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arXiv:2302.03827

Autonomous coherence protection of a two-level system in a fluctuating environment

Fernando Quijandría, Jason Twamley

Published Feb 8, 2023• 0 citations
arXivHTMLPDF

Abstract

We re-examine a scheme generalized by [R. Finkelstein et al, Phys. Rev. X 11, 011008 (2021)], whose original purpose was to remove the effects of static Doppler broadening from an ensemble of non-interacting two-level systems (qubits). This scheme involves the simultaneous application of red and blue detuned drives between a qubit level and an auxiliary level, and by carefully choosing the drive amplitudes and detunings, the drive-induced energy shifts can exactly compensate the inhomogeneous static Doppler-induced frequency shifts - effectively removing the inhomogeneous Doppler broadening. We demonstrate that this scheme is far more powerful and can also protect a single (or even an ensemble), qubit's energy levels from noise which depends on both time and space: the same scheme can greatly reduce the effects of dephasing noise induced by a time-fluctuating environment. As examples we study protection against two types of non-Markovian environments that appear in many physical systems: Gaussian noise and non-Gaussian noise - Random Telegraph Noise. Through numerical simulations we demonstrate the enhancement of the spin coherence time $T_2^*$, of a qubit in a fluctuating environment by three orders of magnitude as well as the refocusing of its initially drifting frequency. This same scheme, using only two drives, can operate on an collection of qubits, providing temporal and spatial stabilization simultaneously and in parallel yielding a collection of high quality near-identical qubits which can be useful for many quantum technologies such as quantum computing and sensing, with the potential to achieve fault tolerant quantum computation much sooner.

