Designing Robust Unitary Gates: Application to Concatenated Composite Pulse

We propose a simple formalism to design unitary gates robust against given systematic errors. This formalism generalizes our previous observation [Y. Kondo and M. Bando, J. Phys. Soc. Jpn. 80, 054002 (2011)] that vanishing dynamical phase in some composite gates is essential to suppress amplitude errors. By employing our formalism, we naturally derive a new composite unitary gate which can be seen as a concatenation of two known composite unitary operations. The obtained unitary gate has high fidelity over a wider range of the error strengths compared to existing composite gates.Comment: 7 pages, 4 figures. Major revision: improved presentation in Sec. 3, references and appendix adde

Coreless and singular vortex lattices in rotating spinor Bose-Einstein condensates

We theoretically investigate vortex-lattice phases of rotating spinor Bose-Einstein condensates (BEC) with the ferromagnetic spin-interaction by numerically solving the Gross-Pitaevskii equation. The spinor BEC under slow rotation can sustain a rich variety of exotic vortices due to the multi-component order parameters, such as the Mermin-Ho and Anderson-Toulouse coreless vortices (the 2-dimensional skyrmion and meron) and the non-axisymmetric vortices with the sifting vortex cores. Here, we present the spin texture of various vortex-lattice states at higher rotation rates and in the presence of the external magnetic field. In addition, the vortex phase diagram is constructed in the plane by the total magnetization $M$ and the external rotation frequency $\Omega$ by comparing the free energies of possible vortices. It is shown that the vortex phase diagram in a $M$-$\Omega$ plane may be divided into two categories; (i) the coreless vortex lattice formed by the several types of Mermin-Ho vortices and (ii) the vortex lattice filling in the cores with the pure polar (antiferromagnetic) state. In particular, it is found that the type-(ii) state forms the composite lattices of coreless and polar-core vortices. The difference between the type-(i) and type-(ii) results from the existence of the singularity of the spin textures, which may be experimentally confirmed by the spin imaging within polarized light recently proposed by Carusotto and Mueller. We also discussed on the stability of triangular and square lattice states for rapidly rotating condensates.Comment: to be published in Phys. Rev.

Improved perfluoroalkylether fluid development

The objective of this program was to optimize and scale up the linear perfluoroalkylether stabilization process and to provide test data regarding the fluids' thermal oxidative stability in the presence of metal alloys. The stabilization of Fomblin Z-25 was scaled up to 300 g of fluid. The modified fluid was stable at 316 C in oxygen in the presence of M-50 alloy for more than 24 hrs but less than 40 hrs; the amount of volatiles produced after 24 hrs was 5.5 mg/g. In the presence of Ti(4Al,4Mn) alloy, under the above conditions, following an exposure of 24 hrs, the amount of volatiles formed was 6.2 mg/g; 56 hrs exposure yielded 13.9 mg/g. The commercial fluid at 288 C (in oxygen) in the presence of M-50 after 15 hrs of exposure decomposed extensively, 342 mg/g; in the presence of Ti(4Al,4Mn) alloy after only 8 hrs at 288 C, the amount of volatiles was 191 mg/g. Formulation of the commercial fluid with C2PN3 additive was not as effective as the stabilization processing. All the perfluoroalkylether fluids studied were stable in nitrogen at 343 C. The thermal oxidative stability in the absence of metal alloys varied, with Aflunox exhibiting the best behavior. All the fluids were degraded in oxygen at 316 C during 24 hrs exposure to Ti(4Al,4Mn) alloy with the exception of a perfluoroalkylether substituted triazine and the modified Z-25

Improved perfluoroalkylether fluid development

The feasibility of transforming a commercial linear perfluoroalkylether fluid into a material stable in the presence of metals and metal alloys in oxidizing atmospheres at 300 C without the loss of the desirable viscosity temperature characteristics was determined. The approach consisted of thermal oxidative treatment in the presence of catalyst to remove weak links, followed by transformation of the created functional groups into phospha-s-triazine linkages. It it found that the experimental material obtained in 66% yield from the commercial fluid exhibits, over an 8 hr period at 300 C in the presence of Ti(4Al, 4Mn) alloy, thermal oxidative stability better by a factor of 2.6x1000 based on volatiles evolved than the commercial product. The viscosity and molecular weight of the developed fluid are unchanged and are essentially identical with the commercial material. No metal corrosion occurs with the experimental fluid at 300 C

