Theses

Quantum technologies and quantum information science promise unprecedented capabilities in computation, sensing, and communication. Realizing these capabilities requires the development of robust quantum platforms tailored to specific information-processing tasks. Among the leading candidates, electronic and nuclear spins in solid-state systems offer an attractive combination of controllability, robustness, and accessibility. In particular, nitrogenvacancy (NV) centers in diamond provide excellent quantum control and long coherence times under ambient conditions, while molecular spin systems offer rich internal structure and exceptional tunability through chemical design. In this thesis, we explore and integrate these platforms to advance both the fundamental understanding and practical applications of spin-based quantum systems. The work is organized around three main directions: understanding decoherence mechanisms in molecular spin qubits, developing hybrid NV–molecular platforms, and enabling quantum sensing and information processing through experimental and computational techniques. First, we develop a combined experimental and theoretical framework to investigate transverse relaxation in molecular spin systems, using copper(II) phthalocyanine (CuPc) as a model platform. By combining pulsed electron paramagnetic resonance (EPR) spectroscopy with cluster correlation expansion (CCE) simulations, we quantitatively disentangle the contributions of nuclear spins, spin–lattice relaxation, and electron–electron dipolar interactions. We find that nuclear spins contribute negligibly to decoherence, while dipolar interactions between electron spins dominate T2 through instantaneous and spectral diffusion, even at moderate spin densities. This framework provides quantitative design guidelines for molecular spin qubits and establishes a transferable methodology for predicting coherence in complex spin environments. Second, we investigate hybrid quantum platforms that combine paramagnetic molecular spins with NV centers in diamond. Molecular systems offer tunability but lack efficient singlespin control, whereas NV centers provide optical addressability and high sensitivity but face scalability challenges due to stochastic formation. To bridge these complementary strengths, we develop a hybrid NV–molecular approach in which shallow NV centers act as local probes of nearby molecular spins. Using T1 relaxometry, we detect and characterize the electron spin ensemble of a CuPc thin film under ambient conditions. Through quantitative modeling of the NV–molecule interaction, we extract key spin parameters inaccessible to conventional EPR and achieve nanometer-scale estimation of NV depth. These results establish the feasibility of hybrid NV–molecular systems and lay the groundwork for their coherent control. Third, we explore molecular qubits based on optically addressable transient electronic states, exemplified by photoexcited pentacene molecules. Despite their finite lifetimes, these systems enable sensing capabilities beyond conventional solid-state defects. We demonstrate microwave vector magnetometry at zero magnetic field and room temperature, and identify nuclear-spin-induced low-frequency noise as the dominant decoherence source. By developing a phase-alternated control protocol, we suppress this noise and extend coherence by more than an order of magnitude, achieving sensitivities of 1 µT / √ Hz with sub-micrometer spatial resolution. We further enhance coherence via nuclear spin hyperpolarization, establishing molecular triplet systems as a powerful platform for quantum sensing. Finally, to extend these advances across disciplines, we develop complementary computational and algorithmic approaches. We introduce a denoising framework for NV dynamical decoupling data that improves the accuracy of extracting nuclear spin coupling parameters. We also propose a communication-efficient quantum algorithm for estimating vector inner products, a key primitive in modern machine learning. Together, these results advance the understanding, control, and application of spin-based quantum systems, and establish new pathways toward scalable and versatile quantum technologies.

Wide-field magnetic imaging using nitrogen-vacancy (NV) centers in diamond can yield high-quality images for various applications, including biology, geology, condensed matter physics, and electronics troubleshooting. These quantum sensors yield widefield-of-view images with micron-scale spatial resolution and operate in ambient conditions. Most of the sensing work with NV centers in diamond has focused on DC and low frequency AC fields. This thesis demonstrates a wide-field magnetic imager and its capabilities with test structures of varying complexity. We overcome the challenges for measuring MHz frequency magnetic fields with a quantum frequency mixing approach.

