The potential of quantum computing has captured the interest of the academic and industrial spheres alike. However, the implementation of quantum systems for advantageous computation requires a good deal of further research, much of which must leverage classical computation techniques. In particular, relatively coherent hardware architectures have been fashioned from a variety of quantum systems, and numerous algorithms that are resilient to the noise of near to moderate-term devices have been proposed. In this thesis, we address both of these critical research fronts, exploring the dynamics of optical quantum systems as quantum information platforms and developing variational quantum algorithms. We also discuss the power of efficient tensor network representations for simulating quantum processes. \vspace{0.4cm} First, in the vein of quantum platforms, we develop physical models and operational protocols for both the Nitrogen-vacancy (NV) center in diamond and the dipole-dipole interactions in atomic arrays with subwavelength latice spacing. In the former, we demonstrate that electron-nuclear spin couplings can facilitate all-optical control of the nitrogen nuclear spin, including the manipulation of optical Rabi drives. As decoherent interactions dominate over coherent oscillations, we develop a Bayesian model comparison/parameter fitting framework to affirm the nature of these dynamics. In the later, we analytically characterize the interaction of multiple quantum emitters in a single array, highlighting the potential for long-lived quantum memory and tuneable quantum interactions. \vspace{0.4cm} Then, in the vein of quantum algorithms, we provide a myriad of solutions for the famed ``barren plateau'' problem, as well as introduce two novel algorithms for the circumvention of local minima in nonconvex training landscapes. In the former, we analytically characterize barren plateaus in terms of the spread of entanglement throughout a quantum landscape, framing it in terms of Langevin noise and devising initialization, entanglement regularization, and alternative measurement basis techniques for its curtailment. In the later, 1) Multi-Basis Encoding techniques are devised to improve the performance of quantum optimization algorithms while requiring fewer qubits, as well as highlighting the key features and advantages of tensor-based quantum machine learning simulation, and 2) a Markov chain Monte Carlo protocol for ergodically exploring the quantum optimization landscape (and thus avoiding local minima) is developed.
The potential of quantum computing has captured the interest of the academic and industrial spheres alike. However, the implementation of quantum systems for advantageous computation requires a good deal of further research, much of which must leverage classical computation techniques. In particular, relatively coherent hardware architectures have been fashioned from a variety of quantum systems, and numerous algorithms that are resilient to the noise of near to moderate-term devices have been proposed. In this thesis, we address both of these critical research fronts, exploring the dynamics of optical quantum systems as quantum information platforms and developing variational quantum algorithms. We also discuss the power of efficient tensor network representations for simulating quantum processes. \vspace{0.4cm} First, in the vein of quantum platforms, we develop physical models and operational protocols for both the Nitrogen-vacancy (NV) center in diamond and the dipole-dipole interactions in atomic arrays with subwavelength latice spacing. In the former, we demonstrate that electron-nuclear spin couplings can facilitate all-optical control of the nitrogen nuclear spin, including the manipulation of optical Rabi drives. As decoherent interactions dominate over coherent oscillations, we develop a Bayesian model comparison/parameter fitting framework to affirm the nature of these dynamics. In the later, we analytically characterize the interaction of multiple quantum emitters in a single array, highlighting the potential for long-lived quantum memory and tuneable quantum interactions. \vspace{0.4cm} Then, in the vein of quantum algorithms, we provide a myriad of solutions for the famed ``barren plateau'' problem, as well as introduce two novel algorithms for the circumvention of local minima in nonconvex training landscapes. In the former, we analytically characterize barren plateaus in terms of the spread of entanglement throughout a quantum landscape, framing it in terms of Langevin noise and devising initialization, entanglement regularization, and alternative measurement basis techniques for its curtailment. In the later, 1) Multi-Basis Encoding techniques are devised to improve the performance of quantum optimization algorithms while requiring fewer qubits, as well as highlighting the key features and advantages of tensor-based quantum machine learning simulation, and 2) a Markov chain Monte Carlo protocol for ergodically exploring the quantum optimization landscape (and thus avoiding local minima) is developed.
