Retraction Note: Exploring the quantum speed limit with computer games.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Exploring the quantum speed limit with computer games.

Humans routinely solve problems of immense computational complexity by intuitively forming simple, low-dimensional heuristic strategies. Citizen science (or crowd sourcing) is a way of exploiting this ability by presenting scientific research problems to non-experts. 'Gamification'--the application of game elements in a non-game context--is an effective tool with which to enable citizen scientists to provide solutions to research problems. The citizen science games Foldit, EteRNA and EyeWire have been used successfully to study protein and RNA folding and neuron mapping, but so far gamification has not been applied to problems in quantum physics. Here we report on Quantum Moves, an online platform gamifying optimization problems in quantum physics. We show that human players are able to find solutions to difficult problems associated with the task of quantum computing. Players succeed where purely numerical optimization fails, and analyses of their solutions provide insights into the problem of optimization of a more profound and general nature. Using player strategies, we have thus developed a few-parameter heuristic optimization method that efficiently outperforms the most prominent established numerical methods. The numerical complexity associated with time-optimal solutions increases for shorter process durations. To understand this better, we produced a low-dimensional rendering of the optimization landscape. This rendering reveals why traditional optimization methods fail near the quantum speed limit (that is, the shortest process duration with perfect fidelity). Combined analyses of optimization landscapes and heuristic solution strategies may benefit wider classes of optimization problems in quantum physics and beyond.

Remote optimization of an ultracold atoms experiment by experts and citizen scientists.

We introduce a remote interface to control and optimize the experimental production of Bose-Einstein condensates (BECs) and find improved solutions using two distinct implementations. First, a team of theoreticians used a remote version of their dressed chopped random basis optimization algorithm (RedCRAB), and second, a gamified interface allowed 600 citizen scientists from around the world to participate in real-time optimization. Quantitative studies of player search behavior demonstrated that they collectively engage in a combination of local and global searches. This form of multiagent adaptive search prevents premature convergence by the explorative behavior of low-performing players while high-performing players locally refine their solutions. In addition, many successful citizen science games have relied on a problem representation that directly engaged the visual or experiential intuition of the players. Here we demonstrate that citizen scientists can also be successful in an entirely abstract problem visualization. This is encouraging because a much wider range of challenges could potentially be opened to gamification in the future.

Optimization of pulses with low bandwidth for improved excitation of multiple-quantum coherences in NMR of quadrupolar nuclei.

We discuss the commonly encountered problem when optimizing nuclear magnetic resonance (NMR) pulses using optimal control that the otherwise very precise NMR theory does not provide as excellent agreement with experiments. We hypothesize that this disagreement is due to phase transients in the pulse due to abrupt phase and amplitude changes resulting in a large bandwidth. We apply the gradient optimization using parametrization algorithm that gives high fidelity pulses with a low bandwidth compared to the typical gradient ascent pulse engineering pulses. Our results obtain a better agreement between experiments and simulations supporting our hypothesis and solution to the problem.

Single-spin addressing in an atomic Mott insulator.

Ultracold atoms in optical lattices provide a versatile tool with which to investigate fundamental properties of quantum many-body systems. In particular, the high degree of control of experimental parameters has allowed the study of many interesting phenomena, such as quantum phase transitions and quantum spin dynamics. Here we demonstrate how such control can be implemented at the most fundamental level of a single spin at a specific site of an optical lattice. Using a tightly focused laser beam together with a microwave field, we were able to flip the spin of individual atoms in a Mott insulator with sub-diffraction-limited resolution, well below the lattice spacing. The Mott insulator provided us with a large two-dimensional array of perfectly arranged atoms, in which we created arbitrary spin patterns by sequentially addressing selected lattice sites after freezing out the atom distribution. We directly monitored the tunnelling quantum dynamics of single atoms in the lattice prepared along a single line, and observed that our addressing scheme leaves the atoms in the motional ground state. The results should enable studies of entropy transport and the quantum dynamics of spin impurities, the implementation of novel cooling schemes, and the engineering of quantum many-body phases and various quantum information processing applications.

Single-atom-resolved fluorescence imaging of an atomic Mott insulator.

