Multilevel quantum systems, or qudits, provide a powerful means to exploit larger Hilbert spaces. In this work, we investigate how flux-tunable superconducting transmons can be practical platforms for qudit-based operations. We examine the properties of a 2-transmon processor with a flux-tunable coupler and assess its suitability for state control and higher-dimensional gates. We also explore the application of Excited State Promoted (ESP) readout to this circuitry, which promises improved qudit readout fidelity. We also introduce a new approach to multilevel control, providing a step toward enhanced quantum algorithm execution.
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.
Qudits provide a resource-efficient alternative to qubits for quantum information processing. The multilevel nature of the transmon, with its individually resolvable transition frequencies, makes it an attractive platform for superconducting circuit-based qudits. In this work, we systematically analyze the trade-offs associated with encoding high-dimensional quantum information in fixed-frequency transmons. Designing high
EJ/EC ratios of up to 325, we observe up to 12 levels (
d=12) on a single transmon. Despite the decreased anharmonicity, we demonstrate process infidelities ${e}_{f}<3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ for qubitlike operations in each adjacent-level qubit subspace in the lowest ten levels. Furthermore, we achieve a ten-state readout assignment fidelity of 93.8% with the assistance of deep neural network classification of a multitone dispersive measurement. We find that the Hahn echo time
T2E for the higher levels is close to the limit of
T1 decay, primarily limited by bosonic enhancement. We verify the recently observed Josephson harmonic model, finding that it yields better predictions for the transition frequencies and charge dispersion. Finally, we show strong
ZZ-like coupling between the higher energy levels in a two-transmon system. Our high-fidelity control and readout methods, in combination with our comprehensive characterization of the transmon model, suggest that the high-
EJ/EC transmon is a powerful tool for exploring excited states in circuit quantum electrodynamics.
Abstract Superconducting fluxonium qubits provide a promising alternative to transmons on the path toward large-scale superconductor-based quantum computing due to their better coherence and larger anharmonicity. A major challenge for multi-qubit fluxonium devices is the experimental demonstration of a scalable crosstalk-free multi-qubit architecture with high-fidelity single-qubit and two-qubit gates, single-shot readout, and state initialization. Here, we present a two-qubit fluxonium-based quantum processor with a tunable coupler element. We experimentally demonstrate fSim-type and controlled-Z-gates with 99.55 and 99.23% fidelities, respectively. The residual ZZ interaction is suppressed down to the few kHz levels. Using a galvanically coupled flux control line, we implement high-fidelity single-qubit gates and ground state initialization with a single arbitrary waveform generator channel per qubit.
Qudits hold great promise for efficient quantum computation and the simulation of high-dimensional quantum systems [1]. However, existing control and measurement schemes for qudit systems scale unfavorably with qudit dimension since they decompose S U ( d ) operations into series of qubitlike rotations and perform measurements on a small number of states [2–6]. Here, we address these challenges by employing simultaneous multifrequency drives to generate rotations and projections in an effective spin- 7 / 2 system mapped onto the energy eigenstates of a superconducting circuit. We implement single-shot readout of the eight states using a multitone dispersive readout ( F assignment = 88.3 % ) and exploit the strong nonlinearity in a high- E J / E C transmon to simultaneously address each transition and realize a spin displacement operator. Combining this displacement operator with a virtual SNAP gate, we realize arbitrary single-qudit unitary operations in O ( d ) physical pulses and extract spin displacement gate fidelities ranging from 0.997 to 0.989 for virtual spins of size j = 1 to j = 7 / 2 . We demonstrate the potential of our control scheme in three ways: the direct measurement of the spin qudit Wigner function, randomized benchmarking of a logical qubit encoded into the qudit state, and randomized benchmarking of the full qudit Clifford group. In the latter experiment, we implement the d -dimensional quantum Fourier transform with an average gate fidelity of 0.91(6) in d = 8 . Our multifrequency approach to qudit control and measurement can be readily extended to other physical platforms that realize a multilevel system coupled to a cavity and can become a building block for efficient qudit-based quantum computation and simulation.
Superconducting quantum processors have largely converged on transmon-based architectures, while alternative qubit modalities with intrinsic error protection have lacked a demonstrated path to scalable system integration. In particular, although tunable-coupler-mediated interactions have been validated for small fluxonium systems, it remains unclear whether such designs can be scaled to a multi-qubit lattice. Here, we establish a scalable fluxonium processor architecture based on a modular qubit-coupler unit cell engineered to suppress residual interactions and spectator errors in a many-qubit lattice. The system enables parallel single-qubit gate fidelities approaching 99.99% and two-qubit CZ gate fidelities around 99%. With an optimized gate duration of 32 ns, the best CZ gate fidelity reaches 99.9%. We further validate this architecture in a 22-qubit processor based on the same configuration, where parallel operations enable the deterministic generation of Greenberger-Horne-Zeilinger states involving up to 10 qubits. Together, these results demonstrate that the fluxonium-tunable-coupler unit cell composes without emergent interaction pathologies and establish fluxonium as a scalable superconducting qubit platform.
Quantum computing offers the potential to surpass classical computing speeds by leveraging quantum entanglement and superposition. However, progress towards fault-tolerant quantum computers is limited by low qubit counts and considerable gate errors. A promising direction involves transitioning from two-level qubits to d-level qudits, expanding the state space beyond conventional qubit-based quantum computers. The superconducting transmon-tunable coupler-transmon (TTT) system has emerged as a key building block of current quantum processors. Recent demonstration has shown its capability to host three-level qudits (qutrits), including the implementation of qutrit controlled-phase (CPhase) gate via an adiabatic scheme. Despite this progress, further modeling or optimization studies for the qudit-based TTT system are still unexplored. In this work, we propose an integrated simulation framework that predicts the cross-Kerr interactions of the TTT system and the fidelities of two-qutrit CPhase gate with the presence of noise effect. We validate the prediction of the cross-Kerr interactions against data from TTT systems reported in the literature. We also identify the conditions for the maximum target frequency in the adiabatic scheme necessary to achieve higher qutrit CPhase gate fidelity. Furthermore, we demonstrate the control-device co-optimization of the system, showing the potential of achieving the highest gate fidelity allowed by the hardware and noise. This work provides valuable insights which can guide the development towards more reliable and powerful superconducting quantum processors.