Recent years have witnessed rapid development in the field of quantum information science. Quantum technologies are promising to revolutionize many fields, ranging from fast computation and simulation to precise sensing and secure communication. While the performance of quantum devices in the current noisy intermediate-scale quantum (NISQ) era is still limited, exploring intriguing applications of various quantum systems has been an active research area. Among the many physical platforms, solid-state spin defects, such as nitrogen-vacancy (NV) center in diamond, have attracted a lot of attentions thanks to their good controllability and long coherence time even at room temperature. In this thesis, we present our efforts in demonstrating promising quantum applications based on the NV system. With microwave and optical pulses, we have good control on the NV center system, which enables us to engineer the desired Hamiltonian and probe the information of quantum states. In particular, the geometry of a quantum state is characterized by the quantum geometric tensor (QGT), which can find applications in simulating topological material and quantum metrology. We experimentally measure the QGT of an engineered Hamiltonian in a single NV center using weak periodic modulation method. Based on it, we are able to reveal the existence of a tensor monopole that characterizes a tensor gauge field in parameter space. Furthermore, we find that the QGT plays a significant role in quantum multi-parameter estimation. It not only quantifies the precision limit when estimating parameters but also links to the attainability of precision bounds. Thanks to the sensitivity studied above, NV centers have emerged as powerful quantum sensors to detect various signals, ranging from electromagnetic fields to temperature, with high sensitivity and spatial resolution. Detecting biological or chemical signals is more challenging, but a promising avenue is to transduce them into magnetic noise that the NV center is sensitive to. We demonstrate this strategy by measuring the rotational Brownian motion of magnetic molecules. Then, exploiting the dipolar interaction between NV centers and magnetic molecules, we design a hybrid sensor that is capable of detecting the SARS-CoV-2 virus RNA with ultrahigh sensitivity and low false negative rate. Finally, we will show that the charge state of NV centers is sensitive to surface modification of nanodiamond, which enables us to design alkali ion sensors with the help of chemical engineering.

Electronic spin defects in the environment of an optically-active spin can be used to increase the size and hence the performance of solid-state quantum registers, especially for applications in quantum metrology and quantum communication. Previous works on multi-qubit electronic-spin registers in the environment of a Nitrogen-Vacancy (NV) center in diamond have only included spins directly coupled to the NV. As this direct coupling is limited by the spin coherence time, it significantly restricts the register’s maximum attainable size. To address this problem, this thesis presents a scalable approach to map out and control a network of interacting environmental spins. We use this approach to characterize a spin network beyond the direct-coupling limit and exploit a weakly-coupled probe spin to mediate the transfer of spin polarization between the central NV and an environmental spin that is not directly coupled to it. We then demonstrate both detection and coherent control of this electronic spin outside the coherence limit of the central NV. Our work paves the way for engineering larger quantum spin registers with the potential to advance nanoscale sensing, enable correlated noise spectroscopy for error correction, and facilitate the realization of spin-chain quantum wires for quantum communication.

Solid-state spin defects have garnered significant interest in recent years due to their potential for various quantum applications, ranging from sensing, simulation to communications. Despite the fast progress of the field in the past decades, numerous challenges remain before these applications can be fully realized in broader scenarios. Among the issues that need to be addressed are deleterious decoherence and low-fidelity control, and the lack of critical capabilities such as vector field sensing at nanoscale and arbitrary frequency field sensing. Additionally, a deeper understanding of the rich dynamics associated with the charge degrees of freedom of various defect states in the material host is necessary. This thesis aims to tackle these challenges and contribute to the development of better quantum sensors and simulators. The study starts with quantum control based on modulated driving, which allows for the engineering of more flexible driving strength and the control of evolution modes. By utilizing modulated control techniques, we experimentally observe high-order effects beyond the traditional rotating wave approximation and protect Rabi coherence by more than one order of magnitude in an ensemble of NV centers in diamond. Moreover, we exploit the modulated driving to simulate dynamical symmetries and characterize their selection rules using projective measurements of the coherence evolution of the system. The same control technique is shown to further design parallel quantum gates for atom array quantum platforms. Inspired by the flexible quantum control in different frames, we develop protocols to improve quantum sensing performances. In sensing coherent signals, we develop a protocol to sense vector ac field at nanoscale using a single spin. To broaden the frequency range of quantum sensors, we develop a quantum mixer to convert off-resonant signal fields to resonant ones, achieving the sensing of arbitrary frequency vector fields. To overcome the challenge of degraded coherence in large (nuclear) spin ensembles, we develop a novel unbalanced echo sequence to refocus the dominant noise in the intrinsic hyperfine interaction and quadrupole terms, which extends the dephasing time of a large spin ensemble to the single spin limit. In sensing stochastic signals, we develop a digital noise spectroscopy approach based on Walsh dynamical decoupling sequences to eliminate systematic error due to approximating frequency filters with delta functions. All these protocols are experimentally demonstrated with NV center platforms. Given that the charge states of defects play an important role in the performance of aforementioned quantum applications due to their influence on the spin state and coherence, we use NV centers to probe the charge dynamics by characterizing the bath spectrum under different optical illumination conditions. With a fast wide-field imaging setup integrated with a SPAD array, we observe the process of charge transport through the redistribution of spin concentration of P1 centers and other spin defects in the bath. The potential tunability of spin concentration in time and spatial domain paves the way for their applications in simulating quantum many-body dynamics such as quantum hydrodynamics. In summary, this thesis studied the improvement of quantum control and the development of better sensors and simulators with solid-state defects. Although experiments in this thesis are performed with spin defects in diamonds, many of the studied topics are general to most quantum platforms, such as modulated control, dynamical decoupling, coherence protection, noise spectroscopy, etc. Thus, we foresee broader applications of the thesis research outcome both in realizing quantum sensors and networks with solid-state spin defects, and in extending the developed control techniques for characterizing and improving the performance of other quantum platforms.

