We develop an efficient numerical approach for simulating the high-power dispersive readout in circuit quantum electrodynamics. In the numerical simulations of the high-power readout, a large-amplitude coherent state induced in a cavity is an obstacle because many Fock states are required to describe such a state. We remove the large-amplitude coherent state from the numerical simulations by simulating the dynamics in a frame where the amplitude of the coherent state is almost absent. Using the developed method, we numerically simulate the high-power dispersive readout of the two-level system and the transmon. Our proposed method succeeds in producing reasonable behaviors of the high-power dispersive readout which can be deduced from the photon-number dependence of the cavity frequency: The high-power dispersive readout works in the two-level-system case while it does not work in the transmon case.
We develop an efficient numerical approach for simulating the high-power dispersive readout in circuit quantum electrodynamics. In the numerical simulations of the high-power readout, a large-amplitude coherent state induced in a cavity is an obstacle because many Fock states are required to describe such a state. We remove the large-amplitude coherent state from the numerical simulations by simulating the dynamics in a frame where the amplitude of the coherent state is almost absent. Using the developed method, we numerically simulate the high-power dispersive readout of the two-level system and the transmon. Our proposed method succeeds in producing reasonable behaviors of the high-power dispersive readout which can be deduced from the photon-number dependence of the cavity frequency: The high-power dispersive readout works in the two-level-system case while it does not work in the transmon case.
A qubit, the quantum counterpart of the classical binary digit, can be constructed based on a system with two possible quantum states. For instance, superconducting circuits have been employed to construct an artificial atom in which ground and excited states are used for two quantum states. The anharmonicity of an artificial atom distinguishes the higher-order excited states from two possible quantum states, although they can interact with the cavity as well. The interaction can be important when a large number of photons are allowed in the cavity and results in a nonlinear effect on a Transmon-cavity system. We studied power-dependent nonlinear behaviors of a Transmon-cavity system. The system exhibits dramatic shifts from a dispersive coupling at a low power regime to punch-out behaviors at high powers. This nonlinearity provides us high fidelity readouts for 2nd excited state as well as 1st excited state.[1]
Robust manipulation and control of quantum systems require a fast and efficient way to read out their state. After cavity quantum electrodynamics (cavity QED) pioneered the manipulation of neutral atoms and ions with light, circuit quantum electrodynamics (circuit QED) became the dominant readout paradigm for artificial atoms such as superconducting circuits, with dispersive readout widely adopted for its stability and efficiency.Recently, longitudinal readout has emerged as a potentially faster readout protocol, but relies on sophisticated parametric modulation, whose underlying mechanisms have remained unclear so far.Longitudinal interactions have been demonstrated across platforms ranging from superconducting qubits to quantum dots, and rely on driving the qubit at the resonator frequency. In different regimes, the coupling emerges parametrically in the drive strength, growing linearly as the drive increases.In this manuscript, we experimentally demonstrate the breakdown of this parametric regime in a two-level quantum dot charge qubit and devise a unifying Floquet theory to establish a universal connection between AC Stark shift, longitudinal coupling and dispersive readout in cQED.We derive analytical results supported by exact numerical simulations that we apply to superconducting and spin-hybrid cQED systems, showcasing the flexibility of faster-than-dispersive longitudinal readout.Inspired by cQED’s readout capabilities in single qubit measurements, we address many-body state readout in quantum simulators.Since the dynamical structure factor (DSF) encodes key information about density excitations in quantum systems, we propose Many-Body Admittance Spectroscopy (MADS) as a weakly invasive method to probe the DSF by analyzing the transmission coefficients of microwave signals coupled to the quantum simulator.We demonstrate the approach on a one-dimensional spinless fermionic chain, representative of quantum dot implementations of the Heisenberg model, and we discuss, supported by numerical simulations obtained using exact diagonalization and density matrix renormalization group (DMRG), the possibility to measure the qualitative modifications of the DSF caused by interactions. Our results highlight the potential of MADS for characterizing the dynamical properties in highly tunable solid-state quantum simulators, extending the toolbox for the readout of quantum simulators.
