Measurement Protocol for the Entanglement Spectrum of Cold Atoms

Entanglement, and, in particular the entanglement spectrum, plays a major role in characterizing many-body quantum systems. While there has been a surge of theoretical works on the subject, no experimental measurement has been performed to date because of the lack of an implementable measurement scheme. Here, we propose a measurement protocol to access the entanglement spectrum of many-body states in experiments with cold atoms in optical lattices. Our scheme effectively performs a Ramsey spectroscopy of the entanglement Hamiltonian and is based on the ability to produce several copies of the state under investigation together with the possibility to perform a global swap gate between two copies conditioned on the state of an auxiliary qubit. We show how the required conditional swap gate can be implemented with cold atoms, either by using Rydberg interactions or coupling the atoms to a cavity mode. We illustrate these ideas on a simple (extended) Bose-Hubbard model where such a measurement protocol reveals topological features of the Haldane phase

CONTROL AND CHARACTERIZATION OF OPEN QUANTUM SYSTEMS

The study of open physical systems concerns finding ways to incorporate the lack of information about the environment into a theory that best describes the behavior of the system. We consider characterizing the environment by using the system as a sensor, mitigating errors, and learning the physics governing systems out of equilibrium with computer algorithms.We characterize long-range correlated errors and crosstalk, which are impor- tant factors that negatively impacts the performance of noisy intermediate-scale quantum (NISQ) computing devices. We propose a compressed sensing method for detecting correlated dephasing errors, assuming only that the correlations are sparse (i.e., at most s pairs of qubits have correlated errors, where s << n(n − 1)/2, and n is the total number of qubits). Our method uses entangled many-qubit GHZ states, and it can detect long-range correlations whose distribution is completely arbitrary, independent of the geometry of the system. Our method is also highly scalable: it requires only s log n measurement settings, in contrast to the naive O(n2) estimate, and efficient classical postprocessing based on convex optimization. For mitigating the effect of errors, we consider measurements in a quantum computer. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. We experimentally il- lustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, resulting in a 30% improvement in detection error over the conventional threshold method. Our approach does not depend on the specific details of the system and can be readily generalized to other quantum computing platforms. To learn about physical systems using computer algorithms, we consider the problem of arrow of time. We show that a machine learning algorithm can learn to discern the direction of time’s arrow when provided with a system’s microscopic trajectory as input. Examination of the algorithm’s decision-making process reveals that it discovers the underlying thermodynamic mechanism and the relevant physical observables. Our results indicate that machine learning techniques can be used to study systems out of equilibrium, and ultimately to uncover physical principles

Simple master equations for describing driven systems subject to classical non-Markovian noise

Driven quantum systems subject to non-Markovian noise are typically difficult to model even if the noise is classical. We present a systematic method based on generalized cumulant expansions for deriving a time-local master equation for such systems. This master equation has an intuitive form that directly parallels a standard Lindblad equation, but contains several surprising features: the combination of driving and non-Markovianity results in effective time-dependent dephasing rates that can be negative, and the noise can generate Hamiltonian renormalizations even though it is classical. We analyze in detail the highly relevant case of a Rabi-driven qubit subject to various kinds of non-Markovian noise including $1/f$ fluctuations, finding an excellent agreement between our master equation and numerically-exact simulations over relevant timescales. The approach outlined here is more accurate than commonly employed phenomenological master equations which ignore the interplay between driving and noise.Comment: 12+4 pages, 6+4 figure

Measurement and feedforward induced entanglement negativity transition

We study the interplay between measurement-induced dynamics and conditional unitary evolution in quantum systems. We numerically and analytically investigate commuting random measurement and feedforward (MFF) processes, and find a sharp transition in their ability to generate entanglement negativity as the number of MFF channels varies. We also establish a direct connection between these findings and transitions induced by random dephasing from an environment with broken time-reversal symmetry. In one variant of the problem, we employ free probability theory to rigorously prove the transition's existence. Furthermore, these MFF processes have dynamic circuit representations that can be experimentally explored on current quantum computing platforms.Comment: 5 pages, 4 figures (main) + 12 pages, 3 figures (supplementary materials

Duration of delayed diagnosis in HIV/AIDS patients in Iran: a CD4 depletion model analysis

ObjectiveDelayed diagnosis of HIV can lead to an inappropriate response to antiretroviral therapy (ART), rapid progression of the disease, and death. It can also carry harmful effects on public health due to the increment of transmission. This study aimed to estimate the duration of delayed diagnosis (DDD) in HIV patients in Iran.MethodsThis hybrid cross-sectional cohort study was conducted on the national HIV surveillance system database (HSSD). Linear mixed effect models with random intercept, random slope, and both were used to estimate the parameters required for the CD4 depletion model to determine the best-fitted model for DDD, stratified by the route of transmission, gender, and age group.ResultsThe DDD was estimated in 11,373 patients including 4,762 (41.87%) injection drug users (IDUs), 512 (4.5%) men who had sexual contact with men (MSM), 3,762 (33.08%) patients with heterosexual contacts, and 2,337 (20.55%) patients who were infected through other routes of HIV transmission. The total mean DDD was 8.41 ± 5.97 years. The mean DDD was 7.24 ± 0.08 and 9.43 ± 6.83 years in male and female IDUs, respectively. In the heterosexual contact group, DDD was obtained as 8.60 ± 6.43 years in male patients and 9.49 ± 7.17 years in female patients. It was also estimated as 9.37 ± 7.30 years in the MSM group. Furthermore, patients infected through other transmission routes were found with a DDD of 7.90 ± 6.74 years for male patients and a DDD of 7.87 ± 5.87 years for female patients.ConclusionA simple CD4 depletion model analysis is represented, which incorporates a pre-estimation step to determine the best-fitted linear mixed model for calculating the parameters required for the CD4 depletion model. Considering such a noticeably high HIV diagnostic delay, especially in older adults, MSM, and heterosexual contact groups, regular periodic screening is required to reduce the DDD