The Hilbert space of a physical qubit typically features more than two energy levels. Using states outside the qubit subspace can provide advantages in quantum computation. To benefit from these advantages, individual states of the d -dimensional qudit Hilbert space have to be discriminated during readout. We propose and analyze two measurement strategies that improve the distinguishability of transmon qudit states. Based on a model describing the readout of a transmon qudit coupled to a resonator, we identify the regime in hardware parameter space where each strategy is optimal. We discuss these strategies in the context of a practical implementation of the default measurement of a ququart on IBM Quantum hardware whose states are prepared by employing higher-order X gates that make use of two-photon transitions. Published by the American Physical Society 2024
The Hilbert space of a physical qubit typically features more than two energy levels. Using states outside the qubit subspace can provide advantages in quantum computation. To benefit from these advantages, individual states of the d -dimensional qudit Hilbert space have to be discriminated during readout. We propose and analyze two measurement strategies that improve the distinguishability of transmon qudit states. Based on a model describing the readout of a transmon qudit coupled to a resonator, we identify the regime in hardware parameter space where each strategy is optimal. We discuss these strategies in the context of a practical implementation of the default measurement of a ququart on IBM Quantum hardware whose states are prepared by employing higher-order X gates that make use of two-photon transitions. Published by the American Physical Society 2024
Photons can carry quantum information not only in two-level systems (qubits) but also in d-level systems known as qudits. A single photon distributed across d optical modes can encode up to log2(d) qubits of information, allowing for more efficient use of quantum resources and increased resilience to noise. This advantage, however, comes at a price: implementing quantum gates and performing measurements in high-dimensional Hilbert spaces is significantly more demanding than in the qubit case. To tackle these challenges, I will present our recent work developing new protocols and optical hardware that enable quantum communication and computation with high-dimensional qudits encoded in the temporal or spatial modes of single and entangled photons. I will discuss our experimental implementations of quantum key distribution using weak coherent pulses [Sulimany et al., NPJ Quantum Information 11, 16 (2025)], single photons from quantum dots [Halevi et al., Optica Quantum 2, 351 (2024)], and entangled photon pairs [Lib et al., Optica Quantum 3, 182 (2025)]. In the latter, we demonstrated projective measurements in two mutually unbiased bases for d=25 using a multi-plane light converter (MPLC). I will also show how the same MPLC platform can be used to perform elementary operations in measurement-based quantum computation with high-dimensional cluster states [Lib and Bromberg, Nat. Photonics 18, 1218 (2024)]. Throughout the talk, I will discuss the tradeoffs between qubit- and qudit-based approaches and highlight the regimes where high-dimensional systems offer a practical advantage.
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.
Abstract Using quantum systems with more than two levels, or qudits, can scale the computational space of quantum processors more efficiently than using qubits, which may offer an easier physical implementation for larger Hilbert spaces. However, individual qudits may exhibit larger noise, and algorithms designed for qubits require to be recompiled to qudit algorithms for execution. In this work, we implemented a two-qubit emulator using a 4-level superconducting transmon qudit for variational quantum algorithm applications and analyzed its noise model. The major source of error for the variational algorithm was readout misclassification error and amplitude damping. To improve the accuracy of the results, we applied error-mitigation techniques to reduce the effects of the misclassification and qudit decay event. The final predicted energy value is within the range of chemical accuracy.
Qubit measurements are central to quantum information processing.In the field of superconducting qubits, standard readout techniques are limited not only by the signal-to-noise ratio, but also by state relaxation during the measurement.In this work, we demonstrate that the limitation due to relaxation can be suppressed by using the many-level Hilbert space of superconducting circuits: In a multilevel encoding, the measurement is corrupted only when multiple errors occur.Employing this technique, we show that we can directly resolve transmon gate errors at the level of one part in 10 3 .Extending this idea, we apply the same principles to the measurement of a logical qubit encoded in a bosonic mode and detected with a transmon ancilla, implementing a proposal by Hann et al. [Phys. Rev. A 98, 022305 (2018)].Qubit state assignments are made based on a sequence of repeated readouts, further reducing the overall infidelity.This approach is quite general, and several encodings are studied; the codewords are more distinguishable when the distance between them is increased with respect to photon loss.The trade-off between multiple readouts and state relaxation is explored and shown to be consistent with the photon-loss model.We report a logical assignment infidelity of 5.8 × 10 -5 for a Fock-based encoding and 4.2 × 10 -3 for a quantum error correction code (the S ¼ 2, N ¼ 1 binomial code).Our results not only improve the fidelity of quantum information applications, but also enable more precise characterization of process or gate errors.
Despite the high measurement fidelity that can now be reached, the dispersive qubit readout of circuit quantum electrodynamics is plagued by a loss of its quantum nondemolition character and a decrease in fidelity with increased measurement strength. In this work, we elucidate the nature of this dynamical process, which we refer to as transmon ionization. We develop a comprehensive framework which provides a physical picture of the origin of transmon ionization. This framework consists of three complementary levels of descriptions: a fully quantized transmon-resonator model, a semiclassical model where the resonator is treated as a classical drive on the transmon, and a fully classical model. Crucially, all three approaches preserve the full cosine potential of the transmon and lead to similar predictions. This framework identifies the multiphoton resonances responsible for transmon ionization. It also allows one to efficiently compute numerical estimates of the photon number threshold for ionization, which are in remarkable agreement with recent experimental results. The tools developed within this work are both conceptually and computationally simple, and we expect them to become an integral part of the theoretical underpinning of all circuit QED experiments. Published by the American Physical Society 2024
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.