The utilization of qudits in quantum systems has led to significant advantages in quantum computation and information processing. Therefore, qudits have gained increased attention in recent research for their precise and efficient operations. In this work, we demonstrate the complete population transfer between the next-adjacent energy levels of a transmon qudit using the Pythagorean coupling method and energy level mapping. We achieve a |0〉 to |2〉 transfer with a process fidelity of 97.76% in the subspace spanned by |0〉 to |2〉. Moreover, the transfer operation is achieved within a remarkably fast timescale, as short as 20 ns. This study may present a promising avenue for enhancing the operation flexibility and efficiency of qudits in future implementations.
The utilization of qudits in quantum systems has led to significant advantages in quantum computation and information processing. Therefore, qudits have gained increased attention in recent research for their precise and efficient operations. In this work, we demonstrate the complete population transfer between the next-adjacent energy levels of a transmon qudit using the Pythagorean coupling method and energy level mapping. We achieve a |0〉 to |2〉 transfer with a process fidelity of 97.76% in the subspace spanned by |0〉 to |2〉. Moreover, the transfer operation is achieved within a remarkably fast timescale, as short as 20 ns. This study may present a promising avenue for enhancing the operation flexibility and efficiency of qudits in future implementations.
We propose a theoretical scheme for implementing nonleaky and accelerated population transfer with a transmon qutrit. For a transmon-regime artificial atom with weak level anharmonicity, the leakage effects on the target population transfer are considerable. Allowed by the level-transition rule, a two-photon resonant interaction can be obtained between the qutrit and microwave drivings. In the regime of large detuning, by adopting the technique of invariant-based inverse engineering, the population transfer with no leakage errors can be sped up drastically when compared with the adiabatic operation. Moreover, the accelerated operation is highly robust against decoherence effects. Thanks to these distinctive advantages, the proposed protocol could offer a promising avenue to optimal quantum operations on transmon artificial atoms.
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.
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.
In recent decades, a lot of effort has been seen to realize and control a large-scale quantum computer. Among the most promising architectures for such a system is that of superconducting circuits. However, a significant challenge with these qubits is the drifts in system parameters. Therefore, controlling thousands or more qubits - which are needed to perform practical applications - becomes increasingly difficult and various control schemes and workarounds are needed to vanquish such obstacles. One approach to cope with the complexity of the system size is to increase the information held per quantum system by introducing an additional state and thereby reduce the number of qubits. Therefore, in this work, we explore a robust population transfer, from the ground to the second excited state, on the first three levels of a superconducting transmon. For a transmon, such a transition cannot occur by single photon absorption. However, because of a second-order process, two-photon transitions from the ground state to the second excited state are possible for a drive at the 02-transition frequency. In existing protocols that drive this population transfer, such as the Raman process and (sa)STIRAP, a common problem is the sensitivity to offsets in frequency and amplitude of the drive pulses. Therefore, in search of a method that realizes such a transfer and is robust to some offsets we took inspiration from \cite{Mppr} and approached the problem through a Landau-Zener process. The Landau-Zener process in this work was a result of modulating the frequency of a one-tone drive around the 02-transition frequency that interchanged the first and third energy levels while avoiding the intermediate level. With this method, the three-level quantum system (approximately) follows the first eigenstate of the Hamiltonian adiabatically to the second excited state. This method showed considerable robustness to both offsets in frequency and amplitude and was eventually tested experimentally on a superconducting transmon. The results showed great agreement with the theory and demonstrates a method that is robust and simple enough to be realized on the majority of control hardware.
As a crucial component of superconducting quantum computing, the three‐energy‐level quantum system, known as qutrit, along with qutrit gates, has garnered significant attention over the past decades, which highlights the significance of accomplishing state transfers between levels in multiqutrit systems as a critical task. Herein, the coupling is constructed via the all‐microwave approach. Both the coupling strength and Alternating Current stark shift are calibrated, based on which a fast (70 ns) state transfer from to is investigated and achieved through the stimulated Raman shortcut‐to‐adiabatic passage.
A qudit (d-level quantum system) has a large Hilbert space and thus can be used to achieve many quantum information and communication tasks. Here, we propose a method to transfer arbitrary d-dimensional quantum states (known or unknown) between two superconducting transmon qudits coupled to a single cavity. The state transfer can be performed by employing resonant interactions only. In addition, quantum states can be deterministically transferred without measurement. Numerical simulations show that high-fidelity transfer of quantum states between two superconducting transmon qudits (d ≤ 5) is feasible with current circuit QED technology. This proposal is quite general and can be applied to accomplish the same task with natural or artificial atoms of a ladder-type level structure coupled to a cavity or resonator.