The subject of this thesis is devoted to a class of multiparticle entangled states known as the cluster-states. In particular, we focused on a system of four spins and studied the entanglement properties of a four-qubit cluster-state, using a set of entanglement measures for quantifying multipartite entanglement. We then experimentally pre-pared the linear cluster-state in a liquid NMR sample of crotonic acid, by applying a set of pulses generated by the Gradient Ascent Pulse Engineering (GRAPE) algorithm on a temporally averaged pseudo-pure state of four carbon spins. While our spectral results were consistent with the creation of a linear cluster-state, the reconstruction of the experimental density matrix via a full state tomography of the system revealed additional challenges in the detection of certain desired spin terms. These problems must be overcome before the system could be studied quantitatively.
The subject of this thesis is devoted to a class of multiparticle entangled states known as the cluster-states. In particular, we focused on a system of four spins and studied the entanglement properties of a four-qubit cluster-state, using a set of entanglement measures for quantifying multipartite entanglement. We then experimentally pre-pared the linear cluster-state in a liquid NMR sample of crotonic acid, by applying a set of pulses generated by the Gradient Ascent Pulse Engineering (GRAPE) algorithm on a temporally averaged pseudo-pure state of four carbon spins. While our spectral results were consistent with the creation of a linear cluster-state, the reconstruction of the experimental density matrix via a full state tomography of the system revealed additional challenges in the detection of certain desired spin terms. These problems must be overcome before the system could be studied quantitatively.
The subject of this thesis are experimental procedures for preparation, manipulation, and detection of specific quantum states of spin systems in the context of quantum computing. Nuclear magnetic resonance (NMR) and electron spin resonance (ESR) methods were used. The systems studied were small molecules in liquid state, small molecules embedded in a liquid crystal matrix, and paramagnetic centers in single crystals. The nuclear 19F spins of 2,3,4-Trifluoroaniline were used as qubits to implement the three-qubit Deutsch-Josza algorithm using high-resolution NMR. A classification of the Deutsch-Josza functions according to the operator representation of the corresponding oracle transformations was given. Different classes of functions may produce full, partial or no entanglement in the output states of the algorithm. This entanglement content is not immediately evident from the output states themselves. A procedure was given for mapping of the output states onto Bell- or GHZ-states by means of local transformations which preserve the entanglement content. A method for the visualization of single-spin unitary transformations was also presented. This visual representation can facilitate analysis and design of shaped rf pulses. For the purpose of quantum computing, it can be useful to suppress couplings between qubits during the application of finite-length single-qubit gates. The feasibility of this idea was demonstrated using small molecules in a liquid crystal matrix. In a series of proof-of-principle experiments, it was shown that the magic-echo sequence can be used to suppress the dipole-dipole coupling between spins and simultaneously selectively address a single spin by a soft rf pulse. The S-bus concept for spin-quantum computing holds some scalability promise and provides a testbed for studies of large, strongly coupled quantum registers. Single-crystal CaF2 weakly doped with Ce was used to implement the concept. The nine 19F nuclear spins adjacent to the paramagnetic Ce-ion serve as qubits while the electron spin plays the role of a quantum bus. The S-bus theory was tested experimentally. Procedures were given for the measurement of parameters characterizing the quantum state of the nuclear spins. An exact numeric treatment of this ten-spin system was done to aid in understanding the experimental findings. For a pair of nuclear spins with negligible direct dipolar coupling, the CNOT operation was implemented. The spin-spin coupling mediated by the bus spin was utilized for that purpose. The four Bell-states of these two distant spins were created. An experiment was performed who's signature allows those four entangled states to be distinguished. The paramagnetic cluster in CaF2:Ce is embedded in an extended network of 19F nuclear spins. This network is a powerful source of decoherence. A number of existing and a newly designed pulse sequence were tested with respect to their ability to suppress decoherence and their aptitude for use in quantum computing.
Quantum simulations, where controllable quantum systems are used to simulate other quantum systems, originally proposed by Richard Feynman, are one of the most remarkable applications of quantum information science. Compared to computation, quantum simulations require much less number of qubits for the m to be practical. In the work described in this thesis, we have performed a few quantum simulations of small quantum systems using Nuclear Magnetic Resonance(NMR) techniques. These simulations have been used to experimentally demonstrate the underlying interesting quantum protocols. All the experiments presented have been carried out using liquid-state or liquid crystal NMR. Numerical pulse optimization techniques have been utilized in some of the experiments, to achieve better control over the spin systems.
The first chapter contains “Introduction” to quantum information processing, NMR, and numerical pulse optimization techniques. In chapter 2, we describe quantum simulation of a 3-spin Heisenberg-XY spin chain having only nearest neighbour interactions. Recently, spin chains having pre-engineered short-range interactions have been proposed to efficiently transfer quantum information between different parts of a quantum information processor. Other important proposals involving these spin chains include generating entangled states and universal quantum computation. However, such engineered interactions do not occur naturally in any system. In such a scenario, the experimental viability of these proposals can be tested by simulating the spin chains in other controllable quantum systems. In this work, we first theoretically study the time evolution of bipartite and tripartite entanglement measures for a 3-spin open ended XY spin chain. Then, by simulating the XY interactions in a 3-spin nuclear spin system, we experimentally generate, (i)a bipartite maximally(pseudo-)entangled state(Bell state) between end qubits, and(ii) multipartite(pseudo-)entangled states(Wand GHZ states),starting from separable pseudo-pure states. Bell state has been generated by using only the natural unitary evolution of the XY spin chain. W-state and GHZ-state have been generated by applying a single-qubit rotation to the second qubit, and a global rotation of all the three qubits respectively after the unitary evolution of the spin chain.