In the past 15 years, quantum sensing of magnetic fields using nitrogen-vacancy (NV) center ensembles in diamond has matured into an established discipline, with several proof of principle demonstrations in condensed matter physics, biological systems, electronics testing, and geomagnetism. However, despite the prospect of comparable magnetic field sensitivity, the performance of NV bulk magnetometers sensing low-frequency fields continues to lag behind that of their atomic vapor cell and superconducting counterparts by about three orders of magnitude. Detecting GHz-frequency fields compares much worse, with an additional three order of magnitude reduction in demonstrated sensitivity. This thesis presents two experimental thrusts designed to improve an NV-ensemble magnetometer by optimizing diamond processing and sensor construction. We first investigate the irradiation and annealing process of diamond samples by developing an NV-charge state spectral decomposition technique, which we use to examine the creation dynamics and diffusion of monovacancies in the diamond lattice. We also examine the behavior of the spin coherence timescales under increasing electron irradiation doses. We then construct an NV-ensemble magnetometer by implementing and expanding upon the best techniques used for diamond growth, microwave delivery, optical excitation and readout, and pulse-control sequences. We use this sensor to demonstrate the most sensitive NV-based bulk magnetometer reported to date in both broadband and narrowband operation, sensing fields in the kHz and GHz frequency range. These experimental efforts demonstrate a deeper understanding and improvement in NV-ensemble magnetometry, opening up new application spaces in several frequency bands of interest.

Quantum thermalization is a generic process that a quantum system reaches its equilibrium. Quantum thermalization lies in the interface of various distinct fields, ranging from condensed matter physics and quantum cosmology to quantum information science. The converging efforts from different fields open up avenues for the development of quantum many-body physics and quantum technology. This thesis presents a study of quantum thermalization in solid-state nuclear spin systems using nuclear magnetic resonance technique. By developing the RF control sequences, novel states, observables and Hamiltonians are created to explore and characterize various quantum thermalization phenomena. Leveraging the intrinsic disorder, a novel method to detect spin dynamics at single-site level is introduced. The method is applied to study hydrodynamics emerged from thermalizing quantum systems. In an interacting integrable system, coexistence of ballistic energy transport and diffusive spin transport is observed. With accurate Hamiltonian engineering RF sequences, the thermalization of driven systems are discussed. The exponentially slow thermalization is observed experimentally by measuring the prethermal energy autocorrelation. Beyond the prethermal energy, an even more robust prethermal conserved quantity is discovered. The result suggests a Floquet phase may exist beyond the prethermal regime. To understand many-body localized (MBL) systems, an algorithm to compute local integrals of motion (LIOMs) is designed. From LIOMs, various localization lengths are extracted and their critical behavior is studied. To further improve the Hamiltonian engineering sequences, the deep reinforcement learning (DRL) techniques are adopted. The sequences designed by the DRL show better decoupling performance than the previously best known sequence. Beyond that, a new and advantageous pattern is discovered from the DRL sequences which serves as a useful building block for more complex Hamiltonian engineering sequences.

