31 research outputs found
High-fidelity composite quantum gates for Raman qubits
We present a general systematic approach to design robust and high-fidelity
quantum logic gates with Raman qubits using the technique of composite pulses.
We use two mathematical tools -- the Morris-Shore and Majorana decompositions
-- to reduce the three-state Raman system to an equivalent two-state system.
They allow us to exploit the numerous composite pulses designed for two-state
systems by extending them to Raman qubits. We construct the NOT, Hadamard, and
rotation gates by means of the Morris-Shore transformation with the same
uniform approach: sequences of pulses with the same phases for each gate but
different ratios of Raman couplings. The phase gate is constructed by using the
Majorana decomposition. All composite Raman gates feature very high fidelity,
beyond the quantum computation benchmark values, and significant robustness to
experimental errors. All composite phases and pulse areas are given by
analytical formulas, which makes the method scalable to any desired accuracy
and robustness to errors.Comment: 6 pages, 5 figure
Non-Hermitian shortcut to stimulated Raman adiabatic passage
We propose a non-Hermitian generalization of stimulated Raman adiabatic
passage (STIRAP), which allows one to increase speed and fidelity of the
adiabatic passage. This is done by adding balanced imaginary (gain/loss) terms
in the diagonal (bare energy) terms of the Hamiltonian and choosing them such
that they cancel exactly the nonadiabatic couplings, providing in this way an
effective shortcut to adiabaticity. Remarkably, for a STIRAP using delayed
Gaussian-shaped pulses in the counter-intuitive scheme the imaginary terms of
the Hamiltonian turn out to be time independent. A possible physical
realization of non-Hermitian STIRAP, based on light transfer in three
evanescently-coupled optical waveguides, is proposed.Comment: 7 pages, 4 figure
Quantum simulation of the Riemann-Hurwitz zeta function
We propose a simple realization of a quantum simulator of the Riemann-Hurwitz
(RH) \zeta\ function based on a truncation of its Dirichlet representation. We
synthesize a nearest-neighbour-interaction Hamiltonian, satisfying the property
that the temporal evolution of the autocorrelation function of an initial bare
state of the Hamiltonian reproduces the RH function along the line \sigma+i
\omega t of the complex plane, with \sigma>1. The tight-binding Hamiltonian
with engineered hopping rates and site energies can be implemented in a variety
of physical systems, including trapped ion systems and optical waveguide
arrays. The proposed method is scalable, which means that the simulation can be
in principle arbitrarily accurate. Practical limitations of the suggested
scheme, arising from a finite number of lattice sites N and from decoherence,
are briefly discussed.Comment: 6 pages, 3 figure
Chiral resolution by composite Raman pulses
We present two methods for efficient detection of chiral molecules based on
sequences of single pulses and Raman pulse pairs. The chiral molecules are
modelled by a closed-loop three-state system with different signs in one of the
couplings for the two enantiomers. One method uses a sequence of three
interaction steps: a single pulse, a Raman pulse, and another single pulse. The
other method uses a sequence of only two interaction steps: a Raman pulse, and
a single pulse. The second method is simpler and faster but requires a more
sophisticated Raman pulse than the first one. Both techniques allow for
straightforward generalizations by replacing the single and Raman pulses with
composite pulse sequences. The latter achieve very high signal contrast and far
greater robustness to experimental errors than by using single pulses. We
demonstrate that both constant-rotation (i.e., with phase compensation) and
variable-rotation (i.e., with phase distortion) composite pulses can be used,
the former being more accurate and the latter being simpler and faster.Comment: 7 pages, 7 figure