We show that a thermally isolated system driven across a quantum phase transition by a noisy control field exhibits anti-Kibble-Zurek behavior, whereby slower driving results in higher excitations. ...We characterize the density of excitations as a function of the ramping rate and the noise strength. The optimal driving time to minimize excitations is shown to scale as a universal power law of the noise strength. Our findings reveal the limitations of adiabatic protocols such as quantum annealing and demonstrate the universality of the optimal ramping rate.
We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed ...and open quantum systems with Markovian decoherence. Our findings support the choice of evolution ansatz in the recently proposed quantum approximate optimization algorithm. Focusing on the Sherrington-Kirkpatrick spin glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian. The optimality of the bang-bang protocols and the characteristic time scale of the pulses provide an efficient parametrization of the protocol and inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems. Furthermore, we find that the success rates of our optimal bang-bang protocols remain high even in the presence of weak external noise and coupling to a thermal bath.
Adiabatic braiding of Majorana zero modes can be used for topologically protected quantum information processing. While extremely robust to many environmental perturbations, these systems are ...vulnerable to noise with high-frequency components. Ironically, slower processes needed for adiabaticity allow more noise-induced excitations to accumulate, resulting in an antiadiabatic behavior that limits the precision of Majorana gates if some noise is present. In a recent publication (2017 Phys. Rev. B 96 075158), fast optimal protocols were proposed as a shortcut for implementing the same unitary operation as the adiabatic braiding in a low-energy effective model. These shortcuts sacrifice topological protection in the absence of noise but provide performance gains and remarkable robustness to noise due to the shorter evolution time. Nevertheless, gates optimized for vanishing noise are suboptimal in the presence of noise. If we know the noise strength beforehand, can we design protocols optimized for the existing unavoidable noise, which will effectively correct the noise-induced errors? We address this question in the present paper, focusing on the same low-energy effective model. We find such optimal protocols using simulated-annealing Monte Carlo simulations. The numerically found pulse shapes, which we fully characterize, are in agreement with Pontryagin's minimum principle, which allows us to arbitrarily improve the approximate numerical results (due to discretization and imperfect convergence) and obtain numerically exact optimal protocols. The protocols are bang-bang (sequence of sudden quenches) for vanishing noise, but contain continuous segments in the presence of multiplicative noise due to the nonlinearity of the master equation governing the evolution. We find that such noise-optimized protocols completely eliminate the above-mentioned antiadiabatic behavior. The final error corresponding to these optimal protocols monotonically decreases with the total time (in three different regimes). A liner fit to 1/τ indicates extrapolation of the cost function to finite value in the τ → ∞ limit. However, quadratic and cubic fits are more suggestive of the cost function extrapolating to zero in the limit of infinite time. Our results set the precision limit of the device as a function of the noise strength and total time.
In this paper, we address the challenge of uncovering patterns in variational optimal protocols for taking the system to ground states of many-body Hamiltonians, using variational quantum algorithms. ...We develop highly optimized classical Monte Carlo (MC) algorithms to find the optimal protocols for transformations between the ground states of the square-lattice XXZ model for finite system sizes. The MC method obtains optimal bang-bang protocols, as predicted by Pontryagin's minimum principle. We identify the minimum time needed for reaching an acceptable error for different system sizes as a function of the initial and target states and uncover correlations between the total time and the wave-function overlap. We determine a dynamical phase diagram for the optimal protocols, with different phases characterized by a topological number, namely, the number of on pulses. Bifurcation transitions as a function of initial and final states, associated with new jumps in the optimal protocols, demarcate these different phases. The number of pulses correlates with the total evolution time. In addition to identifying the topological characteristic above, i.e., the number of pulses, we introduce a correlation function to characterize bang-bang protocols' quantitative geometric similarities. We find that protocols within one phase are indeed geometrically correlated. Identifying and extrapolating patterns in these protocols may inform efficient large-scale simulations on quantum devices.
Here, we present an efficient quantum algorithm to generate a many-body state equivalent to Laughlin’s ν=1/3 fractional quantum Hall state on a digitized quantum computer. Our algorithm only uses ...quantum gates acting on neighboring qubits in a quasi-one-dimensional (1D) setting and its circuit depth is linear in the number of qubits, i.e., the number of Landau orbitals in the second quantized picture. We identify correlation functions that serve as signatures of the Laughlin state and discuss how to obtain them on a quantum computer. We also discuss a generalization of the algorithm for creating quasiparticles in the Laughlin state. This paves the way for several important studies, including quantum simulation of nonequilibrium dynamics and braiding of quasiparticles in quantum Hall states.
Abstract
Introduction
Cognitive behavioral therapy for insomnia (CBT-I) remains the first line treatment for insomnia. CBT-I in comparison with sedative-hypnotics has similar efficacy, but with ...treatment durability and almost no adverse effects. Despite CBT-I being recognized as the best insomnia treatment, access remains limited. Digital CBT-I hopes to address the problem of scale, so as to deliver therapy to the masses. There are now multiple mobile applications available both on smartphone app stores, which claim to deliver evidence based CBT-i. These applications largely come at a cost and patients have to pay to access their services. The goal of this study is to review CBT-i smartphone applications to see if they are indeed validated.
Methods
We performed a search on the two most popular smartphone application platforms: Google Play and Apple Store. We used search terms: sleep, insomnia and CBT-I. We then searched for validation studies for those smartphone applications on Google Scholar. We included studies conducted in the past 10 years. Our second search consisted of reviewing PubMed and Google Scholar for validation studies for CBT-I applications. Our search terms consisted of CBT-I and smartphone, CBT-I and application and CBT-I and digital.
Results
Of the 9 validation studies that we initially found, 6 met our inclusion criteria. 3 were excluded as they did not solely use CBT-I in their applications. All 6 applications reported significant improvement in important sleep quality metrics such as sleep onset latency and total sleep time. 4 studies also reported on a subjective improvement in quality of sleep. 2 studies looked at populations with comorbidities including cannabis use disorder and epilepsy. Both studied again found improvement in sleep quality in those specific populations. There were concerning patterns of bias found amongst the reviewed studies. 3/6 investigators had direct relationships with companies which designed and marketed the applications.
Conclusion
dCBT-I offers an opportunity to increase accessibility to therapy. There are only a limited number of studies which have examined the effectiveness of the applications on the market. There remains serious concerns about the risk of bias and the quality of validation studies which claim to confirm the effectiveness of these applications.
Support (if any)
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