Interactions between a quantum system and its environment are usually inevitable and could lead to decoherence limiting the performance of quantum devices. On the one hand, to build robust quantum devices requires an in-depth characterization of such decoherence mechanism. On the other hand, the extracted environmental information brings us new approaches to investigate novel phases in quantum materials. Thus, probing and characterizing environmental noise is an essential task for both fundamental physics and quantum applications. Existing noise reconstruction methods in quantum systems rely on using approximated delta-like frequency filtering to sample the noise spectrum in frequency domain using dynamical decoupling sequences. In this thesis, we propose a novel digital noise reconstruction method to reconstruct the environmental noise both in frequency and time domains, which avoids the delta function approximation for frequency filtering. By measuring the decoherence of a qubit sensor under a set of Walsh modulation sequences, the (arithmetic) auto-correlation of a stationary Gaussian noise that couples to the quantum sensor is directly reconstructed and the corresponding noise spectrum is then reconstructed through linear transformations (discrete Fourier transform). We systematically compare the typical dynamical decoupling-based noise reconstruction method (the Carr-Purcell-Meiboom-Gill reconstruction method) and the Walsh reconstruction method by evaluating the reconstruction errors of both methods under an Orstein-Unlenbeck noise model, which is commonly adopted to describe the magnetic noise generated by a dipolarly coupled spin bath. Combining theoretical and simulation results, we conclude that the accuracy of our Walsh reconstruction method is only limited by the time-space sampling and can be easily suppressed by increasing the reconstruction order. We then perform a proof-of-principle demonstration using a single nitrogen-vacancy center in diamond to characterize its environmental noise dominated by the carbon-13 nuclear spin bath, and discuss the practical limitations of the reconstruction accuracy and avenues for its improvement. Finally we also introduce several directions of interest for future research.

Quantum sensing and quantum simulation are emerging areas in quantum science and technology with broad applications. In this thesis, we explore Hamiltonian engineering techniques to build better quantum sensors and quantum simulators. In quantum sensing, advanced control techniques are required to extract all the information available about the sensing target from the sensor. Unfortunately, one major challenge to implementing the optimal control sequence-which extracts the maximum information-is the clock rate of the (classical) hardware used to control the sensor. To overcome this challenge, we develop a novel control technique inspired by quantum simulation (“quantum interpolation”) and achieve an effective six picoseconds sampling rate from the hardware-constrained two nanoseconds. This improved sampling rate enables a higher precision in measuring classical fields and the quantum signal arising from a single nuclear spin.

Isolated optically-active solid-state spins such as the Nitrogen-Vacancy (NV) center in diamond have demonstrated good properties as qubits for quantum information tasks. However, engineering larger quantum registers around a central NV enables more powerful applications. For example, a register of nuclear spins around the NV has already demonstrated many quantum protocols such as quantum error correction and entanglement distillation. Still, thanks to their stronger coupling to the NV and external fields, a register of electronic spins would enable new complementary applications, such as quantum enhanced sensing and scalable architectures for quantum computation. In this thesis, three critical steps are demonstrated toward the goal of developing a small-scale quantum information processor based on electronic spins in diamond. First, we develop a method to systematically scale up a system of electronic spins starting from one qubit – the optically-addressable NV – by characterizing the Hamiltonian of nearby optically-dark electron-nuclear spin defects in its microscopic environment. The knowledge of the system Hamiltonian, which characterizes spin defects in the solid, further enables coherent control over the system. Second, we characterize the quantum register of electronic spins with respect to two important aspects: entanglement and decoherence. As entanglement is critical to many quantum information tasks, an accurate characterization of entanglement generated by a quantum device is desired. Therefore, to improve upon the conventional entanglement witness based on the state fidelity, we develop a new metric, called the subspace witness, that is more robust in the presence of local unitary control errors. The subspace witness, at the cost of additional measurements, is insensitive to any combination of single-qubit phase errors accrued during the state-preparation-and-measurement of the target entangled state. Furthermore, as the power of quantum devices is limited by decoherence, a practical (i.e., classical) and predictive noise model for the device is desired. As the first step to characterize the coherence of a multi-qubit register, we demonstrate a method to build a self-consistent classical noise model for individual qubits. For the NV qubit, well isolated from the bath, it is possible to develop a self-consistent model, which not only characterizes the bath but can help develop more robust quantum gates and circuits. However, for a nearby qubit, this is not possible due to a possibly a more complex and quantum bath for this qubit – which, after future investigation, may further scale up the size of the quantum register. Finally, to demonstrate the potential advantage of an electronic spin register, we implement a quantum information task in sensing of external fields. The electronic spins serve to enhance the sensitivity not only via entanglement, but also through a repetitive readout scheme. This result paves the way towards practical quantum advantage in sensing. The methods and results presented in this thesis outline a path toward developing small-scale quantum registers based on electronic spins in diamond and demonstrate their practical applications to enhance a broad range of tasks in quantum information processing.

