4 research outputs found
Optimal control theory for unitary transformations
The dynamics of a quantum system driven by an external field is well
described by a unitary transformation generated by a time dependent
Hamiltonian. The inverse problem of finding the field that generates a specific
unitary transformation is the subject of study. The unitary transformation
which can represent an algorithm in a quantum computation is imposed on a
subset of quantum states embedded in a larger Hilbert space. Optimal control
theory (OCT) is used to solve the inversion problem irrespective of the initial
input state. A unified formalism, based on the Krotov method is developed
leading to a new scheme. The schemes are compared for the inversion of a
two-qubit Fourier transform using as registers the vibrational levels of the
electronic state of Na. Raman-like transitions through the
electronic state induce the transitions. Light fields are found
that are able to implement the Fourier transform within a picosecond time
scale. Such fields can be obtained by pulse-shaping techniques of a femtosecond
pulse. Out of the schemes studied the square modulus scheme converges fastest.
A study of the implementation of the qubit Fourier transform in the Na
molecule was carried out for up to 5 qubits. The classical computation effort
required to obtain the algorithm with a given fidelity is estimated to scale
exponentially with the number of levels. The observed moderate scaling of the
pulse intensity with the number of qubits in the transformation is
rationalized.Comment: 32 pages, 6 figure
Quantum computing implementations with neutral particles
We review quantum information processing with cold neutral particles, that
is, atoms or polar molecules. First, we analyze the best suited degrees of
freedom of these particles for storing quantum information, and then we discuss
both single- and two-qubit gate implementations. We focus our discussion mainly
on collisional quantum gates, which are best suited for atom-chip-like devices,
as well as on gate proposals conceived for optical lattices. Additionally, we
analyze schemes both for cold atoms confined in optical cavities and hybrid
approaches to entanglement generation, and we show how optimal control theory
might be a powerful tool to enhance the speed up of the gate operations as well
as to achieve high fidelities required for fault tolerant quantum computation.Comment: 19 pages, 12 figures; From the issue entitled "Special Issue on
Neutral Particles
Speeding up the spatial adiabatic passage of matter waves in optical microtraps by optimal control
We numerically investigate the performance of atomic transport in optical
microtraps via the so called spatial adiabatic passage technique. Our analysis
is carried out by means of optimal control methods, which enable us to
determine suitable transport control pulses. We investigate the ultimate limits
of the optimal control in speeding up the transport process in a triple well
configuration for both a single atomic wave packet and a Bose-Einstein
condensate within a regime of experimental parameters achievable with current
optical technology.Comment: 17 pages, 14 figure