We analyze several mechanisms leading to errors in a course of measurement of a superconducting flux-biased phase qubit. Insufficiently long measurement pulse may lead to nonadiabatic transitions between qubit states \ensuremath{\mid}1⟩ and \ensuremath{\mid}0⟩, before tunneling through a reduced barrier is supposed to distinguish the qubit states. Finite (though large) ratio of tunneling rates for these states leads to incomplete discrimination between \ensuremath{\mid}1⟩ and \ensuremath{\mid}0⟩. Insufficiently fast energy relaxation after the tunneling of state \ensuremath{\mid}1⟩ may cause the repopulation of the quantum well in which only the state \ensuremath{\mid}0⟩ is supposed to remain. We analyze these types of measurement errors using analytical approaches as well as a numerical solution of the time-dependent Schr\"odinger equation.
We analyze several mechanisms leading to errors in a course of measurement of a superconducting flux-biased phase qubit. Insufficiently long measurement pulse may lead to nonadiabatic transitions between qubit states \ensuremath{\mid}1⟩ and \ensuremath{\mid}0⟩, before tunneling through a reduced barrier is supposed to distinguish the qubit states. Finite (though large) ratio of tunneling rates for these states leads to incomplete discrimination between \ensuremath{\mid}1⟩ and \ensuremath{\mid}0⟩. Insufficiently fast energy relaxation after the tunneling of state \ensuremath{\mid}1⟩ may cause the repopulation of the quantum well in which only the state \ensuremath{\mid}0⟩ is supposed to remain. We analyze these types of measurement errors using analytical approaches as well as a numerical solution of the time-dependent Schr"odinger equation.
In superconducting qubits, the interaction of the qubit degree of freedom with quasiparticles defines a fundamental limitation for the qubit coherence. We develop a theory of the pure dephasing rate ${\ensuremath{\Gamma}}_{\ensuremath{\phi}}$ caused by quasiparticles tunneling through a Josephson junction and of the inhomogeneous broadening due to changes in the occupations of Andreev states in the junction. To estimate ${\ensuremath{\Gamma}}_{\ensuremath{\phi}}$, we derive a master equation for the qubit dynamics. The tunneling rate of free quasiparticles is enhanced by their large density of states at energies close to the superconducting gap. Nevertheless, we find that ${\ensuremath{\Gamma}}_{\ensuremath{\phi}}$ is small compared to the rates determined by extrinsic factors in most of the current qubit designs (phase and flux qubits, transmon, fluxonium). The split transmon, in which a single junction is replaced by a SQUID loop, represents an exception that could make possible the measurement of ${\ensuremath{\Gamma}}_{\ensuremath{\phi}}$. Fluctuations of the qubit frequency leading to inhomogeneous broadening may be caused by the fluctuations in the occupation numbers of the Andreev states associated with a phase-biased Josephson junction. This mechanism may be revealed in qubits with small-area junctions, since the smallest relative change in frequency it causes is of the order of the inverse number of transmission channels in the junction.
Errors in superconducting qubits that are correlated in time and space can pose problems for quantum error correction codes. Radiation from cosmic and terrestrial sources can increase the quasiparticle (QP) density in a superconducting qubit device, resulting in an increased rate of QPs tunneling across proximal Josephson junctions (JJs) and causing correlated errors. Mechanical vibrations, such as those induced by the pulse tube (PT) in a dry dilution refrigerator, are also a known source of correlated errors. We measure two types of errors in the same device, linking the first to ionizing radiation and the second to PT operation. We present a method for distinguishing these two types of errors by their temporal, spatial, and frequency domain features, enabling physically motivated error-mitigation strategies. We also present accelerometer data to study the correlation between PT-induced vibrations and the errors. We measure arrays of transmon qubits where the difference in superconducting gap across the JJ is less than the qubit energy, as well as those where the gap is greater than the qubit energy, which has been shown to mitigate radiation-induced errors. The rate of both types of errors is reduced in these latter devices, suggesting that gap engineering is also protective against PT-induced errors.
We analyze the crosstalk error mechanism in measurement of two capacitively coupled superconducting flux-biased phase qubits. The damped oscillations of the superconducting phase after the measurement of the first qubit may significantly excite the second qubit, leading to its measurement error. The first qubit, which is highly excited after the measurement, is described classically. The second qubit is treated both classically and quantum mechanically. The results of the analysis are used to find the upper limit for the coupling capacitance (thus limiting the frequency of two-qubit operations) for a given tolerable value of the measurement error probability.
