Statistical algorithms for measurement data processing were developed to perform automation of superconducting quantum bits experimental investigations. The first algorithm is aimed to detect the q-bit quantum state changes. The second one is aimed to obtain the efficient resonance frequency estimation for the resonator coupled to a q-bit. All the results were obtained using the statistical approach that employs random nature of measurement data to obtain the optimal estimation rules and statistical hypotheses testing. The numerical modeling was carried out. The results of numerical modeling confirmed the efficiency and expediency of the algorithms obtained.
Statistical algorithms for measurement data processing were developed to perform automation of superconducting quantum bits experimental investigations. The first algorithm is aimed to detect the q-bit quantum state changes. The second one is aimed to obtain the efficient resonance frequency estimation for the resonator coupled to a q-bit. All the results were obtained using the statistical approach that employs random nature of measurement data to obtain the optimal estimation rules and statistical hypotheses testing. The numerical modeling was carried out. The results of numerical modeling confirmed the efficiency and expediency of the algorithms obtained.
An algorithm for estimating the amplitude of the output signal passing through an inductively coupled qubit-resonator system is proposed. In the study of the qubit parameters, multiple experimentally obtained results are averaged. A method for calculating the most accurate value of the amplitude of the output signal using complete sufficient statistics, verified using simulation, has been developed. One of the practical applications of this algorithm is to determine the loss of the relaxation energy of a qubit when its state changes when interacting with pulsed signals.
Abstract An algorithm for estimating the energy of a radio pulse when measuring a superconducting system qubit–resonator consisting of a superconducting resonator and a coupled qubit is proposed. The algorithm is based on the use of complete sufficient statistics and does not require a priori information about the level of additive white Gaussian noise in the process, as well as about the amplitude, initial phase, and temporal position of the radio pulse. The estimates are effective and consistent. The efficiency of the algorithm is estimated by means of computer simulation.
Designing high-precision and efficient protocols is of crucial importance for quantum parameter estimation in practice. Estimation based on continuous quantum measurement is one possible type of this, which also appears to be the most natural choice for continuous dynamical processes. In this work we consider the state-of-the-art superconducting circuit quantum-electrodynamics (QED) systems, where high-quality continuous measurements have been extensively performed in the past decade. Within the framework of Bayesian estimation and particularly using the quantum Bayesian rule in circuit QED, we numerically simulate the likelihood function as an estimator for the Rabi frequency of qubit oscillations. We find that, by proper design of the interaction strength of measurement, the estimate precision can scale with the measurement time beyond the standard quantum limit, which is usually assumed for this type of continuous measurement. This unexpected result is supported by the simulated Fisher information and can be understood as a consequence of the quantum correlation between the output signals by simulating the effect of quantum efficiency of measurement.
It has always been a challenge for researchers to efficiently and accurately post process experimental data which is distorted by the noise. Superconducting microwave devices e.g. resonators, directional filters, beam-splitters etc. operate at frequency of several GHz to THz and temperatures well below critical temperature (Tc) with few exceptions like transition edge sensors where devices are operated at temperatures close to Tc. These devices are measured usually with vector network analyser in terms of scattering parameters. Two kinds of errors, systematic and drift can easily be removed from the measurements taken with VNA. However, random errors are not easy to address and remove due to their unpredictability and randomness. In this manuscript we will present an algorithm to post process experimental data to cope with measurements that have been corrupted or useful spectral response is buried in spurious signal. We have developed a robust and efficient algorithm, implemented in MATLAB, to detect peaks in spectral response, remove baseline and finally estimate parameters of two-port superconductor resonator using an Improved Nelder-Mead Method for unconstrained multidimensional least square minimization. The algorithm has been successfully tested and verified by processing spectral response of half wavelength microwave transmission-line resonator successfully isolating resonator response from noisy background. We were able to compute loaded quality factor, resonance frequency from response data with high reproducibility even from those experimental data sets where resonance spikes were hardly visible.
The potential of superconducting qubits as the medium for a scalable quantum computer has motivated the pursuit of improved interactions within this system. Two challenges for the field of superconducting qubits are measurement fidelity, to accurately determine the state of the qubit, and the efficient transfer of quantum states. In measurement, the current state-of-the-art method employs dispersive readout, by coupling the qubit to a cavity and reading the resulting shift in cavity frequency to infer the qubit's state; however, this is vulnerable to Purcell relaxation, as well as being modeled off a simplified two-level abstraction of the qubit. In state transfer, the existing proposal for moving quantum states is mostly untested against non-idealities that will likely be present in an experiment. In this dissertation, we examine three problems within these two areas.We first describe a new scheme for fast and high-fidelity dispersive measurement specifically designed to circumvent the Purcell Effect. To do this, the qubit-resonator interaction is turned on only when the resonator is decoupled from the environment; then, after the resonator state has shifted enough to infer the qubit state, the qubit-resonator interaction is turned off before the resonator and environment are recoupled. We also show that the effectiveness of this ``Catch-Disperse-Release'' procedure partly originates from quadrature squeezing of the resonator state induced by the Jaynes-Cummings nonlinearity.The Catch-Disperse-Release measurement scheme treats the qubit as a two-level system, which is a common simplification used in theoretical works. However, the most promising physical candidate for a superconducting qubit, the transmon, is a multi-level system. In the second work, we examine the effects of including the higher energy levels of the transmon. Specifically, we expand the eigenstate picture developed in the first work to encompass multiple qubit levels, and examine the resulting changes to the system. In particular, we analyze the population of the non-target eigenstates as a result of this expanded model, and provide an analytical form for these deviations from the simpler model in Catch-Disperse-Release (i.e., the dressed state approximation).Lastly, we assess the robustness of the existing quantum state transfer protocol, testing its performance under typical experimental deviations from the ideal case. We show that the procedure is resilient to almost all non-idealities, except frequency mismatch between the two cavities. We also demonstrate a method to compensate for one such error in frequency-matching.
The majority of Quantum Random Number Generators (QRNG) are designed as converters of a continuous quantum random variable into a discrete classical random bit value. For the resulting random bit sequence to be minimally biased, the conversion process demands an experimenter to fully characterize the underlying quantum system and implement parameter estimation routines. Here we show that conventional approaches to parameter estimation (such as e.g. {\it Maximum Likelihood Estimation}) used on a finite QRNG data sample without caution may introduce binning bias and lead to overestimation of the randomness of the QRNG output. To bypass these complications, we develop an alternative conversion approach based on the Bayesian statistical inference method. We illustrate our approach using experimental data from a time-of-arrival QRNG and numerically simulated data from a vacuum homodyning QRNG. Side-by-side comparison with the conventional conversion technique shows that our method provides an automatic on-line bias control and naturally bounds the best achievable QRNG bit rate for a given measurement record.