Minimal and Robust Composite Two-Qubit Gates with Ising-Type Interaction

We construct a minimal robust controlled-NOT gate with an Ising-type interaction by which elementary two-qubit gates are implemented. It is robust against inaccuracy of the coupling strength and the obtained quantum circuits are constructed with the minimal number (N=3) of elementary two-qubit gates and several one-qubit gates. It is noteworthy that all the robust circuits can be mapped to one-qubit circuits robust against a pulse length error. We also prove that a minimal robust SWAP gate cannot be constructed with N=3, but requires N=6 elementary two-qubit gates.Comment: 7 pages, 2 figure

Gauged WZW models for space-time groups and gravitational actions

In this paper we investigate gauged Wess-Zumino-Witten models for space-time groups as gravitational theories, following the trend of recent work by Anabalon, Willison and Zanelli. We discuss the field equations in any dimension and study in detail the simplest case of two space-time dimensions and gauge group SO(2,1). For this model we study black hole solutions and we calculate their mass and entropy which resulted in a null value for both.Comment: 26 pages, no figure

Unifying Einstein and Palatini gravities

We consider a novel class of $f(\R)$ gravity theories where the connection is related to the conformally scaled metric $\hat g_{\mu\nu}=C(\R)g_{\mu\nu}$ with a scaling that depends on the scalar curvature $\R$ only. We call them C-theories and show that the Einstein and Palatini gravities can be obtained as special limits. In addition, C-theories include completely new physically distinct gravity theories even when $f(\R)=\R$. With nonlinear $f(\R)$, C-theories interpolate and extrapolate the Einstein and Palatini cases and may avoid some of their conceptual and observational problems. We further show that C-theories have a scalar-tensor formulation, which in some special cases reduces to simple Brans-Dicke-type gravity. If matter fields couple to the connection, the conservation laws in C-theories are modified. The stability of perturbations about flat space is determined by a simple condition on the lagrangian.Comment: 17 pages, no figure

Saddle index properties, singular topology, and its relation to thermodynamical singularities for a phi^4 mean field model

We investigate the potential energy surface of a phi^4 model with infinite range interactions. All stationary points can be uniquely characterized by three real numbers $\alpha_+, alpha_0, alpha_- with alpha_+ + alpha_0 + alpha_- = 1, provided that the interaction strength mu is smaller than a critical value. The saddle index n_s is equal to alpha_0 and its distribution function has a maximum at n_s^max = 1/3. The density p(e) of stationary points with energy per particle e, as well as the Euler characteristic chi(e), are singular at a critical energy e_c(mu), if the external field H is zero. However, e_c(mu) \neq upsilon_c(mu), where upsilon_c(mu) is the mean potential energy per particle at the thermodynamic phase transition point T_c. This proves that previous claims that the topological and thermodynamic transition points coincide is not valid, in general. Both types of singularities disappear for H \neq 0. The average saddle index bar{n}_s as function of e decreases monotonically with e and vanishes at the ground state energy, only. In contrast, the saddle index n_s as function of the average energy bar{e}(n_s) is given by n_s(bar{e}) = 1+4bar{e} (for H=0) that vanishes at bar{e} = -1/4 > upsilon_0, the ground state energy.Comment: 9 PR pages, 6 figure

Single-experiment-detectable multipartite entanglement witness for ensemble quantum computing

In this paper we provide an operational method to detect multipartite entanglement in ensemble-based quantum computing. This method is based on the concept of entanglement witness. We decompose the entanglement witness for each class of multipartite entanglement into nonlocal operations in addition to local measurements. Individual single qubit measurements are performed simultaneously, hence complete detection of entanglement is performed in a single run experiment. This approach is particularly important for experiments where it is operationally difficult to prepare several copies of an unknown quantum state and in this sense the introduced scheme in this work is superior to the generally used entanglement witnesses that require a number of experiments and preparation of copies of quantum state.Comment: 9 pages, 5 figures, minor changes have been mad

Synthesis of perfluoroalkylene aromatic diamines

Analogues of methylene dianilines were synthesized, in which the methylene group between the two aromatic nuclei was replaced by various perfluoroalkylene linkage. The hydrolytic thermal, and thermal oxidative stabilities of PMR Polyimides derived from these diamines were determined. Three types of PMR Polyimide discs were fabricated from the dimethyl ester of 3,3', 4,4'-benzophenonetetracarboxylic acid, the methyl ester of 5-norbornene-2,3-dicarboxylic acid, and one of the following three diamines: methyl dianiline, 1,3-bis(4-aminophenyl)hexafluoropropane, and 2,2-bis(4-aminophenyl)hexafluoropropane. The polyimide based on 2,2-bis(4-aminophenyl)hexafluoropropane exhibited the best hydrolytic, thermal, and thermal oxidative stability as determined by moisture uptake and thermogravimetric analysis