Fast, accurate, and low-leakage qubit measurement is a key requirement for quantum error correction. Here, we demonstrate measurement of a superconducting transmon qubit with a total duration of 97(1) ns, defined as the time from the start of the measurement pulse until the measurement-induced error on a subsequent π-pulse operation falls below 10−4. By combining a large state-averaged resonator decay rate of κeff/2π = 30.8 MHz with a dispersive shift close to the optimal SNR-per-photon condition, we achieve an assignment error of 0.17(1)% using a 58-ns measurement pulse, with residual readout photons depleting passively in tens of nanoseconds without an active depletion pulse. Using a repeated-measurement sequence together with a leakage-sensitive measurement, we benchmark the measurement-induced state transitions, finding a per-measurement leakage rate of 2.7(2)×10−5, only twice the background rate and two orders of magnitude below the measurement-induced relaxation rate, which dominates the assignment error. Floquet simulations indicate that the multiphoton resonances present at the operating point are weakly coupled and traversed diabatically, without causing leakage. These results demonstrate that a large resonator decay rate, combined with a dispersive shift close to the optimal SNR-per-photon condition, can enable fast, high-fidelity, low-leakage dispersive readout at small qubit-resonator detuning.
The research work discussed in this thesis deals with the study of superconducting Josephson qubits. Superconducting qubits are solid-state artificial atoms which are based on lithographically defined Josephson tunnel junctions properties. When sufficiently cooled, these superconducting devices exhibit quantized states of charge, flux or junction phase depending on their design parameters. This allows to observe coherent evolutions of their states. The results presented can be divided into two parts. In a first part we investigate operations of superconducting qubits based on the quantum coherence in superconducting quantum interference devices (SQUID). We explain experimental data which has been observed in a SQUID subjected to fast, large-amplitude modifications of its effective potential shape. The motivations for this work come from the fact that in the past few years there have been attempts to interpret the supposed quantum behavior of physical systems, such as Josephson devices, within a classical framework. Moreover, we analyze the possibility of generating GHZ states, namely maximally entangled states, in a quantum system made out of three Josephson qubits. In particular, we investigate the possible limitations of the GHZ state generation due to coupling to bosonic baths. In the second part of the thesis we address a particular cause of decoherence of flux qubits which has been disregarded until now: thermal gradients, which can arise due to accidental non equilibrium quasiparticle distributions. The reason for these detrimental effects is that heat currents flowing through Josephson tunnel junctions in response to a temperature gradient are periodic functions of the phase difference between the electrodes. The phase dependence of the heat current comes from Andreev reflection, namely an interplay between the quasiparticles which carry heat and the superconducting condensate which is sensitive to the superconducting phase difference. Generally speaking, the flux qubit states are characterized by different values of the phase difference through their Josephson junctions. Consequently, the phase-dependent thermal current through a device subject a temperature gradient is related to the phase-dependent qubit states. We study how the thermal currents change according to the state of the qubits hence yielding a measurement of the qubit state. This in turn leads to an impact of temperature gradient on the dynamics of the system. We show that flux qubits in the Delft qubit design can have limitations of the decoherence time to the order of microseconds as a result of this newly discovered source of decoherence. In contrast, the fluxonium qubit is found to be well protected due to its superinductance.
State transitions during qubit measurements are extremely detrimental to quantum tasks that rely on repeated measurements, such as quantum error correction. These state transitions can occur when excessive measurement power leads to qubit excitations outside its computational space. Alternatively, the qubit state can decay rapidly when the measurement protocol inadvertently couples the qubit to lossy modes such as two-level systems (TLSs). We experimentally verify the impact of these TLSs in qubit readout by measuring the transition errors at different qubit flux bias. Because such state transitions during measurements are often localized in frequency space, we demonstrate the ability to avoid them during a fluxonium readout by exploiting the qubit's flux-tunability. By synchronizing the flux bias with the readout photon dynamics, we obtain an optimal readout fidelity of 99 % (98.4 %) in 1 us (0.5 us) integration time. Our work advances the understanding of state transitions in superconducting circuit measurements and demonstrates the potential of fluxonium qubits to achieve fast high-fidelity readout.