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arXiv:2006.11950 · Physical Review Letters

Prediction of Short Time Qubit Readout via Measurement of the Next Quantum Jump of a Coupled Damped Driven Harmonic Oscillator

Massimo Porrati B, Seth Putterman

Published Dec 21, 2020• 3 citations
arXivHTMLPDF

Abstract

The dynamics of the next quantum jump for a qubit [two level system] coupled to a readout resonator [damped driven harmonic oscillator] is calculated. A quantum mechanical treatment of readout resonator reveals nonexponential short time behavior which could facilitate detection of the state of the qubit faster than the resonator lifetime.

DOI
10.1103/physrevlett.125.260403

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The dynamics of the next quantum jump for a qubit [two level system] coupled to a readout resonator [damped driven harmonic oscillator] is calculated. A quantum mechanical treatment of readout resonator reveals nonexponential short time behavior which could facilitate detection of the state of the qubit faster than the resonator lifetime.
A measurement of the time between quantum jumps implies the capability to measure the next jump. During the time between jumps the quantum system is not evolving in a closed or unitary manner. While the wave function maintains phase coherence it evolves according to a non-Hermitian effective Hamiltonian. So under null measurement the timing of the next quantum jump can change by very many orders of magnitude when compared to rates obtained by multiplying lifetimes with occupation probabilities obtained via unitary transformation. The theory developed in 1987 for atomic fluorescence is here extended to transitions in transmon qubits. These systems differ from atoms in that they are read out with a harmonic cavity whose resonance is determined by the state of the qubit. We extend our analysis of atomic fluorescence to this infinite level system by treating the cavity as a quantum system. We find that next photon statistics is highly nonexponential and when implemented will enable faster readout, such as on timescales shorter than the decay time of the cavity. Commonly used heterodyne measurements are applied on timescales longer than the cavity lifetime. The overlap between the next photon theory and the theory of heterodyne measurement which are described according to the stochastic Schr\"odinger equation is elucidated. In the limit of large dispersion the intrinsic error for next jump detection, at short time, tends to zero. Whereas for short-time dyne detection the error remains finite for all values of dispersion.
We study qubit decoherence under generalized dispersive readout, i.e., we investigate a qubit coupled to a resonantly driven dissipative harmonic oscillator. We provide a complete picture by allowing for arbitrarily large qubit-oscillator detuning and by considering also a coupling to the square of the oscillator coordinate, which is relevant for flux qubits. Analytical results for the decoherence time are obtained by a transformation of the qubit-oscillator Hamiltonian to the dispersive frame and a subsequent master equation treatment beyond the Markov limit. We predict a crossover from Markovian decay to a decay with Gaussian shape. Our results are corroborated by the numerical solution of the full qubit-oscillator master equation in the original frame.
We propose a generalization of dispersive qubit readout that provides the time evolution of a flux qubit observable. Our proposal relies on the nonlinear coupling of the qubit to a harmonic oscillator with high frequency, representing a dc superconducting quantum interference device. Information about the qubit dynamics is obtained by recording the oscillator response to resonant driving and subsequent lock-in detection. The measurement process is simulated for the example of coherent qubit oscillations. This corroborates the underlying measurement relation and also reveals that the measurement scheme possesses low backaction and high fidelity.
We investigate the use of driven qubits coupled to a harmonic oscillator to implement a i SWAP gate. By dressing the qubits through an external driving field, the qubits and the harmonic oscillator can be selectively coupled, allowing for the measurement of individual qubit states, as well as leading to effective qubit-qubit interactions. We compare the qubit readout on bare and dressed qubits, and demonstrate that when coupled to low-frequency resonators, dressed qubits provide a more robust readout than bare qubits in the presence of damping and thermal effects. Furthermore, we study the impact of various system parameters on the fidelity of the two-qubit gate, identifying an optimal range for quantum computation. Our findings guide the implementation of high-fidelity quantum gates in experimental setups, for example, those employing nanoscale mechanical resonators.
Quantum mechanics predicts that a vibrating object's energy comes in discrete packets, yet no measurement of its position reveals this discreteness. Resolving individual energy levels requires a qualitatively different measurement, one coupling to the resonator's energy rather than its displacement. We use a superconducting qubit dispersively coupled to a nanomechanical resonator to perform repeated quantum nondemolition measurements of the phonon number. An aligned transfer-print technique integrating the qubit and resonator yields a mechanical lifetime of T1=2.1T_1 = 2.1T1​=2.1 milliseconds and a dispersive shift of 2χ/2π=3282χ/2π= 3282χ/2π=328 kilohertz per phonon. We heralded single-phonon states with 85% fidelity and observed quantum jumps between the resonator's first excited state and ground state. These discontinuous transitions are a striking manifestation of quantum mechanics in a massive, vibrating object.
We propose a generalization of dispersive qubit readout that provides the time evolution of a flux qubit observable.Our proposal relies on the nonlinear coupling of the qubit to a harmonic oscillator with high frequency, representing a dc superconducting quantum interference device.Information about the qubit dynamics is obtained by recording the oscillator response to resonant driving and subsequent lock-in detection.The measurement process is simulated for the example of coherent qubit oscillations.This corroborates the underlying measurement relation and also reveals that the measurement scheme possesses low backaction and high fidelity.