60,060 research outputs found
Time optimal simultaneous control of two level quantum systems
In this paper, we solve the problem of simultaneously driving in minimum time
to arbitrary final conditions, N two level quantum systems subject to
independent controls. The solution of this problem is obtained via an explicit
description of the reachable set of the associated control system on SU(2). The
treatment generalizes previous results on the time optimal control of two level
quantum systems and suggests that similar techniques could be used to solve the
minimum time control problem for a larger class of right invariant systems on
Lie groups
Robustness of high-fidelity Rydberg gates with single-site addressability
Controlled phase (CPHASE) gates can in principle be realized with trapped
neutral atoms by making use of the Rydberg blockade. Achieving the ultra-high
fidelities required for quantum computation with such Rydberg gates is however
compromised by experimental inaccuracies in pulse amplitudes and timings, as
well as by stray fields that cause fluctuations of the Rydberg levels. We
report here a comparative study of analytic and numerical pulse sequences for
the Rydberg CPHASE gate that specifically examines the robustness of the gate
fidelity with respect to such experimental perturbations. Analytical pulse
sequences of both simultaneous and stimulated Raman adiabatic passage (STIRAP)
are found to be at best moderately robust under these perturbations. In
contrast, optimal control theory is seen to allow generation of numerical
pulses that are inherently robust within a predefined tolerance window. The
resulting numerical pulse shapes display simple modulation patterns and their
spectra contain only one additional frequency beyond the basic resonant Rydberg
gate frequencies. Pulses of such low complexity should be experimentally
feasible, allowing gate fidelities of order 99.90 - 99.99% to be achievable
under realistic experimental conditions.Comment: 12 pages, 14 figure
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
Simultaneous time-optimal control of the inversion of two spin 1/2 particles
We analyze the simultaneous time-optimal control of two-spin systems. The two
non coupled spins which differ in the value of their chemical offsets are
controlled by the same magnetic fields. Using an appropriate rotating frame, we
restrict the study to the case of opposite shifts. We then show that the
optimal solution of the inversion problem in a rotating frame is composed of a
pulse sequence of maximum intensity and is similar to the optimal solution for
inverting only one spin by using a non-resonant control field in the laboratory
frame. An example is implemented experimentally using techniques of Nuclear
Magnetic Resonance.Comment: 13 pages, 3 figure
Optimal Control for Generating Quantum Gates in Open Dissipative Systems
Optimal control methods for implementing quantum modules with least amount of
relaxative loss are devised to give best approximations to unitary gates under
relaxation. The potential gain by optimal control using relaxation parameters
against time-optimal control is explored and exemplified in numerical and in
algebraic terms: it is the method of choice to govern quantum systems within
subspaces of weak relaxation whenever the drift Hamiltonian would otherwise
drive the system through fast decaying modes. In a standard model system
generalising decoherence-free subspaces to more realistic scenarios,
openGRAPE-derived controls realise a CNOT with fidelities beyond 95% instead of
at most 15% for a standard Trotter expansion. As additional benefit it requires
control fields orders of magnitude lower than the bang-bang decouplings in the
latter.Comment: largely expanded version, superseedes v1: 10 pages, 5 figure
NMR Techniques for Quantum Control and Computation
Fifty years of developments in nuclear magnetic resonance (NMR) have resulted
in an unrivaled degree of control of the dynamics of coupled two-level quantum
systems. This coherent control of nuclear spin dynamics has recently been taken
to a new level, motivated by the interest in quantum information processing.
NMR has been the workhorse for the experimental implementation of quantum
protocols, allowing exquisite control of systems up to seven qubits in size.
Here, we survey and summarize a broad variety of pulse control and tomographic
techniques which have been developed for and used in NMR quantum computation.
Many of these will be useful in other quantum systems now being considered for
implementation of quantum information processing tasks.Comment: 33 pages, accepted for publication in Rev. Mod. Phys., added
subsection on T_{1,\rho} (V.A.6) and on time-optimal pulse sequences
(III.A.6), redid some figures, made many small changes, expanded reference
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
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