As quantum computing progresses into the new Quantum Utility era—marked by the ca- pability to execute increasingly complex computations with improved fault tolerance—systems exceeding 1,000 qubits have already been demonstrated by Atom Computing and IBM. While the majority of academic and industrial efforts remain focused on qubit-based archi- tectures, built on decades of work in two-state computational logic and algorithms, growing attention is now turning to the untapped potential of qudits—quantum units that ex- tend beyond the binary nature of qubits. Research into qudits is gaining momentum, as increasing the number of computational states per unit can significantly enhance compu- tational power and reduce circuit complexity. This paradigm shift opens the door to more efficient quantum algorithms and hardware architectures. Moreover, hybrid systems that integrate qubits and qudits may provide a powerful bridge between existing technologies and next-generation performance—making qudit research a critical frontier in unlocking the full potential of quantum computing.This dissertation presents a comprehensive framework for implementing a hybrid quan- tum architecture using fluxonium-based qudits. Fluxonium circuits, constructed from a superconducting loop interrupted by a Josephson junction and a large inductance, exhibit strong anharmonicity and non-fixed selection rules. These features enable multiple direct transitions between quantum states, which can be precisely tuned through a set of circuit parameters known as fluxonium characteristic values. A detailed study of these parameters was conducted to identify optimal qudit systems within a ten-dimensional Hilbert space (D = 10), with estimated coherence times comparable to those of conventional qubit sys- tems. Theoretical and numerical tools were developed to extend the approach to higher dimensions. A set of universal qudit logic gates was designed for arbitrary dimensions D = 2^n, as well as some gates and gate combinations in high dimension Hilbert space. The study demonstrates a significant reduction in gate complexity—particularly in the number of driving pulses required for multiply-controlled gates. Additionally, hybrid logic circuits using D = 8 and D = 4 qudits were analyzed, revealing reduced circuit complexity com- pared to qubit-only implementations. In summary, this work shows that fluxonium superconducting circuits are well-suited systems extending the traditional two-level qubit into multi-level qudit operation, where accessing higher energy levels can enhance computational capacity, reduce gate overhead, and enable more efficient quantum algorithms compared to standard qubit architectures.
As quantum computing progresses into the new Quantum Utility era—marked by the ca- pability to execute increasingly complex computations with improved fault tolerance—systems exceeding 1,000 qubits have already been demonstrated by Atom Computing and IBM. While the majority of academic and industrial efforts remain focused on qubit-based archi- tectures, built on decades of work in two-state computational logic and algorithms, growing attention is now turning to the untapped potential of qudits—quantum units that ex- tend beyond the binary nature of qubits. Research into qudits is gaining momentum, as increasing the number of computational states per unit can significantly enhance compu- tational power and reduce circuit complexity. This paradigm shift opens the door to more efficient quantum algorithms and hardware architectures. Moreover, hybrid systems that integrate qubits and qudits may provide a powerful bridge between existing technologies and next-generation performance—making qudit research a critical frontier in unlocking the full potential of quantum computing.This dissertation presents a comprehensive framework for implementing a hybrid quan- tum architecture using fluxonium-based qudits. Fluxonium circuits, constructed from a superconducting loop interrupted by a Josephson junction and a large inductance, exhibit strong anharmonicity and non-fixed selection rules. These features enable multiple direct transitions between quantum states, which can be precisely tuned through a set of circuit parameters known as fluxonium characteristic values. A detailed study of these parameters was conducted to identify optimal qudit systems within a ten-dimensional Hilbert space (D = 10), with estimated coherence times comparable to those of conventional qubit sys- tems. Theoretical and numerical tools were developed to extend the approach to higher dimensions. A set of universal qudit logic gates was designed for arbitrary dimensions D = 2^n, as well as some gates and gate combinations in high dimension Hilbert space. The study demonstrates a significant reduction in gate complexity—particularly in the number of driving pulses required for multiply-controlled gates. Additionally, hybrid logic circuits using D = 8 and D = 4 qudits were analyzed, revealing reduced circuit complexity com- pared to qubit-only implementations. In summary, this work shows that fluxonium superconducting circuits are well-suited systems extending the traditional two-level qubit into multi-level qudit operation, where accessing higher energy levels can enhance computational capacity, reduce gate overhead, and enable more efficient quantum algorithms compared to standard qubit architectures.
