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Register a new userExact quantum Bayesian rule for qubit measurements in circuit QED
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Developing efficient framework for quantum measurements is of essential importance to quantum science and technology. In this work, for the important superconducting circuit-QED setup, we present a rigorous and analytic solution for the effective quantum trajectory equation (QTE) after polaron transformation and converted to the form of Stratonovich calculus. We find that the solution is a generalization of the elegant quantum Bayesian approach developed in arXiv:1111.4016 by Korotokov and currently applied to circuit-QED measurements. The new result improves both the diagonal and offdiagonal elements of the qubit density matrix, via amending the distribution probabilities of the output currents and several important phase factors. Compared to numerical integration of the QTE, the resultant quantum Bayesian rule promises higher efficiency to update the measured state, and allows more efficient and analytical studies for some interesting problems such as quantum weak values, past quantum state, and quantum state smoothing. The method of this work opens also a new way to obtain quantum Bayesian formulas for other systems and in more complicated cases.
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We present and demonstrate a general three-step method for extracting the quantum efficiency of dispersive qubit readout in circuit QED. We use active depletion of post-measurement photons and optimal integration weight functions on two quadratures to maximize the signal-to-noise ratio of the non-steady-state homodyne measurement. We derive analytically and demonstrate experimentally that the method robustly extracts the quantum efficiency for arbitrary readout conditions in the linear regime. We use the proven method to optimally bias a Josephson traveling-wave parametric amplifier and to quantify different noise contributions in the readout amplification chain.
We study ultrastrong-coupling quantum-phase-transition phenomena in a few-qubit system. In the one-qubit case, three second-order transitions occur and the Goldstone mode emerges under the condition of ultrastrong-coupling strength. Moreover, a first-order phase transition occurs between two different superradiant phases. In the two-qubit case, a two-qubit Hamiltonian with qubit-qubit interactions is analyzed fully quantum mechanically. We show that the quantum phase transition is inhibited even in the ultrastrong-coupling regime in this model. In addition, in the three-qubit model, the superradiant quantum phase transition is retrieved in the ultrastrong-coupling regime. Furthermore, the N-qubit model with U(1) symmetry is studied and we find that the superradiant phase transition is inhibited or restored with the qubit-number parity.
Using circuit QED, we consider the measurement of a superconducting transmon qubit via a coupled microwave resonator. For ideally dispersive coupling, ringing up the resonator produces coherent states with frequencies matched to transmon energy states. Realistic coupling is not ideally dispersive, however, so transmon-resonator energy levels hybridize into joint eigenstate ladders of the Jaynes-Cummings type. Previous work has shown that ringing up the resonator approximately respects this ladder structure to produce a coherent state in the eigenbasis (a dressed coherent state). We numerically investigate the validity of this coherent state approximation to find two primary deviations. First, resonator ring-up leaks small stray populations into eigenstate ladders corresponding to different transmon states. Second, within an eigenstate ladder the transmon nonlinearity shears the coherent state as it evolves. We then show that the next natural approximation for this sheared state in the eigenbasis is a dressed squeezed state, and derive simple evolution equations for such states using a hybrid phase-Fock-space description.
The interaction between the electromagnetic field inside a cavity and natural or artificial atoms has played a crucial role in developing our understanding of light-matter interaction, and is central to various quantum technologies. Recently, new regimes beyond the weak and strong light-matter coupling have been explored in several settings. These regimes, where the interaction strength is comparable (ultrastrong) or even higher (deep-strong) than the transition frequencies in the system, can give rise to new physical effects and applications. At the same time, they challenge our understanding of cavity QED. When the interaction strength is so high, fundamental issues like the proper definition of subsystems and of their quantum measurements, the structure of light-matter ground states, or the analysis of time-dependent interactions are subject to ambiguities leading to even qualitatively distinct predictions. The resolution of these ambiguities is also important for understanding and designing next-generation quantum devices that will exploit the ultrastrong coupling regime. Here we discuss and provide solutions to these issues.
Superconducting circuits are one of the leading quantum platforms for quantum technologies. With growing system complexity, it is of crucial importance to develop scalable circuit models that contain the minimum information required to predict the behaviour of the physical system. Based on microwave engineering methods, divergent and non-divergent Hamiltonian models in circuit quantum electrodynamics have been proposed to explain the dynamics of superconducting quantum networks coupled to infinite-dimensional systems, such as transmission lines and general impedance environments. Here, we study systematically common linear coupling configurations between networks and infinite-dimensional systems. The main result is that the simple Lagrangian models for these configurations present an intrinsic natural length that provides a natural ultraviolet cutoff. This length is due to the unavoidable dressing of the environment modes by the network. In this manner, the coupling parameters between their components correctly manifest their natural decoupling at high frequencies. Furthermore, we show the requirements to correctly separate infinite-dimensional coupled systems in local bases. We also compare our analytical results with other analytical and approximate methods available in the literature. Finally, we propose several applications of these general methods to analog quantum simulation of multi-spin-boson models in non-perturbative coupling regimes.
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