Measurement-induced state transitions in a superconducting qubit: Within the rotating-wave approximation
Mostafa Khezri, Alex Opremcak, Zijun Chen, Kevin C. Miao, Matt McEwen, Andreas Bengtsson, T. White, Ofer Naaman, D. Sank, Alexander N. Korotkov, Yu Chen, Vadim Smelyanskiy
Fast nondemolition measurement of superconducting qubits is important for the operation of quantum computers, but readout is constrained by measurement-induced state transitions that shift the qubit population outside of its computational subspace. This work experimentally characterizes the phenomenon and provides an intuitive model to explain its physical process. Surprisingly, the offset charge of the transmon qubit, which is usually ignored, is important in explaining the experiments. These results inform engineering and physics-based solutions to this problem by providing performance limits for the dispersive readout of superconducting qubits.
Fast nondemolition measurement of superconducting qubits is important for the operation of quantum computers, but readout is constrained by measurement-induced state transitions that shift the qubit population outside of its computational subspace. This work experimentally characterizes the phenomenon and provides an intuitive model to explain its physical process. Surprisingly, the offset charge of the transmon qubit, which is usually ignored, is important in explaining the experiments. These results inform engineering and physics-based solutions to this problem by providing performance limits for the dispersive readout of superconducting qubits.
Fast and high-fidelity qubit measurement plays a key role in quantum error correction. In superconducting qubits, measurement is typically performed using a resonant microwave drive on a readout resonator dispersively coupled to the qubit. Shorter measurement times require larger numbers of photons populating the readout resonator, which ultimately leads to undesired measurementinduced state transitions (MIST) of the qubit. MIST can be particularly problematic because these transitions often leave the qubit in a high energy state, and the MIST locations in readout parameter space drift as a function of qubit offset charge. In transmon qubits, these drifts have been avoided using very large qubit-resonator detunings or dedicated offset charge biases. In this work, we take an alternative approach and add an inductive shunt to the transmon to eliminate the offset charge dependence and stabilize the MIST. We experimentally characterize MIST in several different inductively-shunted transmons, in agreement with quantum and semiclassical models for MIST. These results extend to other inductively-shunted qubits.
In quantum information processing one strives for quantum nondemolition (QND) measurements, which are least likely to perturb the subsequent evolution of the system. The authors show, however, that common superconducting-qubit readout schemes are in fact not QND. They identify a mechanism that induces an effective coherent rotation of the qubit, which means that such a scheme is QND only in the limit of infinite measurement time. This affects any protocol where measurement is used during computation, and therefore is of immediate importance to contemporary experiments. Thankfully, the authors also explain how to fix the problem.
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.
Dispersive readout, the current standard for measuring superconducting qubits, relies on relatively easy to engineer, static transverse coupling between a qubit and a detuned cavity mode. However, this method requires circuit design trade-offs between qubit-cavity coupling, cavity-feedline coupling, detuning, and the resultant decoherence introduced by the cavity mode. Additionally, the criteria for performing quantum nondemolition measurements, including reduced cavity photon numbers, further limits speed and fidelity. In this work, we introduce a circuit with pulse-tunable qubit-cavity and cavity-feedline couplings so that the entire qubit-measurement process can be fully optimized. Here, the core measurement process resembles a quantum gate operation between the qubit and the cavity, with the cavity acting like an ancilla, storing the qubit-state information. To fully explore time-dependent effects of the full qubit-cavity dynamics, we go beyond the rotating-wave, Jaynes-Cummings, or dispersive approximations, to develop a pulsed-measurement protocol. In addition, we propose a realistic circuit architecture that can provide a very fast, high-fidelity, QND measurement with near-unit efficiency.
Superconducting qubits are most often measured using dispersive readout, which, ideally, implements a projective quantum non-demolition (QND) measurement. While a larger readout drive can increase the signal and, thus, reduce discrimination errors in the readout, strong microwave drives may also cause non-QND errors by driving the qubit to a state outside the computational subspace. In this work, we experimentally characterize measurement-induced state transitions (MIST) in a fluxonium qubit over its full external flux range. We further numerically calculate the MIST errors, and find that the theory accurately predicts eleven experimentally identified regions with increased MIST. In addition to transitions to higher fluxonium levels, we also find that, at certain flux points, MIST errors are dominated by transitions that include the transmission-line-like array modes of the fluxonium's superinductor. The excellent match between theory and experiment validates that the models accurately predict the occurrence of MIST in these systems, and further highlights the influence of array modes in fluxonium readout.
Many superconducting qubit systems use the dispersive interaction between the qubit and a coupled harmonic resonator to perform quantum state measurement. Previous works have found that such measurements can induce state transitions in the qubit if the number of photons in the resonator is too high. We investigate these transitions and find that they can push the qubit out of the two-level subspace, and that they show resonant behavior as a function of photon number. We develop a theory for these observations based on level crossings within the Jaynes-Cummings ladder, with transitions mediated by terms in the Hamiltonian that are typically ignored by the rotating wave approximation. We find that the most important of these terms comes from an unexpected broken symmetry in the qubit potential. We confirm the theory by measuring the photon occupation of the resonator when transitions occur while varying the detuning between the qubit and resonator.