We present a general framework for finding the time-optimal evolution and the optimal Hamil-tonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to that for the brachistochrone in classical mechanics. We reduce the problem to a formal equation for the Hamiltonian which depends on certain constraint functions specifying the range of available Hamiltonians. For some simple examples of the constraints, we explicitly find the optimal solutions. In quantum mechanics one can change a given state to another by applying a suitable Hamiltonian on the system. In many situations, e.g. quantum computation, it is desirable to know the pathway in the shortest time. In this paper we consider the problem of finding the time-optimal path for the evolution of a pure quantum state and the optimal driving Hamiltonian. Recently, a growing number of works related to this topic have appeared. For instance, Alvarez and Gómez [1] showed that the quantum state in Grover's algorithm [2], known as the optimal quantum search algorithm [3], actually follows a geodesic curve derived from the Fubini-Study metric in the projective space. Khaneja et al. [4] and Zhang et al. [5], using a Cartan decomposition scheme for unitary operations, discussed the time optimal way to realize a two-qubit universal unitary gate under the condition that one-qubit operations can be performed in an arbitrarily short time. On the other hand, Tanimura et al. [6] gave an adiabatic solution to the optimal control problem in holonomic quantum computation, in which a desired unitary gate is generated as the holonomy corresponding to the minimal length loop in the space of control parameters for the Hamiltonian. Schulte-Herbrüggen et al. [7] exploited the differential geometry of the projective unitary group to give the tightest known upper bounds on the actual time complexity of some basic modules of quantum algorithms. More recently, Nielsen [8] introduced a lower bound on the size of the quantum circuit necessary to realize a given unitary operator based on the geodesic distance, with a suitable metric, between the unitary and the identity operators. However, a general method for generating the time optimal Hamiltonian evolution of quantum states was not known until now. Here we are going to study this problem by exploiting the analogy with the so-called brachistochrone problem in classical mechanics and the elementary properties * Electronic address: carlini@th.phys.titech.ac.jp † Electronic address: ahosoya@th.phys.titech.ac.jp ‡ Electronic address: koike@phys.keio.ac.jp § Electronic address: okudaira@th.phys.titech.ac.jp of quantum mechanics. In ordinary quantum mechanics the initial state and the Hamiltonian of a physical system are given and one has to find the final state using the Schrödinger equation. In our work we generalize this framework so as to optimize a certain cost functional with respect to the Hamiltonian as well as the quantum states. The cost functional qu...

We propose and test a theoretical perspective in which a universal hallmark of successful literacy acquisition is the convergence of the speech and orthographic processing systems onto a common network of neural structures, regardless of how spoken words are represented orthographically in a writing system. During functional MRI, skilled adult readers of four distinct and highly contrasting languages, Spanish, English, Hebrew, and Chinese, performed an identical semantic categorization task to spoken and written words. Results from three complementary analytic approaches demonstrate limited language variation, with speech-print convergence emerging as a common brain signature of reading proficiency across the wide spectrum of selected languages, whether their writing system is alphabetic or logographic, whether it is opaque or transparent, and regardless of the phonological and morphological structure it represents.

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Do the neural circuits for reading vary across culture? Reading of visually complex writing systems such as Chinese has been proposed to rely on areas outside the classical left-hemisphere network for alphabetic reading. Here, however, we show that, once potential confounds in cross-cultural comparisons are controlled for by presenting handwritten stimuli to both Chinese and French readers, the underlying network for visual word recognition may be more universal than previously suspected. Using functional magnetic resonance imaging in a semantic task with words written in cursive font, we demonstrate that two universal circuits, a shape recognition system (reading by eye) and a gesture recognition system (reading by hand), are similarly activated and show identical patterns of activation and repetition priming in the two language groups. These activations cover most of the brain regions previously associated with culture-specific tuning. Our results point to an extended reading network that invariably comprises the occipitotemporal visual wordform system, which is sensitive to well-formed static letter strings, and a distinct left premotor region, Exner's area, which is sensitive to the forward or backward direction with which cursive letters are dynamically presented. These findings suggest that cultural effects in reading merely modulate a fixed set of invariant macroscopic brain circuits, depending on surface features of orthographies.cross-cultural invariance | functional magnetic resonance imaging | neuronal recycling | masked priming A pproximately one-fifth of today's world population is still unable to read and write (1). The acquisition of written language does not rely on a specific innate ability but is an education-dependent skill resulting from the learning of mapping rules linking written codes, speech sounds, and word meanings. At the neural level, literacy acquisition imposes various structural and functional changes to the human brain, particularly in the visual cortex where responses become attuned to a specific script, but also in other areas of the temporal and parietal lobes (2, 3).The issue that we raise here is whether those changes vary considerably from one culture to another or whether they consistently engage a universal and largely invariant brain network. Past research indicated that skilled reading universally relies on a posterior left-hemisphere network, including the lateral occipitotemporal visual word-form area (VWFA) for perceptual analysis of written words (4, 5), the inferior parietal and superior temporal cortices involved in print-to-sound translation (6, 7), and lateral temporal cortices involved in access to word meaning (8-10). Reading of alphabetic scripts engages this multicomponent system with only small cultural variation depending on the degree of transparency (11) and grain size (12) of the orthographic system. However, beyond this shared left posterior network, several previous studies with normal (8,13,14) and dyslexic (15, 16) Chinese participants defended a cu...

Many of our actions are influenced by the social context. Traditional approach attributes the influence of the social context to arousal state changes in a socially promotive way. The ideomotor approach, which postulates common coding between perceived events and intended actions, uses a conceptual scheme of ideomotor compatibility to explain self-other interaction. In this study, we recorded reaction times (RTs) and event-related potentials in a Go/NoGo task with stimulus-response (S-R) compatibility arrangement to examine how the social context affects self-other interaction. Although the social facilitation theory predicted that RTs would be faster when acting together with audience rather than acting alone, the ideomotor theory predicted S-R compatibility effects only for the joint condition. The results revealed S-R compatibility on the RTs, lateralized readiness potential of the Go trials, and P3 of the NoGo trials in the joint condition, which were in line with the predictions of the ideomotor theory. Owing to the anticipation of other's actions, self and other's actions are internally and unintentionally coded at the representational level and their functional equivalency can be realized through a common coding framework between perception and action systems. Social facilitation theory was not supported, because we found no significant data differences depending on the setting.