Quantum computers have come a long way since conception, and there is still a long way to go before the dream of universal, fault-tolerant computation is realized. In the near term, quantum computers will occupy a middle ground that is popularly known as the “Noisy, Intermediate-Scale Quantum” (or NISQ) regime. The NISQ era represents a transition in the nature of quantum devices from experimental to computational. There is significant interest in engineering NISQ devices and NISQ algorithms in a manner that will guide the development of quantum computation in this regime and into the era of fault-tolerant quantum computing. In this thesis, we study two aspects of near-term quantum computation. The first of these is the design of device architectures, covered in Chapters 2, 3, and 4. We examine different qubit connectivities on the basis of their graph properties, and present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and graphs with modular structure. Next, we discuss the problem of permuting qubits among the nodes of the connectivity graph using only local operations, also known as routing. Using a fast quantum primitive to reverse the qubits in a chain, we construct a hybrid, quantum/classical routing algorithm on the chain. We show via rigorous bounds that this approach is faster than any SWAP-based algorithm for the same problem. The second part, which spans the final three chapters, discusses variational algorithms, which are a class of algorithms particularly suited to near-term quantum computation. Two prototypical variational algorithms, quantum adiabatic optimization (QAO) and the quantum approximate optimization algorithm (QAOA), are studied for the difference in their control strategies. We show that on certain crafted problem instances, bang-bang control (QAOA) can be as much as exponentially faster than quasistatic control (QAO). Next, we demonstrate the performance of variational state preparation on an analog quantum simulator based on trapped ions. We show that using classical heuristics that exploit structure in the variational parameter landscape, one can find circuit parameters efficiently in system size as well as circuit depth. In the experiment, we approximate the ground state of a critical Ising model with long-ranged interactions on up to 40 spins. Finally, we study the performance of Local Tensor, a classical heuristic algorithm inspired by QAOA on benchmarking instances of the MaxCut problem, and suggest physically motivated choices for the algorithm hyperparameters that are found to perform well empirically. We also show that our implementation of Local Tensor mimics imaginary-time quantum evolution under the problem Hamiltonian.
Variational quantum algorithms (VQAs) have emerged as a promising candidate for realizing quantum advantage in machine learning and optimization tasks on noisy intermediate-scale quantum (NISQ) devices. Despite significant theoretical promise, the practical impact of VQAs is constrained by the exponential growth in computational resources required for classical simulation, the onset of barren plateaus in parameterized landscapes, and the inherent difficulties of scaling classical optimization routines to circuits with many qubits and layers. Addressing these intertwined challenges is essential for both advancing quantum algorithm development and extracting actionable physical insights from modern quantum hardware.This dissertation develops, analyzes, and validates an efficient framework based on approximate tensor ring decompositions for the classical simulation, training, and benchmarking of variational quantum circuits and eigensolvers. The first component of this work formalizes the representation of quantum states and gates within a cyclic tensor ring structure, enabling the compression of parameterized quantum circuits to linear scaling in both qubit number and circuit depth, while preserving essential quantum correlations and entanglement structure. Gate operations are efficiently approximated via truncated singular value decomposition, and novel algorithms for forward propagation and gradient-based training in the tensor ring domain are developed. These methodological advances are systematically benchmarked on standard supervised learning tasks, including Iris and MNIST datasets, and compared to conventional statevector and matrix product state baselines, resulting in competitive accuracy and orders-of-magnitude reductions in simulation cost. Extending this framework, the dissertation also introduces a scalable method for gradient evaluation in variational quantum eigensolvers (VQE) using the approximate tensor ring representation. This approach enables the simulation and training of large circuits for combinatorial optimization problems, supporting practical qubit counts and circuit depths inaccessible to traditional simulation methods. Detailed experiments on the Maximum-Cut optimization problem demonstrate both the computational efficiency and robustness of the tensor ring framework in nontrivial optimization landscapes.Collectively, the results establish approximate tensor ring decomposition as a versatile and powerful framework for advancing quantum machine learning and discrete optimization, supporting both pre-deployment benchmarking on classical hardware and algorithm design for next-generation quantum devices. This work provides a foundation for the further exploration of scalable quantum-classical hybrid algorithms, with implications for quantum simulation, optimization, and beyond.
Quantum machine learning promises to deliver near-term practical quantum computation applications using machine learning tools to optimize quantum hardware for scientific applications. Studies in this direction often propose using variational quantum circuits as the underlying hardware. However, these so-called VQCs exhibit flat landscapes with narrow and concentrated local minima, making their optimization inefficient and thwarting their advantage. This dissertation proposes using quantum many-body systems' dynamics for computation instead of circuits. This Analog quantum machine learning approach (AQML) uses tools from optimal control to deliver more manageable optimization landscapes and helps explain what types of computation are suitable for different hardware. Concretely, I show that arrays of Rydberg atoms can be leveraged to implement reservoir computers with enhanced memory storage and retrieval. I also show that two atom-species Rydberg arrays can reproduce the dynamics of the basic building blocks of artificial neural networks and be used for quantum-enhanced sensing and entanglement detection. This study shows that AQML algorithms are theoretically more expressive than their classical counterparts. Lastly, I show that while AQML algorithms can still exhibit problematic optimization landscapes, flatness can be mitigated, and local minima can be circumvented by co-designing the underlying hardware with the desired task. We exemplify this co-design in the context of quantum chemistry calculations. This dissertation shows that AQML algorithms can be used for various scientific and small-scale applications such as sensing, chemical design, entanglement witnessing, and time-series prediction. However, we still have a way to go before seeing full-scale applications. Instead, this dissertation focuses on theoretical studies and answers the question of what we can compute with quantum hardware's analog dynamics.
