In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

The present work, briefly described below, consists of implementation of several quantum algorithms in an NMR Quantum Information Processor. Game theory gives us mathematical tools to analyze situations of conflict between two or more players who take decisions that influence their welfare. Classical game theory has been applied to various fields such as market strategy, communication theory, biological processes, foreign policies. It is interesting to study the behaviour of the games when the players share certain quantum correlations such as entanglement. Various games have been studied under the quantum regime with the hope of obtaining some insight into designing new quantum algorithms. Chapter 2 presents the NMR implementation of three such algorithms. Experimental NMR implementation given in this chapter are: (i) Three qubit ‘Dilemma’ game with corrupt sources’. The Dilemma game deals with the situation where three players have to choose between going/not going to a bar with a seating capacity of two. It is seen that in the players have a higher payoff if they share quantum correlations. However, the pay-off falls rapidly with increasing corruption in the source qubits. Here we report the experimental NMR implementation of the quantum version of the Dilemma game with and without corruption in the source qubits. (ii) Two qubit ‘Ulam’s game’. This is a two player game where one player has to find out the binary number thought by the other player. This problem can be solved with one query if quantum resources are used. This game has been implemented in a two qubit system in an NMR quantum information processor. (iii) Two qubit ‘Battle of Sexes’ game. This game deal with a situation where two players have conflicting choices but a deep desire to be together. This leads to a dilemma in the classical case. Quantum mechanically this dilemma is resolved and a unique solution emerges. The NMR implementation of the quantum version of this game is also given in this chapter. Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover’s search algorithm and Deutsch-Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, if one uses local adiabatic evolutions, their complexity is of the order √N (where N=2n) [37, 38]. In Chapter 3, the NMR implementation of (i) the Deutsch-Jozsa and the (ii) Grover’s search algorithm using local adiabatic evolution has been presented. In adiabatic algorithm, the system is first prepared in the equal superposition of all the possible states which is the ground state of the beginning Hamiltonian. The solution is encoded in the ground state of the final Hamiltonian. The system is evolved under a linear combination of the beginning and the final Hamiltonian. During each step of the evolution the interpolating Hamiltonian slowly changes from the beginning to the final Hamiltonian, thus evolving the ground state of the beginning Hamiltonian towards the ground state of the final Hamiltonian. At the end of the evolution the system is in the ground state of the final Hamiltonian which is the solution. The final Hamiltonian, for each of the two cases of adiabatic algorithm described in this chapter, are constructed depending on the problem definition. Adiabatic algorithms have been proved to be equivalent to standard quantum algorithms with respect to complexity [39]. NMR implementation of adiabatic algorithms in homonuclear spin systems face problems due to decoherence and complicated pulse sequences. The decoherence destroys the answer as it causes the final state to evolve to a mixed state and in homonuclear systems there is a substantial evolution under the internal Hamiltonian during the application of the soft pulses which prevents the initial state to converge to the solution state. The resolution of these issues are necessary before one can proceed for the implementation of an adiabatic algorithm in a large system. Chapter 4 demonstrates that by using ‘strongly modulated pulses’ for creation of interpolating Hamiltonian, one can circumvent both the problems and thus successfully implement the adiabatic SAT algorithm in a homonuclear three qubit system. The ‘strongly modulated pulses’ (SMP) are computer optimized pulses in which the evolution under the internal Hamiltonian of the system and RF inhomogeneities associated with the probe is incorporated while generating the SMPs. This results in precise implementation of unitary operators by these pulses. This work also demonstrates that the strongly modulated pulses tremendously reduce the time taken for the implementation of the algorithm, can overcome problems associated with decoherence and will be the modality in future implementation of quantum information processing by NMR. Quantum search algorithm, involving a large number of qubits, is highly sensitive to errors in the physical implementation of the unitary operators. This can put an upper limit to the size of the data base that can be practically searched. The lack of robustness of the quantum search algorithm for a large number of qubits, arises from the fact that stringent ‘phase-matching’ conditions are imposed on the algorithm. To overcome this problem, a modified operator for the search algorithm has been suggested by Tulsi [40]. He has theoretically shown that even when there are errors in implementation of the unitary operators, the search algorithm with his modified operator converges to the target state while the original Grover’s algorithm fails. Chapter 5, presents the experimental NMR implementation of the modified search algorithm with errors and its comparison with the original Grover’s search algorithm. We experimentally validate the theoretical predictions made by Tulsi that the introduction of compensatory Walsh-Hadamard and phase-flip operations refocuses the errors. Experimental Quantum Information Processing is in a nascent stage and it would be too early to predict its future. The excitement on this topic is still very prevalent and many options are being explored to enhance the hardware and software know-how. This thesis endeavors in this direction and probes the experimental feasibility of the quantum algorithms in an NMR quantum information processor.

