Quantum Optimal Control via Semi-Automatic Differentiation

We develop a framework of "semi-automatic differentiation" that combines existing gradient-based methods of quantum optimal control with automatic differentiation. The approach allows to optimize practically any computable functional and is implemented in two open source Julia packages, GRAPE.jl and Krotov.jl, part of the QuantumControl.jl framework. Our method is based on formally rewriting the optimization functional in terms of propagated states, overlaps with target states, or quantum gates. An analytical application of the chain rule then allows to separate the time propagation and the evaluation of the functional when calculating the gradient. The former can be evaluated with great efficiency via a modified GRAPE scheme. The latter is evaluated with automatic differentiation, but with a profoundly reduced complexity compared to the time propagation. Thus, our approach eliminates the prohibitive memory and runtime overhead normally associated with automatic differentiation and facilitates further advancement in quantum control by enabling the direct optimization of non-analytic functionals for quantum information and quantum metrology, especially in open quantum systems. We illustrate and benchmark the use of semi-automatic differentiation for the optimization of perfectly entangling quantum gates on superconducting qubits coupled via a shared transmission line. This includes the first direct optimization of the non-analytic gate concurrence.Comment: 30 pages, 2 figures, 2 tables. Accepted in Quantu

Individual differences in the shape of the nasal visual field

AbstractBetween-subject differences in the shape of the nasal visual field were assessed for 103 volunteers 21–85years of age and free of visual disorder. Perimetry was conducted with a stimulus for which contrast sensitivity is minimally affected by peripheral defocus and decreased retinal illumination. One eye each was tested for 103 volunteers free of eye disease in a multi-center prospective longitudinal study. A peripheral deviation index was computed as the difference in log contrast sensitivity at outer (25–29° nasal) and inner (8° from fixation) locations. Values for this index ranged from 0.01 (outer sensitivity slightly greater than inner sensitivity) to −0.7 log unit (outer sensitivity much lower than inner sensitivity). Mean sensitivity for the inner locations was independent of the deviation index (R2<1%), while mean sensitivity for the outer locations was not (R2=38%, p<0.0005). Age was only modestly related to the index, with a decline by 0.017 log unit per decade (R2=10%). Test-retest data for 21 volunteers who completed 7–10 visits yielded standard deviations for the index from 0.04 to 0.17 log unit, with a mean of 0.09 log unit. Between-subject differences in peripheral deviation persisted over two years of longitudinal testing. Peripheral deviation indices were correlated with indices for three other perimetric stimuli used in a subset of 24 volunteers (R2 from 20% to 49%). Between-subject variability in shape of the visual field raises concerns about current clinical visual field indices, and further studies are needed to develop improved indices

Soft X-ray coronal spectra at low activity levels observed by RESIK

The quiet-Sun X-ray emission is important for deducing coronal heating mechanisms, but it has not been studied in detail since the Orbiting Solar Observatory (OSO) spacecraft era. Bragg crystal spectrometer X-ray observations have generally concentrated on flares and active regions. The high sensitivity of the RESIK (REntgenovsky Spectrometer s Izognutymi Kristalami) instrument on the CORONAS-F solar mission has enabled the X-ray emission from the quiet corona to be studied in a systematic way for the first time. Our aim is to deduce the physical conditions of the non-flaring corona from RESIK line intensities in several spectral ranges using both isothermal and multithermal assumptions. We selected and analyzed spectra in 312 quiet-Sun intervals in January and February 2003, sorting them into 5 groups according to activity level. For each group, the fluxes in selected spectral bands have been used to calculate values parameters for the best-fit that lead to a intensities characteristic of each group. We used both isothermal and multitemperature assumptions, the latter described by differential emission measure (DEM) distributions. RESIK spectra cover the wavelength range (3.3-6.1 A). This includes emission lines of highly ionized Si, S, Cl, Ar, and K, which are suitable for evaluating temperature and emission measure, were used. The RESIK spectra during these intervals of very low solar activity for the first time provide information on the temperature structure of the quiet corona. Although most of the emission seems to arise from plasma with a temperature between 2MK and 3MK, there is also evidence of a hotter plasma (T approx. 10MK) with an emission measure 3 orders smaller than the cooler component. Neither coronal nor photospheric element abundances appear to describe the observed spectra satisfactorily.Comment: Submitting 1 Latex and 7 figure file

Knowledge of learning disabilities: the relationship with choice, duty of care and non-aversive approaches