Quantum information science has emerged as one of the most promising fields in contemporary research, relying on both software and hardware innovations. This thesis looks for both algorithms with quantum features that provide advantages over classical algorithms, and better hardware platforms for experiments and quantum computing. The work spans theoretical studies in both algorithm and hardware design, including hybrid quantum-classical algorithms and the development of quantum information processing platforms. The algorithmic part has focused on the performance of a hybrid quantum algorithm - the Grover Quantum Approximate Optimization Algorithm (Grover QAOA) - designed for problems with multiple solutions. In practice, we find its potential for speedup in solution search and its ability to find all solutions. Furthermore, we propose a simplified protocol that reduces the classical complexity of optimizing the algorithm’s parameters, enhancing its practicality for future applications. Our implementation of Grover QAOA for multiple combinatorial optimization problems on trapped-ion quantum computers demonstrates that the algorithm can fulfill its fair-sampling advantage even on noisy devices. In the hardware part, we mainly explore how the motion of cold atoms can either be used to engineer interactions or lead to previously overlooked decoherence. The first hardware platform we discuss is trapped ions, where we focus on implementing individual addressing to natively simulate new types of many-body systems. Our proposal leverages the exceptional controllability of trapped ions to explore dynamical models such as topological pumping. The second hardware platform we study is Rydberg atom lattices, where we investigate the decoherence processes introduced by atomic motion during dynamics. Using the numerical tool of discrete truncated Wigner approximation, we simulate the coupled dynamics of electronic and motional degrees of freedom, demonstrating that atom motion induced by strong van der Waals interactions in Rydberg atoms can lead to significant decoherence in analog simulation experiments. We have also explored specialized topics involving other quantum hardware platforms. One area of study is the reduction of frequency crowding in superconducting circuit quantum chips. By properly designing the frequencies for each transmon qubit, we can improve the manufacturing yield of collision-free processors. Another area focuses on the SU(N) Fermi-Hubbard models on alkaline-earth-metal optical lattice platforms. We have obtained the phase diagram of unit-filling models with imbalanced spin flavors. This work aids future experiments in searching for potential ground states of the unit-filling SU(N) model.
This paper presents a comprehensive review and systematic coverage of foundational quantum optimization algorithms-QAOA, Quantum Annealing, VQE, VQLS, and HHL-tracing their development all the way from Schrödinger's equation through gate-based quantum computing (Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, QFT, Shor's, and Grover's algorithms) to hybrid quantum-classical approaches for NISQ-era hardware. We also present the transverse field Ising model's role in quantum annealing as well as practical hardware implementations with the Chimera, Pegasus, and Zephyr topologies of the D-Wave quantum annealer, addressing key challenges including barren plateaus, circuit trainability, and noise resilience. In the simulations section, quantum computing applications to collaborative filtering and social network optimization have been presented. We introduce two original contributions: (1) a quantum collaborative filtering model based on VQE principles that leverages quantum entanglement to represent user-item relationships, requiring logarithmically fewer parameters than classical embedding methods while accessing exponentially larger state spaces, and demonstrating test RMSE of 0.85 on synthetic data; and (2) a Quantum Social Network (QSN) framework modeling belief dynamics through superposition and entanglement, revealing emergent consensus and polarization phenomena validated via Qiskit simulations. By demonstrating that variational quantum algorithms can tackle real-world recommendation and network optimization problems on current hardware, we bridge theoretical quantum computing with practical machine learning applications and identify concrete pathways toward quantum advantage beyond traditional combinatorial optimization.
Abstract We present a variational quantum circuit (VQC) that utilizes the architecture of a quantum neural network (QNN) to simulate hyperfine interactions in diamond nitrogen vacancy (NV) centers, which is typically a challenging task for traditional computation methods. Isotopes of 13 C, though naturally rare, possess a nuclear spin ( l = 1 2 ) which anisotropically interacts with the NV center’s electron spin, resulting in distinct hyperfine structure and coherence properties. The VQC’s ansatz unitary was implemented stepwise (through optimization Trotter steps) to mimic a multi-layered QNN configuration. The dynamical evolution of the 14 NV- 13 C Hamiltonian was simulated while maintaining flexibility for optimization on noisy intermediate-scale quantum (NISQ) platforms. Qiskit SDK was used to design and execute the circuit on 127-qubit IBM quantum hardware. Ansatz parameters were optimized using six classical optimization algorithms initialized with pseudo-random parameter vectors. We successfully determined optimal ansatz parameters for estimating the minimum energy eigenvalues of the 14 NV- 13 C observable using the VQC’s cost function, enabling us to model the system’s ground state dynamics. Our findings show that gradient-free optimizers are efficient for the designed Hardware Efficient SU(2) 2-local circuit (ESU2) ansatz, characterized by a barren plateau landscape. We further established that a maximally entangled VQC initialization (i.e., GHZ 3 ) retains its entanglement scheme irrespective of the optimization pathway. Hence, this approach highlights the effectiveness of QNN-inspired VQC circuits for accurately simulating NV centers coupled with strongly interacting nearest-neighbor nuclear spins. Our work lays down a foundational step for realizing precise control on near-term quantum hardware that utilizes NV centers, leading to high fidelities.