The technological development of hardware heading toward universal fault-tolerant quantum computation requires a large-scale processing unit with high performance. While fluxonium qubits are promising with high coherence and large anharmonicity, their scalability has not been systematically explored. In this work, we propose a superconducting quantum information processor based on compact high-coherence fluxoniums with suppressed crosstalk, reduced design complexity, improved operational efficiency, high-fidelity gates, and resistance to parameter fluctuations. In this architecture, the qubits are readout dispersively using individual resonators connected to a common bus and manipulated via combined on-chip RF and DC control lines, both of which can be designed to have low crosstalk. A multi-path coupling approach enables exchange interactions between the high-coherence computational states and at the same time suppresses the spurious static ZZ rate, leading to fast and high-fidelity entangling gates. We numerically investigate the cross resonance controlled-NOT and the differential AC-Stark controlled-Z operations, revealing low gate error for qubit-qubit detuning bandwidth of up to 1 GHz. Our study on frequency crowding indicates high fabrication yield for quantum processors consisting of over thousands of qubits. In addition, we estimate low resource overhead to suppress logical error rate using the XZZX surface code. These results promise a scalable quantum architecture with high performance for the pursuit of universal quantum computation.
Quantum processors based on superconducting circuitry have reached the scale of hundreds of qubits and demonstrated computational capabilities that challenge state-of-the-art classical methods for carefully designed problems. Despite these advances, fundamental questions persist over how to best improve and scale the computational power of this emerging technology. Most transmon-based quantum processors encode information in two-level systems, or qubits, leaving the rich multilevel structure of the transmon largely unexploited. In this thesis, we demonstrate how the capabilities of these devices can be meaningfully extended by harnessing this intrinsic multilevel structure to encode qudits — d-level quantum systems that access a larger and more connected Hilbert space than their qubit counterparts. We begin by demonstrating universal single-qudit operation before turning to microwave-activated entanglement to realize scalable two-qudit gates. We present a high-fidelity, fully entangling two-qutrit CZ gate based on a novel tunable cross-Kerr mechanism. We further explore two-qudit gates that selectively entangle subspaces of the full Hilbert space via two-photon multipartite Raman transitions, employing these operations to generate large entangled states across a transmon array. To address the noisy nature of near-term qudit computation, we introduce and characterize error suppression techniques for qudit circuits, including dynamical decoupling and quantum error mitigation. We then synthesize these directions by exploring simulations of quantum systems that have innate multilevel interactions and are therefore well tailored to qudit operation. First we investigate digital quantum simulations of collective neutrino oscillations and the spin-1 truncated Abelian Higgs model, finding error mitigation methods critical for improving circuit performance. Finally, out of equilibrium --- or Floquet --- spin-1 systems are realized using an array of 15 superconducting qutrits to probe a novel Z3 discrete time crystalline (DTC) phase of matter with intrinsically chiral interactions. This DTC result demonstrates that native qudit hardware provides powerful access to non-equilibrium phases rooted in higher discrete symmetries, opening a route to a broader landscape of dynamical orders beyond the Z2 Ising paradigm.
The central question that this project tries to address is the following: Dominance of binary logic in classical computing emerged from deep physical and engineering constraints. I ask if similar constraints force quantum computing toward qubits, or whether today's qubit dominance is merely historical and a temporary technological contingency? Quantum computing today appears to be converging on an architectural choice that reminds us of the trajectory of classical computing: the qubit. Nearly all commercial quantum computing platforms — including those developed by IBM, Google, and Amazon — are built around controllable two-level quantum systems. Superconducting circuits, trapped ions, and photonic encodings are engineered so that a two-dimensional Hilbert space functions as the computational unit. Yet quantum theory does not privilege two-level systems. This contrast between what current devices use and what the theory allows motivates a closer look at the higher-dimensional structures already present in quantum mechanics. The mathematical structure of quantum mechanics naturally accommodates arbitrary-dimensional Hilbert spaces. Atoms possess multiple accessible energy levels. Photons carry orbital angular momentum in high-dimensional spaces. Ions and superconducting circuits inherently support more than two levels. In laboratory settings, three-level systems (qutrits) and higher-dimensional qudits have already been implemented and studied with notable success, and I take these results as evidence that the restriction to qubits is a contingent design preference rather than a theoretical necessity. The working hypothesis guiding this project has been that very little appears to transfer from the classical case. Quantum information theory, noise mechanisms, and error correction principles differ fundamentally from their classical counterparts, I focus on how qudits exploit these differences.Therefore, it's possible that dominance of qubits today may reflect temporary engineering convenience and early platform momentum rather than theoretical inevitability.