Quantum technologies promise to revolutionize many fields, ranging from precise sensing to fast computation. The success of novel technologies based on quantum effects rests on engineering quantum systems robust to decoherence-the uncontrollable decay of quantum coherence, one of the very features that empowers quantum computation. To date, performance of quantum devices in the noisy intermediate-scale quantum (NISQ) era is still limited by decoherence. The long term solution is universal quantum computers that run on fault-tolerant quantum error corrected logical qubits which are immune to decoherence. However, the substantial overhead of qubits and quantum gates quantum error correction (QEC) imposes is thought to greatly limit its utility in NISQ devices.

Precise control of coherent quantum systems could enable new generations of sensing, communication and computing technologies. Such systems, however, are typically noisy and difficult to stabilize. One promising technique to this end is called quantum error correction, which encodes quantum states in such a way that errors can be detected and corrected, much like in classical error-correcting codes. Quantum error-correcting codes usually cast a wide net, in that they are designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. It comes at a cost, however: conventional quantum codes are typically resource-intensive in terms of both the system size and the control operations they require. Yet, in smaller-scale devices the main error sources are often well-understood. In the near term, it may therefore be advantageous to cast a more targeted net through specialized codes. This thesis presents new families of such quantum error-correcting codes, which are adapted either for leading candidate devices, or for near-term applications. The device-adapted codes require exponentially less overhead than conventional codes to achieve the same level of protection, whereas the application-adapted codes can enhance quantum sensors, in which conventional codes cannot readily be used. The new techniques presented in this thesis adapt cornerstones of conventional theory in light of key experimental challenges and opportunities. The ultimate goal of this research is to help bridge the gap between the exacting requirements of proposed quantum technologies and the realities of emerging quantum devices. Bridging this gap is critical, if quantum technologies are to realize their full potential.

How can a quantum many-body system escape the fate of thermalization is of importance to both fundamental study of quantum statistical physics and applications in quantum devices. Here we develop novel experimental and computational tools to address this question. First, novel control techniques are introduced to investigate prethermalization, a process where a quantum system fails to thermalize on a practical timescale. Prethermalization is demonstrated by measuring out-of-time ordered (OTO) correlations in nuclear spin systems with magnetic resonance techniques. Hamiltonian engineering enables tuning the strength of spin-spin interactions and of a transverse magnetic field in a spin chain system, as well as to invert the Hamiltonian sign to reveal OTO correlations. The experiments reveal that at high fields an emergent conserved quantity arises due to prethermalization, and the OTO commutator involving such prethermal conserved quantity saturates after a short time.

Quantum information processing, including quantum computation, quantum communication, and quantum metrology, is expected to be the next-generation information technology capable of outperforming classical devices. The physical platform for quantum information devices requires many-body quantum systems with many interacting qubits (two-level systems), and several experimental systems have been actively studied in recent years for realizing such scalable quantum information processors. Reliable quantum information processing essentially requires robust initialization of the quantum system, robust control protocols and precise measurement. As these indispensable tasks strongly depend on the physical properties and dynamics of the quantum system, the precise characterization of the experimental system, namely quantum system identification, is a crucial prerequisite.

