| dc.description.abstract | Genetic algorithms (GA) are stochastic global search methods based on the
mechanics of natural biological evolution, proposed by John Holland in 1975. Here
in this thesis, we have exploited possible utilities of Genetic Algorithm optimization
in Nuclear Magnetic Resonance (NMR) experiments. We have performed
(i ) Pulse sequence generation and optimization for NMR Quantum Information
Processing, (ii ) efficient creation of NOON states, (iii ) Composite operator design
and (iv ) delay optimization for refocused quantitative INEPT. We have generated
time optimal as well as robust pulse sequences for popular quantum gates. A
Matlab package is developed for basic Target unitary operator to pulse sequence
optimization and is explained with an example.
Chapter 1 contains a brief introduction to NMR, Quantum computation and Genetic
algorithm optimization. Experimental unitary operator decomposition using
Genetic Algorithm is explained in Chapter 2. Starting from a two spin homonu-
clear system (5-Bromofuroic acid), we have generated hard pulse sequences for
performing (i ) single qubit rotation, (ii ) controlled NOT gates and (iii ) pseudo
pure state creation, which demonstrates universal quantum computation in such
systems. The total length of the pulse sequence for the single qubit rotation of an
angle π/2 is less than 500µs, whereas the conventional method (using a selective
soft pulse) would need a 2ms shaped pulse. This substantial shortening in time
can lead to a significant advantage in quantum circuits. We also demonstrate the
creation of Long Lived Singlet State and other Bell states, directly from thermal
equilibrium state, with the shortest known pulse sequence. All the pulse sequences
generated here are generic i.e., independent of the system and the spectrometer.
We further generalized this unitary operator decomposition technique for a variable
operators termed as Fidelity Profile Optimization (FPO) (Chapter 3) and
performed quantum simulations of Hamiltonian such as Heisenberg XY interaction
and Dzyaloshinskii-Moriya interaction. Exact phase (φ) dependent experimental
unitary decompositions of Controlled-φ and Controlled Controlled-φ are solved
using first order FPO. Unitary operator decomposition for experimental quantum
simulation of Dzyaloshinskii-Moriya interaction in the presence of Heisenberg XY
interaction is solved using second order FPO for any relative strengths of interactions
(γ) and evolution time (τ ). Experimental gate time for this decomposition
is invariant under γ or τ , which can be used for relaxation independent studies of
the system dynamics. Using these decompositions, we have experimentally verified
the entanglement preservation mechanism suggested by Hou et al. [Annals of
Physics, 327 292 (2012)].
NOON state or Schrodinger cat state is a maximally entangled N qubit state
with superposition of all individual qubits being at |0 and being at |1 . NOON
states have received much attention recently for their high precession phase
measurements, which enables the design of high sensitivity sensors in optical interfer-
ometry and NMR [Jones et al. Science, 324 1166(2009)]. We have used Genetic
algorithm optimization for efficient creation of NOON states in NMR (Chapter 4).
The decompositions are, (i ) a minimal in terms of required experimental resources
– radio frequency pulses and delays – and have (ii ) good experimental fidelity.
A composite pulse is a cluster of nearly connected rf pulses which emulate the
effect of a simple spin operator with robust response over common experimental
imperfections. Composite pulses are mainly used for improving broadband de-
coupling, population inversion, coherence transfer and in nuclear overhauser effect
experiments. Composite operator is a generalized idea where a basic operator
(such as rotation or evolution of zz coupling) is made robust against common
experimental errors (such as inhomogeneity / miscalibration of rf power or errror
in evaluation of zz coupling strength) by using a sequence of basic operators
available for the system. Using Genetic Algorithm optimization, we have designed
and experimentally verified following composite operators, (i ) broadband rotation
pulses, (ii ) rf inhomogeneity compensated rotation pulses and (iii ) zz evolution
operator with robust response over a range of zz coupling strengths (Chapter 5).
We also performed rf inhomogeneity compensated Controlled NOT gate.
Extending Genetic Algorithm optimization in classical NMR applications, we have
improved the quantitative refocused constant-time INEPT experiment (Q-INEPT-
CT) of M¨kel¨ et al. [JMR 204(2010) 124-130] with various optimization constraints
. The improved ‘average polarization transfer’ and ‘min-max difference’
of new delay sets effectively reduces the experimental time by a factor of two
(compared with Q-INEPT-CT, M¨kel¨ et al.) without compromising on accuracy
(Chapter 6). We also introduced a quantitative spectral editing technique based
on average polarization transfer. These optimized quantitative experiments are
also described in Chapter 6.
Time optimal pulse sequences for popular quantum gates such as, (i ) Controlled
Hadamard (C-H) gate, (ii ) Controlled-Controlled-NOT (CCNOT) Gate and (iii )
Controlled SWAP (C-S) gate are optimized using Genetic Algorithm (Appendix.
A). We also generated optimal sequences for Quantum Counter circuits, Quantum
Probability Splitter circuits and efficient creation of three spin W state. We
have developed a Matlab package based on GA optimization for three spin target
operator to pulse sequence generator. The package is named as UOD (Unitary
Operator Decomposition) is explained with an example of Controlled SWAP gate
in Appendix. B.
An algorithm based on quantum phase estimation, which discriminates quantum
states non-destructively within a set of arbitrary orthogonal states, is described
and experimentally verified by a NMR quantum information processor (Appendix.
C). The procedure is scalable and can be applied to any set of orthogonal states.
Scalability is demonstrated through Matlab simulation. | en_US |
