Hybrid quantum-classical systems make it possible to utilize existing quantum computers to their fullest extent. Within this framework, parameterized quantum circuits can be thought of as machine learning models with remarkable expressive power. This Review presents components of these models and discusses their application to a variety of data-driven tasks such as supervised learning and generative modeling. With experimental demonstrations carried out on actual quantum hardware, and with software actively being developed, this rapidly growing field could become one of the first instances of quantum computing that addresses real world problems.

European Union; German Centre for Infection Research; German Research Council; and German Ministry for Education and Research.

The dimeric form of the kinesin motor and neck domain from rat brain with bound ADP has been solved by X-ray crystallography. The two heads of the dimer are connected via a coiled-coil alpha-helical interaction of their necks. They are broadly similar to one another; differences are most apparent in the head-neck junction and in a moderate reorientation of the neck helices in order to adopt to the coiled-coil conformation. The heads show a rotational symmetry (approximately 120 degrees) about an axis close to that of the coiled-coil. This arrangement is unexpected since it is not compatible with the microtubule lattice. In this arrangement, the two heads of a kinesin dimer could not have equivalent interactions with microtubules.

We have determined the X-ray structure of rat kinesin head and neck domains. The folding of the core motor domain resembles that of human kinesin reported recently [Kull, F. J., et al. (1996) Nature 380, 550-554]. Novel features of the structure include the N-terminal region, folded as a beta-strand, and the C-terminal transition from the motor to the rod domain, folded as two beta-strands plus an alpha-helix. This helix is the beginning of kinesin's neck responsible for dimerization of the motor complex and for force transduction. Although the folding of the motor domain core is similar to that of a domain of myosin (an actin-dependent motor), the position and angle of kinesin's neck are very different from those of myosin's stalk, suggesting that the two motors have different mechanisms of force transduction. The N- and C-terminal ends of the core motor, thought to be responsible for the directionality of the motors [Case, R. B., et al. (1997) Cell 90, 959-966], take the form of beta-strands attached to the central beta-sheet of the structure.

We have decorated microtubules with monomeric and dimeric kinesin constructs, studied their structure by cryoelectron microscopy and three-dimensional image reconstruction, and compared the results with the x-ray crystal structure of monomeric and dimeric kinesin. A monomeric kinesin construct (rK354, containing only a short neck helix insufficient for coiled-coil formation) decorates microtubules with a stoichiometry of one kinesin head per tubulin subunit (α–β-heterodimer). The orientation of the kinesin head (an anterograde motor) on the microtubule surface is similar to that of ncd (a retrograde motor). A longer kinesin construct (rK379) forms a dimer because of the longer neck helix forming a coiled-coil. Unexpectedly, this construct also decorates the microtubule with a stoichiometry of one head per tubulin subunit, and the orientation is similar to that of the monomeric construct. This means that the interaction with microtubules causes the two heads of a kinesin dimer to separate sufficiently so that they can bind to two different tubulin subunits. This result is in contrast to recent models and can be explained by assuming that the tubulin–kinesin interaction is antagonistic to the coiled-coil interaction within a kinesin dimer.

The present structure reflects the open conformation of the enzyme which is probably stabilized through two residues, a lysine and an arginine, located in the cleft between the domains. Binding of the negatively charged UDPGlcNAc to these residues could neutralize the repulsive force between the two domains, thereby allowing the movement of a catalytically active cysteine residue towards the cleft.

Microtubule-dependent motors of the kinesin family convert the energy from ATP hydrolysis into mechanical work in order to transport vesicles and organelles along microtubules. The motor domains of several kinesins have been solved by X-ray diffraction, but the conformational changes associated with force development remain unknown. Here we describe conformational properties of kinesin that might be related to the mechanism of action. First, we have evaluated the conformational variability among all known kinesin structures and find they are concentrated in six areas, most of which are functionally important either in microtubule binding or in linking the core motor to the stalk. Secondly, we show that there is an important difference between kinesins when compared with myosins or GTPases (with which kinesin motor domains bear structural and catalytic similarities); in the diphosphate-state (with bound ADP), all kinesins show a`tight' nucleotide-binding pocket, comparable with myosin or GTPases in the triphosphate state, whose nucleotide-binding pockets become open, or`loose', following nucleotide hydrolysis. Thus, kinesin-ADP appears to be in a tense state, resembling that observed in myosin-ATP or p21 ras -GTP.

The quantum approximate optimization algorithm (QAOA) is a prospective near-term quantum algorithm due to its modest circuit depth and promising benchmarks. However, an external parameter optimization required in QAOA could become a performance bottleneck. This motivates studies of the optimization landscape and search for heuristic ways of parameter initialization. In this work we visualize the optimization landscape of the QAOA applied to the MaxCut problem on random graphs, demonstrating that random initialization of the QAOA is prone to converging to local minima with sub-optimal performance. We introduce the initialization of QAOA parameters based on the Trotterized quantum annealing (TQA) protocol, parameterized by the Trotter time step. We find that the TQA initialization allows to circumvent the issue of false minima for a broad range of time steps, yielding the same performance as the best result out of an exponentially scaling number of random initializations. Moreover, we demonstrate that the optimal value of the time step coincides with the point of proliferation of Trotter errors in quantum annealing. Our results suggest practical ways of initializing QAOA protocols on near-term quantum devices and reveals new connections between QAOA and quantum annealing.