The reliable detection of single quantum particles has revolutionized the field of quantum optics and quantum information processing. For several years, researchers have aspired to extend such detection possibilities to larger-scale, strongly correlated quantum systems in order to record in situ images of a quantum fluid in which each underlying quantum particle is detected. Here we report fluorescence imaging of strongly interacting bosonic Mott insulators in an optical lattice with single-atom and single-site resolution. From our images, we fully reconstruct the atom distribution on the lattice and identify individual excitations with high fidelity. A comparison of the radial density and variance distributions with theory provides a precise in situ temperature and entropy measurement from single images. We observe Mott-insulating plateaus with near-zero entropy and clearly resolve the high-entropy rings separating them, even though their width is of the order of just a single lattice site. Furthermore, we show how a Mott insulator melts with increasing temperature, owing to a proliferation of local defects. The ability to resolve individual lattice sites directly opens up new avenues for the manipulation, analysis and applications of strongly interacting quantum gases on a lattice. For example, one could introduce local perturbations or access regions of high entropy, a crucial requirement for the implementation of novel cooling schemes.

Squeezing and Entanglement of Density Oscillations in a Bose-Einstein Condensate.

The dispersive interaction of atoms and a far-detuned light field allows nondestructive imaging of the density oscillations in Bose-Einstein condensates. Starting from a ground state condensate, we investigate how the measurement backaction leads to squeezing and entanglement of the quantized density oscillations. We show that properly timed, stroboscopic imaging and feedback can be used to selectively address specific eigenmodes and avoid excitation of nontargeted modes of the system.

Using games to understand the mind.

Board, card or video games have been played by virtually every individual in the world. Games are popular because they are intuitive and fun. These distinctive qualities of games also make them ideal for studying the mind. By being intuitive, games provide a unique vantage point for understanding the inductive biases that support behaviour in more complex, ecological settings than traditional laboratory experiments. By being fun, games allow researchers to study new questions in cognition such as the meaning of 'play' and intrinsic motivation, while also supporting more extensive and diverse data collection by attracting many more participants. We describe the advantages and drawbacks of using games relative to standard laboratory-based experiments and lay out a set of recommendations on how to gain the most from using games to study cognition. We hope this Perspective will lead to a wider use of games as experimental paradigms, elevating the ecological validity, scale and robustness of research on the mind.

Measuring Cognitive Abilities in the Wild: Validating a Population-Scale Game-Based Cognitive Assessment.

Rapid individual cognitive phenotyping holds the potential to revolutionize domains as wide-ranging as personalized learning, employment practices, and precision psychiatry. Going beyond limitations imposed by traditional lab-based experiments, new efforts have been underway toward greater ecological validity and participant diversity to capture the full range of individual differences in cognitive abilities and behaviors across the general population. Building on this, we developed Skill Lab, a novel game-based tool that simultaneously assesses a broad suite of cognitive abilities while providing an engaging narrative. Skill Lab consists of six mini-games as well as 14 established cognitive ability tasks. Using a popular citizen science platform (N = 10,725), we conducted a comprehensive validation in the wild of a game-based cognitive assessment suite. Based on the game and validation task data, we constructed reliable models to simultaneously predict eight cognitive abilities based on the users' in-game behavior. Follow-up validation tests revealed that the models can discriminate nuances contained within each separate cognitive ability as well as capture a shared main factor of generalized cognitive ability. Our game-based measures are five times faster to complete than the equivalent task-based measures and replicate previous findings on the decline of certain cognitive abilities with age in our large cross-sectional population sample (N = 6369). Taken together, our results demonstrate the feasibility of rapid in-the-wild systematic assessment of cognitive abilities as a promising first step toward population-scale benchmarking and individualized mental health diagnostics.

Quantum teleportation between light and matter.

Quantum teleportation is an important ingredient in distributed quantum networks, and can also serve as an elementary operation in quantum computers. Teleportation was first demonstrated as a transfer of a quantum state of light onto another light beam; later developments used optical relays and demonstrated entanglement swapping for continuous variables. The teleportation of a quantum state between two single material particles (trapped ions) has now also been achieved. Here we demonstrate teleportation between objects of a different nature--light and matter, which respectively represent 'flying' and 'stationary' media. A quantum state encoded in a light pulse is teleported onto a macroscopic object (an atomic ensemble containing 10 caesium atoms). Deterministic teleportation is achieved for sets of coherent states with mean photon number (n) up to a few hundred. The fidelities are 0.58 +/- 0.02 for n = 20 and 0.60 +/- 0.02 for n = 5--higher than any classical state transfer can possibly achieve. Besides being of fundamental interest, teleportation using a macroscopic atomic ensemble is relevant for the practical implementation of a quantum repeater. An important factor for the implementation of quantum networks is the teleportation distance between transmitter and receiver; this is 0.5 metres in the present experiment. As our experiment uses propagating light to achieve the entanglement of light and atoms required for teleportation, the present approach should be scalable to longer distances.

