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Investigating The Use Of Quadrupolar Nuclei for NMR-Based Quantum Information Processing

T. Milbourne

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

In this thesis, we apply quantum logic gates to a two-qubit register using the techniques of nuclear magnetic resonance (NMR spectroscopy). We create a lyotropic solution of sodium decyl sulfate (SDS), deuterium oxide (D2O), and decanol in the nematic phase, which functions as our quantum register. Using sequences of single-quantum selective pulses, we generate pseudopure initial states. Using SR, a MatLab-based spin response simulator, we check that the pulse sequences produce the appropriate pseudopure states. We then apply a CNOT quantum logic gate to each initial state. Each pseudopure state reacts as expected to the CNOT gate: while some extra excitations occur, they are generally small compared to the rest of the spectrum. These extra excitations may be the result of imperfect phase cycling in our pseudopure pulse sequences, which would leave non-zero coherences between states. These coherences could interfere with the resulting NMR spectra, producing the addition observed excitations.

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In this thesis, we apply quantum logic gates to a two-qubit register using the techniques of nuclear magnetic resonance (NMR spectroscopy). We create a lyotropic solution of sodium decyl sulfate (SDS), deuterium oxide (D2O), and decanol in the nematic phase, which functions as our quantum register. Using sequences of single-quantum selective pulses, we generate pseudopure initial states. Using SR, a MatLab-based spin response simulator, we check that the pulse sequences produce the appropriate pseudopure states. We then apply a CNOT quantum logic gate to each initial state. Each pseudopure state reacts as expected to the CNOT gate: while some extra excitations occur, they are generally small compared to the rest of the spectrum. These extra excitations may be the result of imperfect phase cycling in our pseudopure pulse sequences, which would leave non-zero coherences between states. These coherences could interfere with the resulting NMR spectra, producing the addition observed excitations.
Nuclear magnetic resonance spectroscopy has demonstrated significant experimental progress toward the development of quantum computations. The developments so far have taken place mainly through the use of spin 12 nuclei. In this paper we describe the use of a spin 32 nucleus, oriented in a liquid crystal matrix for the creation of pseudopure states and the implementation of a complete set of two-qubit reversible logic gates using single-quantum transition-selective pulses, extending the range of practice of NMR toward quantum computation.
Physical implementation of quantum-information processing by liquid-state nuclear magnetic resonance, using weakly coupled spin-12\frac{1}{2}21​ nuclei of a molecule, is well established. Nuclei with spin>1/2\mathrm{spin}>1/2spin>1/2 oriented in liquid-crystalline matrices is another possibility. Such systems have multiple qubits per nuclei and large quadrupolar couplings resulting in well separated lines in the spectrum. So far, creation of pseudopure states and logic gates has been demonstrated in such systems using transition selective radio-frequency pulses. In this paper we report two developments. First, we implement a quantum algorithm that needs coherent superposition of states. Second, we use evolution under quadrupolar coupling to implement multiqubit gates. We implement the Deutsch-Jozsa algorithm on a spin-32\frac{3}{2}23​ (2 qubit) system. The controlled-NOT operation needed to implement this algorithm has been implemented here by evolution under the quadrupolar Hamiltonian. To the best of our knowledge, this method has been implemented for the first time in quadrupolar systems. Since the quadrupolar coupling is several orders of magnitude greater than the coupling in weakly coupled spin-12\frac{1}{2}21​ nuclei, the gate time decreases, increasing the clock speed of the quantum computer.
Nuclear magnetic resonance (NMR) is one of the experimental schemes for quantum computation. Most initial state of quantum algorithm in NMR computation is the pseudopure state. Until now, there are several methods to prepare pseudopure state. This note, based on the idea of controlled-not (CNOT) gates combination, has analyzed the characteristics of this method in the odd- and even-qubit system. Also, we have designed the pulse sequence for a 4-qubit sample to obtain pseudopure state, and realized it in the experiment. This method reduces the complexity of experiment and gives a high signal-to-noise (S/N) ratio.
Theoretical Quantum Information Processing (QIP) has matured from the use of qubits to the use of qudits (systems having states >2). Whereas most of the experimental implementations have been performed using qubits, little experimental work has been carried out using qudits as yet. In this paper we demonstrate experimental realization of a qutrit system by nuclear magnetic resonance (NMR), utilizing deuterium (spin-1) nuclei partially oriented in liquid crystalline phase. Preparation of pseudopure states and implementation of unitary operations are demonstrated in this single-qutrit system, using transition selective pulses.
The premise of nuclear magnetic resonance (NMR) quantum computing is that pseudopure quantum states, for which the populations of all energy levels but one are equal, can be used instead of pure quantum states. However, for systems with a large number of quantum bits (qubits), it would require elaborate pulse sequences with many steps to prepare these pseudopure states. To overcome this problem, a method using pairs of pseudopure states (POPS) instead of individual pseudopure states as the basis for NMR quantum computing is introduced here. The POPS approach has a significant advantage over the existing methods that, regardless of the number of qubits, only a single step is needed to prepare each pair of pseudopure states. A detailed analysis of a 16-level spin system is given, and the results of applying a c2{c}^{2}c2-NOT quantum logic gate (a controlled-NOT gate conditional upon the state of two other qubits) to all the POPS in the system are presented.