Laser-cooled atoms offer an excellent platform for testing new ideas of quantum control and measurement. I will discuss experiments where we use light and magnetic fields to drive and monitor non-trivial quantum dynamics of a large spin-angular momentum associated with an atomic hyperfine ground state. We can design Hamiltonians to generate arbitrary spin states and perform a full quantum state reconstruction of the results. We have implemented and verified time optimal controls to generate a broad variety of spin states, including spin-squeezed states useful for metrology. Yields achieved are of the range 0.8-0.9.We present a first experimental demonstration of the quantum kicked top, a popular paradigm for quantum and classical chaos. We make `movies' of the evolving quantum state which provides a direct observation of phase space dynamics of this system. The spin dynamics seen in the experiment includes dynamical tunneling between regular islands, rapid spreading of states throughout the chaotic sea, and surprisingly robust signatures of classical phase space structures. Our data show differences between regular and chaotic dynamics in the sensitivity to perturbations of the quantum kicked top Hamiltonian and in the average electron-nuclear spin entanglement during the first 40 kicks. The difference, while clear, is modest due to the small size of the spin.

In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

Atomic defects in solids offer access to atom-like quantum properties without complex trapping methods while displaying a rich physics due to interactions with their solid-state environment. Such properties have made them an advantageous building block for quantum information processing, in particular to construct a quantum network, where information would be encoded in spins and transferred between nodes through photons. Among defects in solids, the negatively charged silicon-vacancy centre in diamond (SiV$^{−}$) has attracted attention for its very promising optical properties for such a network. In this thesis, we investigate the spin properties of the silicon-vacancy centre as a potential spin-photon interface. First, we use resonant excitation of an SiV$^{−}$ centre in an external magnetic field to selectively address different electronic states and analyse the resulting fluorescence. We find evidence of selection rules in the optical transitions revealing that the centre possesses an electronic spin S = 1/2. Making use of the dependence of such selection rules on the applied magnetic field orientation, we resonantly drive two optical transitions forming a $\Lambda$-scheme. In the double resonance condition, we achieve coherent population trapping, whereby the SiV$^{−}$ is pumped into a dark state corresponding to a superposition of the two addressed ground states of opposite spin. This technique allows us to evaluate the coherence time of the dark state and hence of the spin, while demonstrating the possibility of all-optical control of the spin when a $\Lambda$-scheme is available. We then use resonant optical pulses to initialise and read out the spin state of a single SiV$^{−}$. By tuning a microwave pulse into resonance between two ground states of opposite spin, we demonstrate optically detected magnetic resonance. Subsequently, by varying the duration of a resonant microwave pulse, we achieve coherent control of a single SiV$^{−}$ electronic spin. Through Ramsey interferometry, we measure a spin dephasing time of 115 $\pm$ 9 ns. We then investigate interactions of the SiV$^{−}$ with its environment. We analyse the hyperfine interaction of the SiV$^{−}$ spin with the nuclear spin of $^{29}$Si, with a view to taking advantage of the long-lived nuclear spin in the future. We show that single-phonon-mediated excitations between electronic states of the SiV$^{−}$ are the dominant spin dephasing and population decay mechanism and evaluate how external strain alters optical selection rules and can be used to improve the coherence time of the spin.

In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

Photonics has consistently played an important role in the investigation of quantum-enhanced technologies and the corresponding study of fundamental quantum phenomena. The majority of these experiments have relied on the free space propagation of light between bulk optical components. This relatively simple and flexible approach often provides the fastest route to small proof-of-principle demonstrations. Unfortunately, such experiments occupy significant space, are not inherently phase stable, and can exhibit significant scattering loss which severely limits their use. Integrated photonics offers a scalable route to building larger quantum states of light by surmounting these barriers. In the first half of this thesis, we describe the operation of on-chip heralded sources of single photons. Loss plays a critical role in determining whether many quantum technologies have any hope of outperforming their classical analogues. Minimizing loss leads us to choose Spontaneous Four-Wave Mixing (SFWM) in a silica waveguide for our source design; silica exhibits extremely low scattering loss and emission can be efficiently coupled to the silica chips and fibers that are widely used in quantum optics experiments. We show there is a straightforward route to maximizing heralded photon purity by minimizing the spectral correlations between emitted photon pairs. Fabrication of identical sources on a large scale is demonstrated by a series of high-visibility interference experiments. This architecture offers a promising route to the construction of nonclassical states of higher photon number by operating many on-chip SFWM sources in parallel. In the second half, we detail one of the first proof-of-principle demonstrations of a new intermediate model of quantum computation called boson sampling. While likely less powerful than a universal quantum computer, boson sampling machines appear significantly easier to build and may allow the first convincing demonstration of a quantum-enhanced computation in the not-distant future. Boson sampling requires a large interferometric network which are challenging to build with bulk optics, we therefore perform our experiment on-chip. We model the effect of loss on our postselected experiment and implement a circuit characterization technique that accounts for this loss. Experimental imperfections, including higher-order emission from our photon pair sources and photon distinguishability, are modeled and found to explain the sampling error observed in our experiment.