DOI
10.48550/arxiv.2302.03827

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We re-examine a scheme generalized by [R. Finkelstein et al, Phys. Rev. X 11, 011008 (2021)], whose original purpose was to remove the effects of static Doppler broadening from an ensemble of non-interacting two-level systems (qubits). This scheme involves the simultaneous application of red and blue detuned drives between a qubit level and an auxiliary level, and by carefully choosing the drive amplitudes and detunings, the drive-induced energy shifts can exactly compensate the inhomogeneous static Doppler-induced frequency shifts - effectively removing the inhomogeneous Doppler broadening. We demonstrate that this scheme is far more powerful and can also protect a single (or even an ensemble), qubit's energy levels from noise which depends on both time and space: the same scheme can greatly reduce the effects of dephasing noise induced by a time-fluctuating environment. As examples we study protection against two types of non-Markovian environments that appear in many physical systems: Gaussian noise and non-Gaussian noise - Random Telegraph Noise. Through numerical simulations we demonstrate the enhancement of the spin coherence time T2∗T_2^*T2∗​, of a qubit in a fluctuating environment by three orders of magnitude as well as the refocusing of its initially drifting frequency. This same scheme, using only two drives, can operate on an collection of qubits, providing temporal and spatial stabilization simultaneously and in parallel yielding a collection of high quality near-identical qubits which can be useful for many quantum technologies such as quantum computing and sensing, with the potential to achieve fault tolerant quantum computation much sooner.
We implement dynamical decoupling techniques to mitigate noise and enhance the lifetime of an entangled state that is formed in a superconducting flux qubit coupled to a microscopic two-level system. By rapidly changing the qubit's transition frequency relative to the two-level system, we realize a refocusing pulse that reduces dephasing due to fluctuations in the transition frequencies, thereby improving the coherence time of the entangled state. The coupling coherence is further enhanced when applying multiple refocusing pulses, in agreement with our 1/f noise model. The results are applicable to any two-qubit system with transverse coupling and they highlight the potential of decoupling techniques for improving two-qubit gate fidelities, an essential prerequisite for implementing fault-tolerant quantum computing.
Superconducting circuits are a leading platform for quantum computing. However, their coherence times are still limited and exhibit temporal fluctuations. Those phenomena are often attributed to the coupling between qubits and material defects that can be well described as an ensemble of two-level systems (TLSs). Among them, charge fluctuators inside amorphous oxide layers contribute to both low-frequency 1/f1/f1/f charge noise and high-frequency dielectric loss, causing fast qubit dephasing and relaxation. Moreover, spectral diffusion from mutual TLS interactions varies the noise amplitude over time, fluctuating the qubit lifetime. Here, we propose to mitigate those harmful effects by engineering the relevant TLS noise spectral densities. Specifically, our protocols smooth the high-frequency noise spectrum and suppress the low-frequency noise amplitude via depolarizing and dephasing the TLSs, respectively. As a result, we predict a drastic stabilization in qubit lifetime and an increase in qubit pure dephasing time. Our detailed analysis of feasible experimental implementations shows that the improvement is not compromised by spurious coupling from the applied noise to the qubit.
Quantum coherences are paramount resources for applications, such as quantum-enhanced light-harvesting or quantum computing, which are fragile against environmental noise.We here derive generalized quantum master equations using perturbation theory in order to describe the effective time evolution of finite-size quantum systems subject to static noise on all time scales.We then analyze the time evolution of the coherences under energy broadening noise in a variety of systems characterized by both short-and long-range interactions and by strongly correlated and fully uncorrelated noise -a single qubit, a lattice model with on-site disorder and a potential ladder, and a Bose-Hubbard dimer with random interaction strength-and show that couplings can partially protect the system from the ensemble-averaging induced loss of coherence.Our work suggests that suitably tuned couplings could be employed to counteract part of the dephasing detrimental to quantum applications.Conversely, tailored noise distributions can be utilized to reach target nonequilibrium quantum states.
Two-level systems (TLSs) are the major source of dephasing of spin qubits in numerous quantum computing platforms. In spite of much effort, it has been difficult to substantially mitigate the effects of this noise or, in many cases, to fully understand its physical origin. We propose a method to make progress on both of these issues. When an oscillating field is applied to a TLS, stochastic resonance can occur and the noise spectrum is moved to higher frequencies. This shift in the TLS noise spectrum will increase the dephasing times of the qubits that they influence. Furthermore, the details of this effect depend on the physical properties of the noise sources. Thus one can use qubit spectroscopy to investigate their physical properties, specifically the extent to which the TLSs themselves possess quantum coherence. We find that it should be possible to determine the dephasing rate and the energy-level separation of the TLS themselves in this way.
Two-level systems (TLS) are the major source of dephasing of spin qubits in numerous quantum computing platforms. In spite of much effort, it has been difficult to substantially mitigate the effects of this noise or, in many cases, to fully understand its physical origin. We propose a method to make progress on both of these issues. When an oscillating field is applied to a TLS, stochastic resonance can occur and the noise spectrum is moved to higher frequencies. This shift in the TLS noise spectrum will increase the dephasing times of the qubits that they influence. Furthermore, the details of this effect depend on the physical properties of the noise sources. Thus one can use qubit spectroscopy to investigate their physical properties, specifically the extent to which the TLS themselves possess quantum coherence. We find that it should be possible to determine the dephasing rate and the energy level separation of the TLS themselves in this way.
We study the dynamics of dephasing in a quantum two-level system by modeling both 1/f1/f1/f and high-frequency noise by random telegraph processes. Our approach is based on a so-called spin-fluctuator model in which a noisy environment is modeled by a large number of fluctuators. In the continuous limit we obtain an effective random process (ERP) that is described by a distribution function of the fluctuators. In a simplified model, we reduce the ERP to the two (slow and fast) ensembles of fluctuators. Using this model, we study decoherence in a superconducting flux qubit and we compare our theoretical results with the available experimental data. We demonstrate good agreement of our theoretical predictions with the experiments. Our approach can be applied to many quantum systems, such as biological complexes, semiconductors, superconducting, and spin qubits, where the effects of interaction with the environment are essential.