This thesis presents a study of many-spin dynamics using a Nuclear Magnetic Resonance (NMR) simulator. A novel correlation metric was designed and experimentally measured in a solid state spin chain system to investigate the dynamics of quantum information transport. By using control techniques to tune the parameters of the system interactions, the effects of disorder and interaction on the dynamics were investigated experimentally. It was shown that in the absence disorder can quench the spread of quantum information; while with weak interaction and disorder, quantum information can spread, albeit slowly. Having found a connection between the correlation metric and the recently proposed out-of-time ordered commutator, the correlation metric was used to experimentally probe a transition between ergodic and prethermal dynamics. Future experiments using out-of-time ordered commutators as a tool to probe many-body localization transition are discussed.

The nitrogen-vacancy (NV) center in diamond has emerged as a promising platform for high-sensitivity, vector magnetic field detection and high spatial resolution magnetic-field imaging due to its unique combination of optical and spin properties. NV diamond magnetometry has enabled a wide array of applications from the noninvasive measurement of a single neuron action potential to the mapping [mu]T-fields in [mu]m-size meteorite grains. To further improve the magnetic sensitivity of an ensemble NV magnetometer, the growth and processing of the host diamond must be taken into account. This thesis presents a systematic study of the effects of diamond processing on bulk chemical-vapor-deposition diamond. In particular, NV charge-state composition and spin decoherence times are measured for diamonds irradiated with 1 MeV electrons at doses of 1×1015-5×1019 e-/cm2 and thermally annealed at temperatures of 850°C and 1250°C. The study provides an optimal range for diamond processing and shows the quenching of the NV center at high irradiation dosage from the creation of additional vacancy-related defects.

This thesis describes experimental and theoretical work making contributions in the general areas of quantum metrology, simulation and control. Specifically, we describe new approaches for high resolution magnetic resonance imaging using quantum sensors, that could potentially achieve the determination of single molecular structure. We show experiments that boost the sensing resolution of these sensors by over a factor of 100. We also develop separate methods for the sensitive detection of DC magnetic fields, and rotations. Also developed are techniques for the engineering of many-body Hamiltonians with restricted just global control fields, a task of wide interest for quantum simulation. Finally the toolbox available for quantum control is expanded for various applications in quantum information processing and simulation.

This thesis introduces and experimentally demonstrates coherent control techniques to exploit electron spins in diamond for applications in quantum information processing and quantum sensing. Specifically, optically-detected magnetic double resonance measurements are performed on quantum states of single and multiple electron spins associated with nitrogen-vacancy centers and paramagnetic centers in synthetic diamond crystals. The Walsh reconstruction method is introduced as a general framework to estimate the parameters of deterministic and stochastic time-varying fields with quantum sensors. The Walsh method generalizes sampling techniques based on dynamical decoupling sequences and enables measuring the temporal profile of time-varying magnetic fields with increased precision in the presence of noise and environmental fluctuations. Coherent control techniques are further introduced to identify, integrate, and exploit unknown quantum systems located in the environment of a quantum probe. In particular, entangled states of two and three electron spins in diamond are created to estimate the amplitude of time-varying magnetic fields. These results demonstrate a scalable approach to measure time-varying fields with quantum probes in solid-state materials for applications in environment-assisted quantum metrology, such as real-time functional imaging of neural activity at the level of a single neuron, magnetic resonance spectroscopy and imaging of biological complexes in living cells; and characterization of the structure and dynamics of new magnetic materials.

The precise control of a system which behaves according to the principles of quantum mechanics is an indispensable task in order to fully harness unique properties of quantum mechanics, such as superposition and entanglement, for practical applications. Leveraging the quantum nature of the system would enable for example the implementation of quantum computation and quantum metrology. However, any realistic quantum system is inevitably coupled to its environment. The interaction with its surroundings irrevocably destroys the quantum nature of the system: mitigating decoherence is thus one of the central problems in quantum control. In this thesis, we develop novel control methods to protect a qubit from decoherence by two distinct approaches and demonstrate them experimentally using the nitrogen-vacancy (NV) center in diamond. The first method rests on an open-loop control scheme and it is tailored to improve quantum sensing tasks. We develop a continuous dynamical decoupling (CoDD) method that allows us to tune the degree of protection from a dephasing environment. Exploiting this flexibility, we show that the CoDD can be used to measure magnetic fields with sensitivity comparable to existing methods, while providing superior versatility in practical experimental settings. This protocol can adapt to various sensing conditions, such as measurement time and sensitive frequency, that might occur in biological and material science. The second method exploits a coherent feedback protocol. We take advantage of a long-lived nuclear spin as an ancillary spin to protect the qubit of interest from decoherence. We show that the protocol protects the qubit as long as open-loop dynamical decoupling control schemes and it can be used against more general types of noise than the open-loop protocol. This method thus offers an alternative protocol to protect the qubit from decoherence in quantum computation and quantum metrology.

