Directly accessible entangling gates for capacitively coupled singlet-triplet qubits

The recent experimental advances in capacitively coupled singlet-triplet qubits, particularly the demonstration of entanglement, opens the question of what type of entangling gates the system's Hamiltonian can produce directly via a single square pulse. We address this question by considering the system's Hamiltonian from first principles and using the representation of its nonlocal properties in terms of local invariants. In the analysis we include the three different ways in which the system can be biased and their effect on the generation of entangling gates. We find that, in one of the possible biasing modes, the Hamiltonian has an especially simple form, which can directly generate a wide range of different entangling gates including the iSWAP gate. Moreover, using the complete form of the Hamiltonian we find that, for any biasing mode, a CNOT gate can be generated directly.Comment: 10 pages, 5 figure

Entanglement dynamics of two Ising-coupled qubits with nonperpendicular local driving fields

We present an approximate analytical solution to the dynamic equation of two Ising-coupled qubits with oscillating classical control fields that are nonperpendicular to the static drift fields. This is a situation that has recently arisen in some solid-state experiments. With our solution we derive the analytical expressions for the local invariants as well as the local rotations needed to isolate a purely nonlocal gate. This determines the set of parameters that are required to generate any entangling gate. Moreover, we use our results to describe a recent experimental work on capacitively coupled singlet-triplet qubits in GaAs and discuss possible differences for a similar device in silicon.Comment: 6 pages, 3 figure

Dynamically Correcting a CNOT Gate for any Systematic Logical Error

We derive a set of composite pulse sequences that generates CNOT gates and correct all systematic errors within the logical subspace to arbitrary order. These sequences are applicable for any two-qubit interaction Hamiltonian, and make no assumptions about the underlying noise mechanism except that it is constant on the timescale of the operation. We do assume access to error-free single-qubit gates, so single-qubit gate imperfections eventually limit the achievable fidelity. However, since single-qubit gates generally have much higher fidelities than two-qubit gates in practice, these pulse sequences offer useful dynamical correction for a wide range of coupled qubit systems.Comment: 4 + pages, and 2 pages of supplemental materia

SAdS black holes and spacetime atoms: a heuristic approach

In this work, both extended phase space and holographic equipartition approaches are employed to develop an exact Van der Waals description of non--rotating $D=4$ SAdS black holes as an ensemble of spacetime atoms. After a possible microscopical interaction model is introduced, statistical mechanics techniques, with certain heuristic gravitational constraints, are used to derive the equation of state and the Bekenstein--Hawking entropy. The procedure is generalized to the charged $D=4$ SAdS black hole and to arbitrary $D\ge 3$ dimensions for the uncharged cases.Comment: Accepted for publication in Gen. Rel. Gra

Linear Whitham-Boussinesq modes in channels of constant cross-section

We study normal modes for the linear water wave problem in infinite straight channels of bounded constant cross-section. Our goal is to compare semianalytic normal mode solutions known in the literature for special triangular cross-sections, namely isosceles triangles of equal angle of 45 and 60 degrees, see Lamb [17], Macdonald [19] , Greenhill [11], Packham [23], and Groves [12], to numerical solutions obtained using approximations of the non-local Dirichlet-Neumann operator for linear waves, specifically an ad-hoc approximation proposed in [25], and a first order truncation of the systematic depth expansion by Craig, Guyenne, Nicholls, and Sulem [6]. We consider cases of transverse (i.e. 2-D) modes and longitudinal modes, i.e. 3-D modes with sinusoidal dependence in the longitudinal direction. The triangular geometries considered have slopping beach boundaries that should in principle limit the applicability of the approximate Dirichlet-Neumann operators. We nevertheless see that the approximate operators give remarkably close results for transverse even modes, while for odd transverse modes we have some discrepancies near the boundary. In the case of longitudinal modes, where the theory only yields even modes, the different approximate operators show more discrepancies for the first two longitudinal modes and better agreement for higher modes. The ad-hoc approximation is generally closer to exact modes away from the boundary.Comment: Submitted manuscript 2018. arXiv admin note: substantial text overlap with arXiv:1710.0478

