374 research outputs found
Controlling qubit networks in polynomial time
Future quantum devices often rely on favourable scaling with respect to the
system components. To achieve desirable scaling, it is therefore crucial to
implement unitary transformations in an efficient manner. We develop an upper
bound for the minimum time required to implement a unitary transformation on a
generic qubit network in which each of the qubits is subject to local time
dependent controls. The set of gates is characterized that can be implemented
in a time that scales at most polynomially in the number of qubits.
Furthermore, we show how qubit systems can be concatenated through controllable
two body interactions, making it possible to implement the gate set efficiently
on the combined system. Finally a system is identified for which the gate set
can be implemented with fewer controls. The considered model is particularly
important, since it describes electron-nuclear spin interactions in NV centers
Cooperating or Fighting with Control Noise in the Optimal Manipulation of Quantum Dynamics
This paper investigates the impact of control field noise on the optimal
manipulation of quantum dynamics. Simulations are performed on several
multilevel quantum systems with the goal of population transfer in the presence
of significant control noise. The noise enters as run-to-run variations in the
control amplitude and phase with the observation being an ensemble average over
many runs as is commonly done in the laboratory. A genetic algorithm with an
improved elitism operator is used to find the optimal field that either fights
against or cooperates with control field noise. When seeking a high control
yield it is possible to find fields that successfully fight with the noise
while attaining good quality stable results. When seeking modest control
yields, fields can be found which are optimally shaped to cooperate with the
noise and thereby drive the dynamics more efficiently. In general, noise
reduces the coherence of the dynamics, but the results indicate that population
transfer objectives can be met by appropriately either fighting or cooperating
with noise, even when it is intense.Comment: Scientific Workplace Late
Dynamic Homotopy and Landscape Dynamical Set Topology in Quantum Control
We examine the topology of the subset of controls taking a given initial
state to a given final state in quantum control, where "state" may mean a pure
state |\psi>, an ensemble density matrix \rho, or a unitary propagator U(0,T).
The analysis consists in showing that the endpoint map acting on control space
is a Hurewicz fibration for a large class of affine control systems with vector
controls. Exploiting the resulting fibration sequence and the long exact
sequence of basepoint-preserving homotopy classes of maps, we show that the
indicated subset of controls is homotopy equivalent to the loopspace of the
state manifold. This not only allows us to understand the connectedness of
"dynamical sets" realized as preimages of subsets of the state space through
this endpoint map, but also provides a wealth of additional topological
information about such subsets of control space.Comment: Minor clarifications, and added new appendix addressing scalar
control of 2-level quantum system
Control of quantum phenomena: Past, present, and future
Quantum control is concerned with active manipulation of physical and
chemical processes on the atomic and molecular scale. This work presents a
perspective of progress in the field of control over quantum phenomena, tracing
the evolution of theoretical concepts and experimental methods from early
developments to the most recent advances. The current experimental successes
would be impossible without the development of intense femtosecond laser
sources and pulse shapers. The two most critical theoretical insights were (1)
realizing that ultrafast atomic and molecular dynamics can be controlled via
manipulation of quantum interferences and (2) understanding that optimally
shaped ultrafast laser pulses are the most effective means for producing the
desired quantum interference patterns in the controlled system. Finally, these
theoretical and experimental advances were brought together by the crucial
concept of adaptive feedback control, which is a laboratory procedure employing
measurement-driven, closed-loop optimization to identify the best shapes of
femtosecond laser control pulses for steering quantum dynamics towards the
desired objective. Optimization in adaptive feedback control experiments is
guided by a learning algorithm, with stochastic methods proving to be
especially effective. Adaptive feedback control of quantum phenomena has found
numerous applications in many areas of the physical and chemical sciences, and
this paper reviews the extensive experiments. Other subjects discussed include
quantum optimal control theory, quantum control landscapes, the role of
theoretical control designs in experimental realizations, and real-time quantum
feedback control. The paper concludes with a prospective of open research
directions that are likely to attract significant attention in the future.Comment: Review article, final version (significantly updated), 76 pages,
accepted for publication in New J. Phys. (Focus issue: Quantum control
Optimal suppression of defect generation during a passage across a quantum critical point
The dynamics of quantum phase transitions are inevitably accompanied by the
formation of defects when crossing a quantum critical point. For a generic
class of quantum critical systems, we solve the problem of minimizing the
production of defects through the use of a gradient-based deterministic optimal
control algorithm. By considering a finite size quantum Ising model with a
tunable global transverse field, we show that an optimal power law quench of
the transverse field across the Ising critical point works well at minimizing
the number of defects, in spite of being drawn from a subset of quench
profiles. These power law quenches are shown to be inherently robust against
noise. The optimized defect density exhibits a transition at a critical ratio
of the quench duration to the system size, which we argue coincides with the
intrinsic speed limit for quantum evolution.Comment: 5 pages, 4 figures. The first two authors contributed equally to this
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