Device-independent cryptography provides security in various tasks whilst removing an assumption that cryptographers previously thought of as crucial -- complete trust in the machinations of their experimental apparatus. The theory of Bell inequalities as a proof of indeterminism within nature allows for secure device-independent schemes requiring neither trust in the cryptographers' devices nor reliance on the completeness of quantum mechanics. However, the extreme paranoia attributable to the relaxed assumptions within device independence requires an explicit consideration of the previously assumed ability of the experimenters to freely make random choices. This thesis addresses the so-called `free will loophole', presenting Bell tests and associated cryptographic protocols robust against adversarial manipulation of the random number generators with which measurements in a Bell test are selected. We present several quantitative measures for this experimental free will, otherwise known as measurement dependence. We discuss how an eavesdropper maliciously preprogramming the experimenters' untrusted devices can falsely simulate the violation of a Bell inequality. We also bound the amount of Bell violation achievable within a certain degree of measurement dependence. This analysis extends to device-independent randomness expansion, bounding the guessing probability and estimating the amount of privacy amplification required to distil private randomness. The protocol is secure against either arbitrary no-signalling or quantum adversaries. We also consider device-independent key distribution, studying adversarial models that exploit the free will loophole. Finally, we examine a model correlated between the random number generators and Bell devices across multiple runs of a Bell test. This enables an explicit exposition of the optimal cheating strategy and how the correlations manifest themselves within this strategy. We prove that there remain Bell violations for a sufficiently high, yet non-maximal degree of measurement dependence which cannot be simulated by a classical attack, regardless of how many runs of the experiment those choices are correlated over.

To address key challenges for both quantum communication and quantum computing applications in a simultaneous manner, we propose to employ the photon angular momentum approach by invoking the well-known fact that photons carry both the spin angular momentum (SAM) and the orbital angular momentum (OAM). SAM is associated with polarization, while OAM is associated with azimuthal phase dependence of the complex electric field. Given that OAM eigenstates are mutually orthogonal, in principle, an arbitrary number of bits per single photon can be transmitted. The ability to generate/analyze states with different photon angular momentum, by using either holographic or interferometric methods, allows the realization of quantum states in multidimensional Hilbert space. Because OAM states provide an infinite basis state, while SAM states are 2-D only, the OAM can also be used to increase the security for quantum key distribution (QKD) applications and improve computational power for quantum computing applications. The goal of this paper is to describe photon angular momentum based deterministic universal quantum qudit gates, namely, {generalized-X, generalized-Z, generalized-CNOT} qudit gates, and different quantum modules of importance for various applications, including (fault-tolerant) quantum computing, teleportation, QKD, and quantum error correction. For instance, the basic quantum modules for quantum teleportation applications include the generalized-Bell-state generation module and the QFT-module. The basic quantum module for quantum error correction and fault-tolerant computing is the nonbinary syndrome calculator module. The basic module for entanglement assisted QKD is either the generalized-Bell-state generation module or the Weyl-operator-module. The possibility of implementing all these modules in integrated optics is discussed as well. Finally, we provide security analysis of entanglement assisted multidimensional QKD protocols, employing the proposed qudit modules, by taking into account the imperfect generation of OAM modes.

This thesis is concerned with studying the fascinating quantum properties of real-world nanostructures embedded in a noisy condensed matter environment. The interaction with light is used for controlling and manipulating the quantum state of the systems considered here. In some instances, laser pulses also provide a way of actively probing and controlling environmental interactions. The first two research chapters assess two different ways of performing all-optical spin qubit gates in self-assembled quantum dots. The principal conclusion is that an `adiabatic' control technique holds the promise of achieving a high fidelity when all primary sources of decoherence are taken into account. In the next chapter, it is shown that an optically driven quantum dot exciton interacting with the phonons of the surrounding lattice acts as a heat pump. Further, a model is developed which predicts the temperature-dependent damping of Rabi oscillations caused by bulk phonons, finding an excellent agreement with experimental data. A different system is studied in the following chapter: two electron spin qubits with no direct interaction, yet both exchange-coupled to an optically active mediator spin. The results of this study show that these general assumptions are sufficient for generating controlled electron spin entanglement over a wide range of parameters, even in the presence of noise. Finally, the Radical Pair model of the avian compass is investigated in the light of recent experimental results, leading to the surprising prediction that the electron spin coherence time in this molecular system seems to approach the millisecond timescale.