The Nitrogen-Vacancy (NV) defect in diamond has shown considerable promise in the field of small scale magnetometry due to its high localization and retention of favorable optical properties at ambient conditions. Current methods of magnetometry with the NV center achieve high sensitivity to fields aligned with the defect axis; however, with most present methods transverse fields are not directly measurable. The all-optical method of NV magnetometry provides a means to detect transverse fields by monitoring changes in the overall fluorescence profile. In this work the all-optical method is extended to ensembles of non-interacting NV centers. By establishing an external bias field aligned with the (1, 1, 1) axis, the magnitude of an unknown transverse field can be unambiguously identified through the measurement of the signal curvature. The angular orientation can be determined up to a two-fold degeneracy by observing the change in signal curvature produced when the bias field is shifted off-axis. The magnetometry method explored in this thesis thus provides good sensitivity to transverse fields, while reducing to a minimum the experimental apparatus required to operate the magnetometer.

In this thesis, we discuss two problems of quantum dynamics in the presence of alternating controls. Alternating controls arise in many protocols designed to extend the duration over which a qubit is a useful computational resource. This is accomplished by control sequences that either retard decoherence, or that accomplish a quantum operation in as short a time as possible. The first problem tackles the use of a composite-pulse control sequence known as ‘rotary-echo’ for quantum magnetometry purposes. The sequence consists in the continuous drive of a qubit, with field phases that alternate at specific intervals. We implement such a magnetometry protocol using an electronic qubit in diamond, and experimentally confirm the flexibility yielded by the tuning of sequence parameters that achieves a good compromise between decoherence resilience and sensitivity. The second problem theoretically investigates the time-optimal evolution of a qubit in the case of a restricted control set composed of alternating rotations around two non-parallel axes on the Bloch sphere. Using accessible algebraic methods, we show that experimental parameters, such as the angle between the two rotation axes, restrict the necessary structure of time-optimal sequences. We propose to implement such an evolution through alternate driving as an advantageous alternative to the slow, noisy direct addressing of a nuclear qubit anisotropically hyperfine-coupled to an electronic spin in diamond.

Coherence and entanglement in multi-spin systems are valuable resources for quantum information processing. In this thesis, I explore the manipulation of quantum information in complex multi-spin systems, with particular reference to Nuclear Magnetic Resonance implementations. In systems with a few spins, such as molecules in the liquid phase, the use of multi-spin coherent states provides a hedge against the noise, via the encoding of information in logical degrees of freedom distributed over several spins. Manipulating multi-spin coherent states also increases the complexity of quantum operations required in a quantum processor. Here I present schemes to mitigate this problem, both in the state initialization, with particular attention to bulk ensemble quantum information processing, and in the coherent control and gate implementations. In the many-body limit provided by nuclear spins in single crystals, the limitations in the available control increase the complexity of manipulating the system; also, the equations of motion are no longer exactly solvable even in the closed-system limit. Entanglement and multi-spin coherences are essential for extending the control and the accessible information on the system. I employ entanglement in a large ensemble of spins in order to obtain an amplification of the small perturbation created by a single spin on the spin ensemble, in a scheme for the measurement of a single nuclear spin state. I furthermore use multiple quantum coherences in mixed multi-spin states as a tool to explore many-body behavior of linear chain of spins, showing their ability to perform quantum information processing tasks such as simulations and transport of information. The theoretical and experimental results of this thesis suggest that although coherent multi-spin states are particularly fragile and complex to control they could make possible the execution of quantum information processing tasks that have no classical counterparts.