3,969 research outputs found
Complete controllability of finite-level quantum systems
Complete controllability is a fundamental issue in the field of control of
quantum systems, not least because of its implications for dynamical
realizability of the kinematical bounds on the optimization of observables. In
this paper we investigate the question of complete controllability for
finite-level quantum systems subject to a single control field, for which the
interaction is of dipole form. Sufficient criteria for complete controllability
of a wide range of finite-level quantum systems are established and the
question of limits of complete controllability is addressed. Finally, the
results are applied to give a classification of complete controllability for
four-level systems.Comment: 14 pages, IoP-LaTe
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
Orbits of quantum states and geometry of Bloch vectors for -level systems
Physical constraints such as positivity endow the set of quantum states with
a rich geometry if the system dimension is greater than two. To shed some light
on the complicated structure of the set of quantum states, we consider a
stratification with strata given by unitary orbit manifolds, which can be
identified with flag manifolds. The results are applied to study the geometry
of the coherence vector for n-level quantum systems. It is shown that the
unitary orbits can be naturally identified with spheres in R^{n^2-1} only for
n=2. In higher dimensions the coherence vector only defines a non-surjective
embedding into a closed ball. A detailed analysis of the three-level case is
presented. Finally, a refined stratification in terms of symplectic orbits is
considered.Comment: 15 pages LaTeX, 3 figures, reformatted, slightly modified version,
corrected eq.(3), to appear in J. Physics
Criteria for reachability of quantum states
We address the question of which quantum states can be inter-converted under
the action of a time-dependent Hamiltonian. In particular, we consider the
problem applied to mixed states, and investigate the difference between pure
and mixed-state controllability introduced in previous work. We provide a
complete characterization of the eigenvalue spectrum for which the state is
controllable under the action of the symplectic group. We also address the
problem of which states can be prepared if the dynamical Lie group is not
sufficiently large to allow the system to be controllable.Comment: 14 pages, IoP LaTeX, first author has moved to Cambridge university
([email protected]
Experimental Hamiltonian identification for controlled two-level systems
We present a strategy to empirically determine the internal and control Hamiltonians for an unknown two-level system (black box) subject to various (piecewise constant) control fields when direct readout by measurement is limited to a single, fixed observable
Control of non-controllable quantum systems: A quantum control algorithm based on Grover iteration
A new notion of controllability, eigenstate controllability, is defined for
finite-dimensional bilinear quantum mechanical systems which are neither
strongly completely controllably nor completely controllable. And a quantum
control algorithm based on Grover iteration is designed to perform a quantum
control task of steering a system, which is eigenstate controllable but may not
be (strongly) completely controllable, from an arbitrary state to a target
state.Comment: 7 pages, no figures, submitte
Is the voice an auditory face?: An ALE meta-analysis comparing vocal and facial emotion processing
This meta-analysis compares the brain structures and mechanisms involved in facial and vocal emotion recognition. Neuroimaging studies contrasting emotional with neutral (face: N = 76, voice: N = 34) and explicit with implicit emotion processing (face: N = 27, voice: N = 20) were collected to shed light on stimulus and goal-driven mechanisms, respectively. Activation likelihood estimations were conducted on the full data sets for the separate modalities and on reduced, modality-matched data sets for modality comparison. Stimulus-driven emotion processing engaged large networks with significant modality differences in the superior temporal (voice-specific) and the medial temporal (face-specific) cortex. Goal-driven processing was associated with only a small cluster in the dorsomedial prefrontal cortex for voices but not faces. Neither stimulus- nor goal-driven processing showed significant modality overlap. Together, these findings suggest that stimulus-driven processes shape activity in the social brain more powerfully than goal-driven processes in both the visual and the auditory domains. Yet, whereas faces emphasize subcortical emotional and mnemonic mechanisms, voices emphasize cortical mechanisms associated with perception and effortful stimulus evaluation (e.g. via subvocalization). These differences may be due to sensory stimulus properties and highlight the need for a modality-specific perspective when modeling emotion processing in the brain
Controlled phase gate for solid-state charge qubits
We describe a mechanism for realizing a controlled phase gate for solid-state
charge qubits. By augmenting the positionally defined qubit with an auxiliary
state, and changing the charge distribution in the three-dot system, we are
able to effectively switch the Coulombic interaction, effecting an entangling
gate. We consider two architectures, and numerically investigate their
robustness to gate noise.Comment: 14 pages, 11 figures, 2 tables, RevTeX
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