In chapter 3, we simulate a 3-spin quantum transverse Ising spin system in a triangular configuration, and show that multipartite quantum correlations can be used to distinguish between the frustrated and non-frustrated regimes in the ground state of this spin system. The ground state of the spin system has been prepared by using adiabatic state preparation method. Gradient ascent pulse engineering technique has been utilized to efficiently realize the adiabatic evolution of the spin system. To analyse the experimental ground state of the system, we employ two different multipartite quantum correlation measures, generated from monogamy studies of bipartite quantum correlations.
Chapter 4 contains a digital…
The quantum nature of bulk ensemble NMR quantum computing --the center of recent heated debate, is addressed. Concepts of the mixed state and entanglement are examined, and the data in a 2 qubit liquid NMR quantum computation are analyzed. It is pointed out that the key problem in the current debate is the understanding of entanglement in a mixed state system. The following points are concluded in this Letter: 1)Density matrix describes the "state" of an average particle in an ensemble. It can not describe the state of an individual particle in an ensemble in detail; 2) Entanglement is a property of the wave function of a quantum particle(such as an molecule in a liquid NMR sample). Separability of the density matrix can not be used to measure the entanglement of mixed ensemble; 3)The evolution of states in bulk-ensemble NMR quantum computation is quantum mechanical; 4) The coefficient before the effective pure state density matrix, ε, is an measure of the simultaneity of the molecules in an ensemble. It reflects the intensity of the NMR signal and has no significance in quantifying the entanglement in the bulk ensemble NMR system. We conclude that the liquid NMR quantum computation is genuine, not just classical simulations.
Entanglement lies at the heart of quantum mechanics and challenged the intuition of physicists ever since it was discovered. At the same time, it is a powerful tool that serves as a key resource for quantum communication and quantum computation schemes. Many of these applications rely on multiparticle entanglement, whose description, generation and manipulation became therefore a very active field in theoretical and experimental quantum information science. The goals are here to classify and understand the different types of entanglement, to find new applications and to control and analyze the quantum states experimentally. In this thesis, the experimental observation and analysis of two different types of four-photon polarization entangled states is presented: The cluster state and the symmetric Dicke state with two excitations. For this purpose, experimental setups based on spontaneous parametric down conversion and linear optics with conditional detection were designed. They allowed to observe the cluster state with a fidelity of 74.1 % and the symmetric Dicke state with a fidelity of 84.4 %. The cluster state experiment included the development of a new instrument that is of interest for linear optics quantum logic in general: A probabilistic controlled phase gate that is, due to the simplification of a previous approach, highly stable and can actually be used in multiphoton experiments. The quality of the gate is evaluated by analyzing its entangling capability and by performing full process tomography. The achieved results demonstrate that this device is well suited for implementation in various multiphoton quantum information protocols. In order to study the observed quantum states, efficient analysis tools are introduced. It was possible to verify that essential properties of the ideal states are indeed reproduced in the experiment, among others, the presence of genuine four-partite entanglement. A particular focus is put on the behavior of the states under projective measurements and photon loss. Several new insights in their entanglement structure are revealed and verified experimentally. We further demonstrate properties that are characteristic for the entanglement classes of the states. These can be used to infer the applicability of the observed states for certain distributed quantum communication applications. The presented experiments are generic for the design of setups to observe cluster- and symmetric Dicke states with a higher number of photons. Furthermore, also the efficient non-tomographic methods for state analysis we employ can directly be generalized to experiments with higher qubit numbers, where the reduction of the experimental effort for state analysis is even more crucial.
In recent years, the performance of different entanglement indicators obtained directly from tomograms has been assessed in continuous-variable and hybrid quantum systems. In this paper, we carry out this task in the case of spin systems. We compute the entanglement indicators from actual experimental data obtained from three liquid-state nuclear magnetic resonance (NMR) experiments and compare them with standard entanglement measures calculated from the corresponding density matrices, both experimentally reconstructed and numerically computed. The gross features of entanglement dynamics and spin squeezing properties are found to be reproduced by these entanglement indicators. However, the extent to which these indicators and spin squeezing track the entanglement during time evolution of the multipartite systems in the NMR experiments is very sensitive to the precise nature and strength of interactions as well as the manner in which the full system is partitioned into subsystems. We also use the IBM quantum computer to implement equivalent circuits that capture the dynamics of the multipartite system in one of the NMR experiments and carry out a similar comparative assessment of the performance of tomographic indicators. This exercise shows that these indicators can estimate the degree of entanglement without necessitating detailed state reconstruction procedures, establishing the advantage of the tomographic approach.
In recent years, the performance of different entanglement indicators obtained directly from tomograms has been assessed in continuous-variable and hybrid quantum systems. In this paper, we carry out this task in the case of spin systems. We compute the entanglement indicators from actual experimental data obtained from three liquid-state NMR experiments, and compare them with standard entanglement measures calculated from the corresponding density matrices, both experimentally reconstructed and numerically computed. The gross features of entanglement dynamics and spin squeezing properties are found to be reproduced by these entanglement indicators. However, the extent to which these indicators and spin squeezing track the entanglement during time evolution of the multipartite systems in the NMR experiments is very sensitive to the precise nature and strength of interactions as well as the manner in which the full system is partitioned into subsystems. We also use the IBM quantum computer to implement equivalent circuits that capture the dynamics of the multipartite system in one of the NMR experiments. We compute and compare the entanglement indicators obtained from the tomograms corresponding to the experimental execution and simulation of these equivalent circuits. This exercise shows that these indicators can estimate the degree of entanglement without necessitating detailed state reconstruction procedures, establishing the advantage of the tomographic approach.