The present study examines the relationship between the knowledge of the diagnostic criteria for a learning disability (based on DSM IV criteria), care practices and experience in health care and social care staff. Responses to a questionnaire were analysed in terms of participants emphasis on: recognizing duty of care; enabling choice; non-aversive and aversive strategies. Results indicated that the knowledge of the criteria for a learning disability was limited, with only I6% of the sample correctly identifying all three criteria. There were no significant differences between the two groups in relation to experience or level of knowledge. No clear cut differences were found between the groups in relation to tendency to emphasize a particular management approach, with the strategies adopted appearing to be influenced by vignettes used in this study. Participants tended to give responses that identified both a recognition of their duty of care to clients and the need to enable choice. Limitations of this study are discussed

Principles of tractor atom interferometry

We present possible design concepts for a tractor atom interferometer (TAI) based on three-dimensional confinement and transport of ultracold atoms. The confinement reduces device size and wave-packet dispersion, enables arbitrary holding times, and facilitates control to create complex trajectories that allow for optimization to cancel unwanted sensitivity, fast splitting and recombination, and suppression of detrimental nonadiabatic excitation. Thus, the design allows for further advancement of compact, high-sensitivity, quantum sensing technology. In particular, we focus on the implementation of quantum-enhanced accelerometers and gyroscopes. We discuss TAI protocols for both spin-dependent and scalar trapping potentials. Using optimal control theory, we demonstrate the splitting of the wave function on a time scale two orders of magnitude shorter than the previous proposal using adiabatic dynamics, thus maximizing the time spent at full separation, where the interferometric phase is accumulated. Lastly, we explore the possibility of including non-classical correlations between the atoms to improve sensitivity. The performance estimates for TAI give a promising perspective for atom-interferometry-based sensing, significantly exceeding the sensitivities of current state-of-the-art devices.Comment: 10 pages, 5 figure

Anharmonicity, vibrational instability and Boson peak in glasses

We show that a {\em vibrational instability} of the spectrum of weakly interacting quasi-local harmonic modes creates the maximum in the inelastic scattering intensity in glasses, the Boson peak. The instability, limited by anharmonicity, causes a complete reconstruction of the vibrational density of states (DOS) below some frequency $\omega_c$, proportional to the strength of interaction. The DOS of the new {\em harmonic modes} is independent of the actual value of the anharmonicity. It is a universal function of frequency depending on a single parameter -- the Boson peak frequency, $\omega_b$ which is a function of interaction strength. The excess of the DOS over the Debye value is $\propto\omega^4$ at low frequencies and linear in $\omega$ in the interval $\omega_b \ll \omega \ll \omega_c$. Our results are in an excellent agreement with recent experimental studies.Comment: LaTeX, 8 pages, 6 figure

Physical Origin of the Boson Peak Deduced from a Two-Order-Parameter Model of Liquid

We propose that the boson peak originates from the (quasi-) localized vibrational modes associated with long-lived locally favored structures, which are intrinsic to a liquid state and are randomly distributed in a sea of normal-liquid structures. This tells us that the number density of locally favored structures is an important physical factor determining the intensity of the boson peak. In our two-order-parameter model of the liquid-glass transition, the locally favored structures act as impurities disturbing crystallization and thus lead to vitrification. This naturally explains the dependence of the intensity of the boson peak on temperature, pressure, and fragility, and also the close correlation between the boson peak and the first sharp diffraction peak (or prepeak).Comment: 5 pages, 1 figure, An error in the reference (Ref. 7) was correcte

Momentum transfer using chirped standing wave fields: Bragg scattering

We consider momentum transfer using frequency-chirped standing wave fields. Novel atom-beam splitter and mirror schemes based on Bragg scattering are presented. It is shown that a predetermined number of photon momenta can be transferred to the atoms in a single interaction zone.Comment: 4 pages, 3 figure

Coherent control using adaptive learning algorithms

We have constructed an automated learning apparatus to control quantum systems. By directing intense shaped ultrafast laser pulses into a variety of samples and using a measurement of the system as a feedback signal, we are able to reshape the laser pulses to direct the system into a desired state. The feedback signal is the input to an adaptive learning algorithm. This algorithm programs a computer-controlled, acousto-optic modulator pulse shaper. The learning algorithm generates new shaped laser pulses based on the success of previous pulses in achieving a predetermined goal.Comment: 19 pages (including 14 figures), REVTeX 3.1, updated conten