The basic element of circuit quantum electrodynamics (cQED) is a cavity resonator strongly coupled to a superconducting qubit. Since the inception of the field, the choice of the cavity frequency was, with a few exceptions, been limited to a narrow range around 7 GHz due to a variety of fundamental and practical considerations. Here we report the first cQED implementation, where the qubit remains a regular transmon at about 5 GHz frequency, but the cavity's fundamental mode raises to 21 GHz. We demonstrate that (i) the dispersive shift remains in the conventional MHz range despite the large qubit-cavity detuning, (ii) the quantum efficiency of the qubit readout reaches 8%, (iii) the qubit's energy relaxation quality factor exceeds 107, (iv) the qubit coherence time reproducibly exceeds 100μs and can reach above 300μs with a single echoing π-pulse correction. The readout error is currently limited by an accidental resonant excitation of a non-computational state, the elimination of which requires minor adjustments to the device parameters. Nevertheless, we were able to initialize the qubit in a repeated measurement by post-selection with 2×10−3 error and achieve 4×10−3 state assignment error. These results encourage in-depth explorations of potentially transformative advantages of high-frequency cavities without compromising existing qubit functionality.
The speed and fidelity of dispersive readout of superconducting qubits should improve by increasing the amplitude of the measurement drive. Experiments show, however, that beyond some drive amplitude there is always a saturation or drop in fidelity, often associated with a decrease in qubit energy relaxation time T1. A simple Lindblad master equation does not capture the latter effect. More involved approaches based on effective master equations rely on strong assumptions about the spectra of the system and the bath and only partially agree with observations. Here, we perform a first-principles simulation of the full unitary dynamics of dispersive readout by considering the circuit QED Hamiltonian coupled to a microscopic model for the measurement transmission line, allowing for its arbitrary spectrum, including filters. Our access to the dynamics of the bath degrees of freedom allows us to investigate the emission spectrum of the system as a function of drive power. We show how the dependence of qubit T1 on readout drive amplitude is sensitive to the details of the bath spectrum. In particular, we find that T1 drops with increasing drive amplitude when a Purcell notch filter is placed at the qubit frequency, and that the Lindblad master equation shows general qualitative defects compared to the first-principles model.
Time-dependent drives play a crucial role in quantum computing efforts with circuit quantum electrodynamics. They enable single-qubit control and entangling logical operations, as well as qubit readout. However, their presence can lead to deleterious effects such as large ac-Stark shifts and unwanted qubit transitions ultimately reflected into reduced control or readout fidelities. Qubit cloaking was introduced by Lled\'o et al. [C. Lled\'o, R. Dassonneville, A. Moulinas et al., Nat. Commun. 14, 6313 (2023)] to temporarily decouple the qubit from the coherent photon population of a driven cavity, allowing for the application of arbitrary displacements to the cavity field while avoiding the deleterious effects on the qubit. For qubit readout, cloaking permits us to prearm the cavity with an, in principle, arbitrarily large number of photons, in anticipation of the qubit-state-dependent evolution of the cavity field, allowing for improved readout strategies. Here, we take a closer look at two such strategies: first, arm-and-release readout, introduced together with qubit cloaking, where after arming the cavity, the cloaking mechanism is released and the cavity field evolves under the application of a constant drive amplitude; and, second, an arm-and-longitudinal readout scheme, where the cavity drive amplitude is slowly modulated after the release. We show that the two schemes complement each other, offering an improvement over standard dispersive readout for any values of the dispersive interaction and the cavity decay rate, as well as any target measurement integration time. Our results provide a recommendation for improving qubit readout without changes to the standard circuit-QED architecture.
The dispersive-readout scheme enables quantum nondemolition measurement of superconducting qubits. An increased readout power can shorten the readout time and reduce the state-discrimination error but can promote qubit transitions into higher noncomputational states. The ability to predict the onset of these measurement-induced state transitions can aid the optimization of qubit circuits and provide means for comparing the readout performance of different qubit types. Building upon the concept of dressed coherent states, we consider two straightforward metrics for determining the maximum number of photons that can be used for dispersive readout without causing state transitions. We focus on the fluxonium readout to demonstrate the independence of the metrics from any qubit-type-specific approximations. The dispersive readout of transmons and other superconducting qubits can be treated universally in the same fashion.