Linear guided modes and Whitham-Boussinesq model for variable topogra

In this article we study two classical linear water wave problems, i) normal modes of infinite straight channels of bounded constant cross-section, and ii) trapped longitudinal modes in domains with unbounded constant cross-section. Both problems can be stated using linearized free surface potential flow theory, and our goal is to compare known analytic solutions in the literature to numerical solutions obtained using an ad-hoc but simple approximation of the non-local Dirichlet-Neumann operator for linear waves proposed in [vargas2016whitham]. To study normal modes in channels with bounded cross-section we consider special symmetric triangular cross-sections, namely symmetric triangles with sides inclined at $45^{\circ}$ and $60^{\circ}$ to the vertical, and compare modes obtained using the non-local Dirichlet-Neumann operator to known semi-exact analytic expressions by Lamb [lamb1932hydrodynamics], Macdonald [macdonald1893waves] , Greenhill [greenhill1887wave], Packham [packham1980small], and Groves [groves1994hamiltonian]. These geometries have slopping beach boundaries that should in principle limit the applicability of our approximate Dirichlet-Neumann operator. We nevertheless see that the operator gives remarkably close results for even modes, while for odd modes we have some discrepancies near the boundary. For trapped longitudinal modes in domains with an infinite cross-section we consider a piecewise constant depth profile and compare modes computed with the nonlocal operator modes to known analytic solutions of linearized shallow water theory by Miles [miles1972wave], Lin, Juang and Tsay [lin2001anomalous], see also [mei2005theory]. This is a problem of significant geophysical interest, and the proposed model is shows to give quantitatively similar results for the lowest trapped modes.Comment: Submitted to Wave Motion Journal, October, 201

A robust operating point for capacitively coupled singlet-triplet qubits

Singlet-triplet qubits in lateral quantum dots in semiconductor heterostructures exhibit high-fidelity single-qubit gates via exchange interactions and magnetic field gradients. High-fidelity two-qubit entangling gates are challenging to generate since weak interqubit interactions result in slow gates that accumulate error in the presence of noise. However, the interqubit electrostatic interaction also produces a shift in the local double well detunings, effectively changing the dependence of exchange on the gate voltages. We consider an operating point where the effective exchange is first order insensitive to charge fluctuations while maintaining nonzero interactions. This "sweet spot" exists only in the presence of interactions. We show that working at the interacting sweet spot can directly produce maximally entangling gates and we simulate the gate evolution under realistic 1/f noise. We report theoretical two-qubit gate fidelities above 99% in GaAs and Si systems.Comment: 6 pages, 4 figure

Edge states of moir\'e structures in graphite

We address the origin of bead-like edge states observed by scanning tunneling microscopy (STM) in moir\'e patterns of graphite. Low-bias scanning tunneling spectroscopy measurements indicate these edge states are centered around AB stacking sites, contrarily to the common assumption of them being at AA sites. This shift of the intensity of the beads with respect to the bulk moir\'e pattern has been corroborated by a tight-binding calculation of the edge states in bilayer nanoribbons. Our results are valid not only for graphite but also for few-layer graphene, where these states have also been recently observed.Comment: 5 pages, 4 figures. To be published in Physical Revew

Corresponding states law for a generalized Lennard-Jones potential

It was recently shown that vapor-liquid coexistence densities derived from Mie and Yukawa models collapse to define a single master curve when represented against the difference between the reduced second virial coefficient at the corresponding temperature and that at the critical point. In this work we further test this proposal for another generalization of the Lennard-Jones pair potential. This is carried out for vapor-liquid coexistence densities, surface tension, and vapor pressure, along a temperature window set below the critical point. For this purpose we perform molecular dynamics simulations by varying the potential softness parameter to produce from very short to intermediate attractive ranges. We observed all properties to collapse and yield master curves. Moreover, the vapor-liquid curve is found to share the exact shape of the Mie and attractive Yukawa. Furthermore, the surface tension and the logarithm of the vapor pressure are linear functions of this difference of reduced second virial coefficients.Comment: 19 pages, 7 figure

\textit{Ab Initio} Study of the Magnetic Behavior of Metal Hydrides: A Comparison with the Slater-Pauling Curve

We investigated the magnetic behavior of metal hydrides FeH$_{x}$, CoH$_{x}$ and NiH$_{x}$ for several concentrations of hydrogen ($x$) by using Density Functional Theory calculations. Several structural phases of the metallic host: bcc ($\alpha$), fcc ($\gamma$), hcp ($\varepsilon$), dhcp ($\varepsilon'$), tetragonal structure for FeH$_{x}$ and $\varepsilon$-$\gamma$ phases for CoH$_{x}$, were studied. We found that for CoH$_{x}$ and NiH$_{x}$ the magnetic moment ($m$) decreases regardless the concentration $x$. However, for FeH$_{x}$ systems, $m$ increases or decreases depending on the variation in $x$. In order to find a general trend for these changes of $m$ in magnetic metal hydrides, we compare our results with the Slater-Pauling curve for ferromagnetic metallic binary alloys. It is found that the $m$ of metal hydrides made of Fe, Co and Ni fits the shape of the Slater-Pauling curve as a function of $x$. Our results indicate that there are two main effects that determine the $m$ value due to hydrogenation: an increase of volume causes $m$ to increase, and the addition of an extra electron to the metal always causes it to decrease. We discuss these behaviors in detail.Comment: 6 page