Inequality and fairness with heterogeneous endowments.

People differ in intelligence, cognitive ability, personality traits, motivation, and similar valued and, to a large degree, inherited characteristics that determine success and achievements. When does individual heterogeneity lead to a fair distribution of rewards and outcomes? Here, we develop this question theoretically and then test it experimentally for a set of structural conditions in a specific interaction situation. We first catalogue the functional relationship between individual endowments and outcomes to distinguish between fairness concepts such as meritocracy, equality of opportunity, equality of outcomes, and Rawl's theory of justice. We then use an online experiment to study which of these fairness patterns emerge when differently endowed individuals can share their resources with others, depending on whether information about others' endowments and outcomes is available. We find that while visible outcomes lessen inequality by decreasing the statistical dispersion of outcomes across the group, endowments need to be visible for better equality of opportunity for the most disadvantaged.

Geometry of turbulent dissipation and the Navier-Stokes regularity problem.

The question of whether a singularity can form in an initially regular flow, described by the 3D incompressible Navier-Stokes (NS) equations, is a fundamental problem in mathematical physics. The NS regularity problem is super-critical, i.e., there is a 'scaling gap' between what can be established by mathematical analysis and what is needed to rule out a singularity. A recently introduced mathematical framework-based on a suitably defined 'scale of sparseness' of the regions of intense vorticity-brought the first scaling reduction of the NS super-criticality since the 1960s. Here, we put this framework to the first numerical test using a spatially highly resolved computational simulation performed near a 'burst' of the vorticity magnitude. The results confirm that the scale is well suited to detect the onset of dissipation and provide numerical evidence that ongoing mathematical efforts may succeed in closing the scaling gap.

Experimental demonstration of quantum memory for light.

The information carrier of today's communications, a weak pulse of light, is an intrinsically quantum object. As a consequence, complete information about the pulse cannot be perfectly recorded in a classical memory, even in principle. In the field of quantum information, this has led to the long-standing challenge of how to achieve a high-fidelity transfer of an independently prepared quantum state of light onto an atomic quantum state. Here we propose and experimentally demonstrate a protocol for such a quantum memory based on atomic ensembles. Recording of an externally provided quantum state of light onto the atomic quantum memory is achieved with 70 per cent fidelity, significantly higher than the limit for classical recording. Quantum storage of light is achieved in three steps: first, interaction of the input pulse and an entangling field with spin-polarized caesium atoms; second, subsequent measurement of the transmitted light; and third, feedback onto the atoms using a radio-frequency magnetic pulse conditioned on the measurement result. The density of recorded states is 33 per cent higher than the best classical recording of light onto atoms, with a quantum memory lifetime of up to 4 milliseconds.

Non-destructive Faraday imaging of dynamically controlled ultracold atoms.

We describe an easily implementable method for non-destructive measurements of ultracold atomic clouds based on dark field imaging of spatially resolved Faraday rotation. The signal-to-noise ratio is analyzed theoretically and, in the absence of experimental imperfections, the sensitivity limit is found to be identical to other conventional dispersive imaging techniques. The dependence on laser detuning, atomic density, and temperature is characterized in a detailed comparison with theory. Due to low destructiveness, spatially resolved images of the same cloud can be acquired up to 2000 times. The technique is applied to avoid the effect of shot-to-shot fluctuations in atom number calibration, to demonstrate single-run vector magnetic field imaging and single-run spatial imaging of the system's dynamic behavior. This demonstrates that the method is a useful tool for the characterization of static and dynamically changing properties of ultracold atomic clouds.

Polarization squeezing by optical faraday rotation.

We show that it is possible to generate continuous-wave fields and pulses of polarization squeezed light by sending classical, linearly polarized laser light twice through an atomic sample which causes an optical Faraday rotation of the field polarization. We characterize the performance of the process and we show that an appreciable degree of squeezing can be obtained under realistic physical assumptions.