities in the range between 4.2 K and
260 K. From these measurements positive values for the ordinary and the
anomalous Hall coefficients were derived. The relation between anomalous Hall
resistivity (rhoAN) and longitudinal resistivity is quadratic, rhoAN rho^2 xx,
revealing an intrinsic origin of the anomalous Hall effect. Finally, at low
temperature in the transversal geometry a negative magnetoresistance of about
0.2 % was measured
Vibronic coupling and core-hole localization in K-shell excitations of ethylene
A new high-resolution measurement of the C 1s near-edge photoabsorption spectrum of the ethylene molecule is reported. An analysis of the vibrational structure in the C 1s-π* band indicates strong excitation of non-totally-symmetry modes and the importance of vibronic coupling. The latter phenomenon provides a mechanism for core-hole localization in the final state
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