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IEEE International Conference on Problems of Informatics, Electronics and Radio Engineering (PIERE)

The Amplitude of Output Signal Estimation in the Study of Quantum Superconducting Structures

Anastasiya E. Koltakova, Sergey E. Radchenko, Вострецов Алексей Геннадьевич

Published Dec 10, 2020• 0 citations
Publisher

Abstract

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.

DOI
10.1109/piere51041.2020.9314674

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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.
We analyze the dynamics of a qubit-resonator system coupled with a thermal bath and external electromagnetic fields. Using the evolution equations for the set of Heisenberg operators that describe the whole system, we derive an expression for the resonator field, that includes the resonator-drive, the resonator-bath, and resonator-qubit interactions. The renormalization of the resonator frequency, caused by the qubit-resonator interaction, is accounted for. Using the solutions for the resonator field, we derive the equation that describes the qubit dynamics. The dependence of the qubit evolution during the measurement time on the fidelity of a single-shot measurement is studied. The relation between the fidelity and measurement time is shown explicitly. We proposed a novel adiabatic method for the phase qubit measurement. The method utilizes a low-frequency, quasi-classical resonator inductively coupled to the qubit. The resonator modulates the qubit energy, and the back reaction of the qubit causes a shift in the phase of the resonator. The resonator phase shift can be used to determine the qubit state. We have simulated this measurement taking into the account the energy levels outside the phase qubit manifold. We have shown that, for qubit frequencies in the range of 8-12GHZ, a resonator frequency of 500 MHz and a measurement time of 100 ns, the phase difference between the two qubit states is greater than 0.2 rad. This phase difference exceeds the measurement uncertainty, and can be detected using a classical phase-meter. A fidelity of 0.9999 can be achieved for a relaxation time of 0.5 ms. We also model and simulate a microstrip-SQUID amplifier of frequency about 500 MHz, which could be used to amplify the resonator oscillations in the phase qubit adiabatic measurement. The voltage gain and the amplifier noise temperature are calculated. We simulate the preparation of a generalized Bell state and compute the relaxation times required for achieving high fidelities. We consider two capacitively coupled phase qubits similar to that used in the experimental work of R. Bialczak et al. (Nature Physics, 6, 409, 2010). The Bell state was created using a NOT gate and a universal entangling gate. We solved the equation of motion for the density matrix with the Bloch relaxation times, T{sub 1} and T{sub 2}. For every qubit we took into consideration all the states in the shallow well including the states outside the qubit manifold. Also we took into consideration unwanted interaction between the qubits during the application of the NOT gate. The NOT gate was implemented using a Gaussian pulse assuming the frequency difference between the two qubits is 200 MHz. An entangling gate was implemented reducing this frequency difference to zero. We have found the optimal parameters for the Gaussian pulse and the optimal duration for the entangling gate. We have shown that the maximum fidelity of 0.99 can be achieved for the minimum relaxation time, T{sub 1} = 1.2 {micro}s, if T{sub 2} = 2T{sub 1}. By slightly increasing the required value of T{sub 1}, one can sharply reduce the required value for T{sub 2}.
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.
We study the dynamics of a qubit-resonator system, when the resonator is driven by two signals. The interaction of the qubit with the high-amplitude driving we consider in terms of the qubit dressed states. Interaction of the dressed qubit with the second probing signal can essentially change the amplitude of this signal. We calculate the transmission amplitude of the probe signal through the resonator as a function of the qubit’s energy and the driving frequency detuning. The regions of increase and attenuation of the transmitted signal are calculated and demonstrated graphically. We present the influence of the signal parameters on the value of the amplification, and discuss the values of the qubit-resonator system parameters for an optimal amplification and attenuation of the weak probe signal.
We study the dynamics of a qubit-resonator system, when the resonator is driven by two signals. The interaction of the qubit with the high-amplitude driving we consider in terms of the qubit dressed states. Interaction of the dressed qubit with the second probing signal can essentially change the amplitude of this signal. We calculate the transmission amplitude of the probe signal through the resonator as a function of the qubit's energy and the driving frequency detuning. The regions of increase and attenuation of the transmitted signal are calculated and demonstrated graphically. We present the influence of the signal parameters on the value of the amplification, and discuss the values of the qubit-resonator system parameters for an optimal amplification and attenuation of the weak probe signal.
This paper reports on the results of the investigation of a superconducting flux quantum bit (qubit) in the quasi-dispersive regime, where the frequency of a probe signal even though is lower than, but, nevertheless, close to the excitation frequency of the qubit. In this regime, in contrast to the known experiments, the interaction of the qubit with a waveguide leads not only to a shift of the resonance frequency, which is characteristic of the dispersive regime, but also to a significant broadening of the resonance line due to the spontaneous emission of the qubit. On the basis of the analysis of the amplitude–frequency characteristic of the transmission signal, this makes it possible to determine, under single-frequency excitation, the characteristic parameters of the qubit inductively coupled to the coplanar resonator.