Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed.With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupledcluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits.PACS numbers: quantum computation, quantum chemistry, quantum algorithms

Ring geometries have fascinated experimental and theoretical physicists over many years. Open rings connected to leads allow the observation of the Aharonov-Bohm effect [1], a paradigm of quantum mechanical phase coherence [2,3]. The phase coherence of transport through a quantum dot embedded in one arm of an open ring has been demonstrated [4]. The energy spectrum of closed rings [5] has only recently been analysed by optical experiments [6,7] and is the basis for the prediction of persistent currents [8] and related experiments [9-11]. Here we report magnetotransport experiments on a ring-shaped semiconductor quantum dot in the Coulomb blockade regime [12]. The measurements allow us to extract the discrete energy levels of a realistic ring, which are found to agree well with theoretical expectations. Such an agreement, so far only found for few-electron quantum dots, is here extended to a many-electron system [13]. In a semiclassical language our results indicate that electron motion is governed by regular rather than chaotic motion, an unexplored regime in many-electron quantum dots.

We demonstrate control of the electron number down to the last electron in tunable few-electron quantum dots defined in catalytically grown InAs nanowires. Using low temperature transport spectroscopy in the Coulomb blockade regime, we propose a method to directly determine the magnitude of the spin-orbit interaction in a two-electron artificial atom with strong spin-orbit coupling. Because of a large effective g factor |g(*)|=8+/-1, the transition from a singlet S to a triplet T+ ground state with increasing magnetic field is dominated by the Zeeman energy rather than by orbital effects. We find that the spin-orbit coupling mixes the T+ and S states and thus induces an avoided crossing with magnitude Delta(SO)=0.25+/-0.05 meV. This allows us to calculate the spin-orbit length lambda(SO) approximately 127 nm in such systems using a simple model.

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We present harmonic transverse voltage measurements of current-induced thermoelectric and spin-orbit torque (SOT) effects in ferromagnet/normal metal bilayers, in which thermal gradients produced by Joule heating and SOT coexist and give rise to ac transverse signals with comparable symmetry and magnitude. Based on the symmetry and field-dependence of the transverse resistance, we develop a consistent method to separate thermoelectric and SOT measurements. By addressing first ferromagnet/light metal bilayers with negligible spin-orbit coupling, we show that in-plane current injection induces a vertical thermal gradient whose sign and magnitude are determined by the resistivity difference and stacking order of the magnetic and nonmagnetic layers.We then study ferromagnet/heavy metal bilayers with strong spin-orbit coupling, showing that second harmonic thermoelectric contributions to the transverse voltage may lead to a significant overestimation of the antidamping SOT. We find that thermoelectric effects are very strong in Ta(6nm)/Co(2.5nm) and negligible in Pt(6nm)/Co(2.5nm) bilayers. After including these effects in the analysis of the transverse voltage, we find that the antidamping SOTs in these bilayers, after normalization to the magnetization volume, are comparable to those found in thinner Co layers with perpendicular magnetization, whereas the field-like SOTs are about an order of magnitude smaller.