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.
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.
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.
The simulation of large-scale quantum systems is one of the most sought-after applications of quantum computers. Of particular interest for near-term demonstrations of quantum computational advantage are analog quantum simulations, which employ analog controls instead of digitized gates. Most analog quantum simulations to date, however, have been performed using qubit-based processors, despite the fact that many physical systems are more naturally represented in terms of qudits (i.e., d-level systems). Motivated by this, we present an experimental realization of the Lipkin-Meshkov-Glick (LMG) model using an analog simulator based on a single superconducting transmon qudit with up to d=9 levels. This is accomplished by moving to a rotated frame in which evolution under any time-dependent local field and one-axis twisting can be realized by the application of multiple simultaneous drives. Combining this analog drive scheme with universal control and single-shot readout of the qudit state, we provide a detailed study of five finite-size precursors of quantum criticality in the LMG model: dynamical phase transitions, closing of the energy gap, Kibble-Zurek-like dynamics, statistics of the order parameter, and excited-state phase transitions. For each experiment we devise a protocol for extracting the relevant properties which does not require any prior knowledge of the system eigenstates, and can therefore be readily extended to higher dimensions or more complicated models. Our results cement high-dimensional transmon qudits as an exciting path towards simulating many-body physics.
Qudits, generalizations of qubits to multilevel quantum systems, offer enhanced computational efficiency by encoding more information per lattice cell, avoiding costly swap operations and providing even exponential speedup in some cases. Utilizing the d -level manifold, however, requires high-speed gate operations because of the stronger decoherence at higher levels. While analytical control methods have proven effective for qubits in achieving fast gates with minimal control errors, their extension to qudits is nontrivial due to the increased complexity of the energy-level structure arising from additional ancillary states. In this work, we present a universal pulse construction for generating rapid, high-fidelity unitary rotations between adjacent qudit levels, thereby providing a prescription for any gate in SU ( d ) . Control errors in these operations are effectively analyzed within a four-level subspace, including two leakage levels with approximately opposite detuning. By identifying the optimal degrees of freedom, we derive concise analytical pulse schemes that suppress multiple control errors and outperform existing methods. Remarkably, our approach achieves consistent coherent error scaling across all levels, approaching the quantum speed limit independently of parameter variations between levels. Numerical validation on transmon circuits demonstrates significant improvements in gate fidelity for various qudit sizes aiming for 10 − 4 error. This method provides a scalable solution for improving qudit control and can be broadly applied to other quantum systems with ladder structures or operations involving multiple ancillary levels.
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.
Qutrits offer the potential for enhanced quantum computation by exploiting an enlarged Hilbert space. However, the synthesis of high-fidelity and fast qutrit gates, particularly for single qutrits, remains an ongoing challenge, as it involves overcoming intrinsic constraints in quantum platforms. Here, we develop a novel framework for the efficient implementation of a single-qutrit gate set via coherent control, leveraging SU(3) dynamics while obviating platform-specific constraints such as those arising from the selection rule. As a proof-of-principle demonstration, we realize 35-ns qutrit hadamard and x gates using a superconducting transmon, achieving an average fidelity of 99.5%, as verified by randomized benchmarking. We further demonstrate two paradigmatic quantum circuits, which can be naturally extended to scalable qudit algorithms for phase estimation and parity check. In addition, we propose an SU(3)-based decomposition strategy for an arbitrary single-qutrit gate and numerically demonstrate its substantial efficiency improvement over conventional SU(2)-based protocols. By addressing the challenge of efficiently implementing single-qutrit gates, our protocol paves the way for realizing high-performance qutrit processors in diverse quantum platforms.
Mitigating ancilla-mediated error channels is a critical challenge in controlling high-quality superconducting cavities using circuit quantum electrodynamics (cQED). We address this by weakening the dispersive coupling while demonstrating fast, high-fidelity multimode control through transmon-mediated sideband interactions. We implement transmon-cavity SWAP gates with speeds up to 30 times larger than the bare dispersive coupling. Combined with transmon rotations, this enables universal state preparation in a single mode, though achieving unitary gates and extending control to multiple modes remains a challenge. In this work, we overcome this limitation by introducing two control strategies: (i) a shelving technique that stores populations in sideband-transparent states, and (ii) a method that exploits the dispersive shift to implement photon-number-selective transmon-cavity SWAP gates. We use these protocols to prepare Fock and binomial code states across any of the ten modes of a multimode cavity with millisecond coherence times—serving as a multimode quantum memory. We demonstrate unitaries that encode and decode an arbitrary qubit state from the transmon into corresponding vacuum and Fock state superpositions, as well as entangled NOON states of cavity mode pairs—a scheme extendable to arbitrary multimode Fock encodings in the cavity modes. Furthermore, we implement a new binomial encoding gate that converts arbitrary transmon superpositions into binomial code states in any cavity mode at a rate exceeding the dispersive shifts in our system, achieving an average post-selected state fidelity of 96.3% in a 4 μ s gate time. By using precalibrated transmon and sideband pulses, our work demonstrates multimode control with significantly reduced calibration overhead, enabling efficient unitary operations using sideband interactions in multimode cQED systems.