Fluxonium qubits, designed to mitigate charge noise and enhance anharmonicity, are among the most promising superconducting platforms for quantum computing. To understand and exploit their quantum properties and design novel fluxonium-based architectures with improved functionalities, these systems require an accurate Hamiltonian formulation to capture their energy level structure and quantum dynamics. This work presents a systematic method for constructing the Hamiltonian for multi-loop circuits that partitions the system into a set of uncoupled harmonic oscillators and a coupled anharmonic part originating from the Josephson circuit elements, allowing clear identification of independent modes and isolating the nonlinearity in the Josephson terms. While demonstrated for fluxonium-type multi-loop circuits, this method can be generalized to other superconducting qubit architectures within the broader context of circuit QED, making it a versatile tool for exploring different circuit configurations. Our systematic and flexible modeling approach forms the theoretical basis for the qubit measurement and control experiments validating multi-loop fluxonium architectures.
This review examines the seminal work by Amelio et al. (2026) on quantum simulation using fluxonium qutrit arrays, highlighting its contributions to engineering exotic bosonic Hamiltonians beyond the standard Bose-Hubbard model. We summarize the key findings, including the identification of four operational regimes for fluxonium qutrits and their implications for simulating strongly correlated matter, lattice gauge theories, and non-Abelian topological states. A comparative analysis with prior research in superconducting circuits, ultracold atoms, and other qudit platforms reveals both synergies and distinctions, emphasizing the unique tunability of fluxonium systems. Critical evaluation addresses strengths in coherence and scalability while noting limitations in decoherence and higher-level leakage. We extend the ideas to unexplored domains, such as hybrid qubit-qutrit integration, two-dimensional lattices with synthetic gauge fields, and applications in quantum error correction. This coherent synthesis positions fluxonium qutrit arrays as a promising frontier in analog quantum simulation. Mamun, SM (2026)……………………..1 Advancements in Superconducting Qutrit Architectures: A Comprehensive Review and Extension of Fluxonium-Based Quantum Simulators Also available on Academia.edu: https://www.academia.edu/attachments/131651006/download_file?s=portfolio
Superconducting qubits are a leading platform for quantum computation, yet decoherence and scalability challenges continue to limit progress toward fault-tolerant systems. This review synthesizes research on architectures, noise sources, and error correction to clarify performance trade-offs and guide development. The transition from Transmon to Fluxonium has dramatically improved qubit performance, achieving millisecond-scale coherence times. However, this success reveals a fundamental limit of coherence now being primarily restricted by the physical properties of the materials, specifically dielectric losses occurring at the Josephson junction leads and within the surrounding materials. As overcoming these material limits becomes increasingly difficult, system-level engineering determines whether high-coherence qubits can scale.Scaling quantum systems is difficult because current cooling and control systems create too much heat and this forces a shift to integrated digital superconducting circuits and cryogenic light-based links. While these hardware challenges restrict scaling, experiments in error correction show that logical qubits can already outperform physical ones. For example, a distance-7 surface code improved logical qubit lifetime by 2.4×. Achieving practical fault tolerance, however, requires moving beyond simple error models. Future systems must combine techniques like Dynamical Decoupling and Machine Learning-based Optimal Control with dynamic classical control capable of handling complex, correlated faults such as Multi-Bit Burst Errors. Progress in materials, cryogenic system integration for control, and adaptive error management must advance together to realize scalable, high-fidelity quantum hardware.