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

Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace

When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free subspace are known to correct such collective errors. We construct simple quantum circuits, which implement these collective error correction codes, for a small number $n$ of physical qubits. A single logical qubit is encoded with $n=3$ and $n=4$, while two logical qubits are encoded with $n=5$. The recursive relations among the subspaces employed in noiseless subsystem and decoherence free subspace play essential r\^oles in our implementation. The recursive relations also show that the number of gates required to encode $m$ logical qubits increases linearly in $m$.Comment: 9 pages, 3 figure

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

Potential formulation of the dispersion relation for a uniform, magnetized plasma with stationary ions in terms of a vector phasor

The derivation of the helicon dispersion relation for a uniform plasma with stationary ions subject to a constant background magnetic field is reexamined in terms of the potential formulation of electrodynamics. Under the same conditions considered by the standard derivation, the nonlinear self-coupling between the perturbed electron flow and the potential it generates is addressed. The plane wave solution for general propagation vector is determined for all frequencies and expressed in terms of a vector phasor. The behavior of the solution as described in vacuum units depends upon the ratio of conductivity to the magnitude of the background field. Only at low conductivity and below the cyclotron frequency can significant propagation occur as determined by the ratio of skin depth to wavelength.Comment: 10 pages, 6 figures, major revision, final version, to appear in Po

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

Geometric Aspects of Composite Pulses

Unitary operations acting on a quantum system must be robust against systematic errors in control parameters for reliable quantum computing. Composite pulse technique in nuclear magnetic resonance (NMR) realises such a robust operation by employing a sequence of possibly poor quality pulses. In this article, we demonstrate that two kinds of composite pulses, one compensates for a pulse length error in a one-qubit system and the other compensates for a J-coupling error in a twoqubit system, have vanishing dynamical phase and thereby can be seen as geometric quantum gates, which implement unitary gates by the holonomy associated with dynamics of cyclic vectors defined in the text.Comment: 20 pages, 4 figures. Accepted for publication in Philosophical Transactions of the Royal Society

Soldered Bundle Background for the De Sitter Top

We prove that the mathematical framework for the de Sitter top system is the de Sitter fiber bundle. In this context, the concept of soldering associated with a fiber bundle plays a central role. We comment on the possibility that our formalism may be of particular interest in different contexts including MacDowell-Mansouri theory, two time physics and oriented matroid theory.Comment: 12 pages, Latex; some improvements introduced, reference added, typos correcte

Kinematic Orbits and the Structure of the Internal Space for Systems of Five or More Bodies

The internal space for a molecule, atom, or other n-body system can be conveniently parameterised by 3n-9 kinematic angles and three kinematic invariants. For a fixed set of kinematic invariants, the kinematic angles parameterise a subspace, called a kinematic orbit, of the n-body internal space. Building on an earlier analysis of the three- and four-body problems, we derive the form of these kinematic orbits (that is, their topology) for the general n-body problem. The case n=5 is studied in detail, along with the previously studied cases n=3,4.Comment: 38 pages, submitted to J. Phys.

A cosmological model in Weyl-Cartan spacetime: I. Field equations and solutions

In this first article of a series on alternative cosmological models we present an extended version of a cosmological model in Weyl-Cartan spacetime. The new model can be viewed as a generalization of a model developed earlier jointly with Tresguerres. Within this model the non-Riemannian quantities, i.e. torsion $T^{\alpha}$ and nonmetricity $Q_{\alpha \beta}$, are proportional to the Weyl 1-form. The hypermomentum $\Delta_{\alpha \beta}$ depends on our ansatz for the nonmetricity and vice versa. We derive the explicit form of the field equations for different cases and provide solutions for a broad class of parameters. We demonstrate that it is possible to construct models in which the non-Riemannian quantities die out with time. We show how our model fits into the more general framework of metric-affine gravity (MAG).Comment: 22 pages, 2 figures, uses IOP preprint styl

Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors

One of the defining properties of the conventional three-dimensional ("$\mathbb{Z}_2$-", or "spin-orbit"-) topological insulator is its characteristic magnetoelectric effect, as described by axion electrodynamics. In this paper, we discuss an analogue of such a magnetoelectric effect in the thermal (or gravitational) and the magnetic dipole responses in all symmetry classes which admit topologically non-trivial insulators or superconductors to exist in three dimensions. In particular, for topological superconductors (or superfluids) with time-reversal symmetry which lack SU(2) spin rotation symmetry (e.g. due to spin-orbit interactions), such as the B phase of $^3$He, the thermal response is the only probe which can detect the non-trivial topological character through transport. We show that, for such topological superconductors, applying a temperature gradient produces a thermal- (or mass-) surface current perpendicular to the thermal gradient. Such charge, thermal, or magnetic dipole responses provide a definition of topological insulators and superconductors beyond the single-particle picture. Moreover we find, for a significant part of the 'ten-fold' list of topological insulators found in previous work in the absence of interactions, that in general dimensions the effective field theory describing the space-time responses is governed by a field theory anomaly. Since anomalies are known to be insensitive to whether the underlying fermions are interacting or not, this shows that the classification of these topological insulators is robust to adiabatic deformations by interparticle interactions in general dimensionality. In particular, this applies to symmetry classes DIII, CI, and AIII in three spatial dimensions, and to symmetry classes D and C in two spatial dimensions.Comment: 16 pages, 2 figure