46 research outputs found
Counteracting systems of diabaticities using DRAG controls: The status after 10 years
The task of controlling a quantum system under time and bandwidth limitations
is made difficult by unwanted excitations of spectrally neighboring energy
levels. In this article we review the Derivative Removal by Adiabatic Gate
(DRAG) framework. DRAG is a multi-transition variant of counterdiabatic
driving, where multiple low-lying gapped states in an adiabatic evolution can
be avoided simultaneously, greatly reducing operation times compared to the
adiabatic limit. In its essence, the method corresponds to a convergent version
of the superadiabatic expansion where multiple counterdiabaticity conditions
can be met simultaneously. When transitions are strongly crowded, the system of
equations can instead be favorably solved by an average Hamiltonian (Magnus)
expansion, suggesting the use of additional sideband control. We give some
examples of common systems where DRAG and variants thereof can be applied to
improve performance.Comment: 7 pages, 2 figure
Superfast Cooling
Currently laser cooling schemes are fundamentally based on the weak coupling
regime. This requirement sets the trap frequency as an upper bound to the
cooling rate. In this work we present a numerical study that shows the
feasibility of cooling in the strong coupling regime which then allows cooling
rates that are faster than the trap frequency with state of the art
experimental parameters. The scheme we present can work for trapped atoms or
ions as well as mechanical oscillators. It can also cool medium size ions
chains close to the ground state.Comment: 5 pages 4 figure
The EPR experiment in the energy-based stochastic reduction framework
We consider the EPR experiment in the energy-based stochastic reduction
framework. A gedanken set up is constructed to model the interaction of the
particles with the measurement devices. The evolution of particles' density
matrix is analytically derived. We compute the dependence of the
disentanglement rate on the parameters of the model, and study the dependence
of the outcome probabilities on the noise trajectories. Finally, we argue that
these trajectories can be regarded as non-local hidden variables.Comment: 11 pages, 5 figure
On the relation between Bell inequalities and nonlocal games
We investigate the relation between Bell inequalities and nonlocal games by
presenting a systematic method for their bilateral conversion. In particular,
we show that while to any nonlocal game there naturally corresponds a unique
Bell inequality, the converse is not true. As an illustration of the method we
present a number of nonlocal games that admit better odds when played using
quantum resourcesComment: v3 changes: Updates to reflect PLA version. 1 examples changed.
Physics Letters A (accepted for publication
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
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
Transition Decomposition of Quantum Mechanical Evolution
We show that the existence of the family of self-adjoint Lyapunov operators
introduced in [J. Math. Phys. 51, 022104 (2010)] allows for the decomposition
of the state of a quantum mechanical system into two parts: A past time
asymptote, which is asymptotic to the state of the system at t goes to minus
infinity and vanishes at t goes to plus infinity, and a future time asymptote,
which is asymptotic to the state of the system at t goes to plus infinity and
vanishes at t goes to minus infinity. We demonstrate the usefulness of this
decomposition for the description of resonance phenomena by considering the
resonance scattering of a particle off a square barrier potential. We show that
the past time asymptote captures the behavior of the resonance. In particular,
it exhibits the expected exponential decay law and spatial probability
distribution.Comment: Accepted for publication in Int. J. Theor. Phy
Quantum walks: a comprehensive review
Quantum walks, the quantum mechanical counterpart of classical random walks,
is an advanced tool for building quantum algorithms that has been recently
shown to constitute a universal model of quantum computation. Quantum walks is
now a solid field of research of quantum computation full of exciting open
problems for physicists, computer scientists, mathematicians and engineers.
In this paper we review theoretical advances on the foundations of both
discrete- and continuous-time quantum walks, together with the role that
randomness plays in quantum walks, the connections between the mathematical
models of coined discrete quantum walks and continuous quantum walks, the
quantumness of quantum walks, a summary of papers published on discrete quantum
walks and entanglement as well as a succinct review of experimental proposals
and realizations of discrete-time quantum walks. Furthermore, we have reviewed
several algorithms based on both discrete- and continuous-time quantum walks as
well as a most important result: the computational universality of both
continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing
Journa