Interest rate option pricing with volatility humps

A development of a simple model in which interest rate claims are priced in the Heath-Jarrow-Morton paradigm and so incorporate full information on the term structure. The volatility structure for forward rates is humped and includes as a special case the exponentially dampened volatility structure used in the generalized Vasicek model.Interest rates ; Options (Finance)

Surface-electrode ion trap with integrated light source

An atomic ion is trapped at the tip of a single-mode optical fiber in a cryogenic (8 K) surface-electrode ion trap. The fiber serves as an integrated source of laser light, which drives the quadrupole qubit transition of $^{88}$Sr$^+$. Through \emph{in situ} translation of the nodal point of the trapping field, the Gaussian beam profile of the fiber output is imaged, and the fiber-ion displacement, in units of the mode waist at the ion, is optimized to within $0.13\pm0.10$ of the mode center despite an initial offset of $3.30\pm0.10$. Fiber-induced charging at $125 \mu$W is observed to be ${\sim}10$ V/m at an ion height of $670 \mu$m, with charging and discharging time constants of $1.6\pm0.3$ s and $4.7\pm0.6$ s respectively. This work is of importance to large-scale, ion-based quantum information processing, where optics integration in surface-electrode designs may be a crucial enabling technology.Comment: 4 pages, 4 figure

Finite geometry models of electric field noise from patch potentials in ion traps

We model electric field noise from fluctuating patch potentials on conducting surfaces by taking into account the finite geometry of the ion trap electrodes to gain insight into the origin of anomalous heating in ion traps. The scaling of anomalous heating rates with surface distance, $d$, is obtained for several generic geometries of relevance to current ion trap designs, ranging from planar to spheroidal electrodes. The influence of patch size is studied both by solving Laplace's equation in terms of the appropriate Green's function as well as through an eigenfunction expansion. Scaling with surface distance is found to be highly dependent on the choice of geometry and the relative scale between the spatial extent of the electrode, the ion-electrode distance, and the patch size. Our model generally supports the $d^{-4}$ dependence currently found by most experiments and models, but also predicts geometry-driven deviations from this trend

Quantum gate characterization in an extended Hilbert space

We describe an approach for characterizing the process of quantum gates using quantum process tomography, by first modeling them in an extended Hilbert space, which includes non-qubit degrees of freedom. To prevent unphysical processes from being predicted, present quantum process tomography procedures incorporate mathematical constraints, which make no assumptions as to the actual physical nature of the system being described. By contrast, the procedure presented here ensures physicality by placing physical constraints on the nature of quantum processes. This allows quantum process tomography to be performed using a smaller experimental data set, and produces parameters with a direct physical interpretation. The approach is demonstrated by example of mode-matching in an all-optical controlled-NOT gate. The techniques described are non-specific and could be applied to other optical circuits or quantum computing architectures.Comment: 4 pages, 2 figures, REVTeX (published version

Type-II Quantum Algorithms

We review and analyze the hybrid quantum-classical NMR computing methodology referred to as Type-II quantum computing. We show that all such algorithms considered so far within this paradigm are equivalent to some classical lattice-Boltzmann scheme. We derive a sufficient and necessary constraint on the unitary operator representing the quantum mechanical part of the computation which ensures that the model reproduces the Boltzmann approximation of a lattice-gas model satisfying semi-detailed balance. Models which do not satisfy this constraint represent new lattice-Boltzmann schemes which cannot be formulated as the average over some underlying lattice gas. We close the paper with some discussion of the strengths, weaknesses and possible future direction of Type-II quantum computing.Comment: To appear in Physica

Laser-induced charging of microfabricated ion traps

Electrical charging of metal surfaces due to photoelectric generation of carriers is of concern in trapped ion quantum computation systems, due to the high sensitivity of the ions' motional quantum states to deformation of the trapping potential. The charging induced by typical laser frequencies involved in doppler cooling and quantum control is studied here, with microfabricated surface electrode traps made of aluminum, copper, and gold, operated at 6 K with a single Sr$^+$ ion trapped 100 $\mu$m above the trap surface. The lasers used are at 370, 405, 460, and 674 nm, and the typical photon flux at the trap is 10$^{14}$ photons/cm$^2$/sec. Charging is detected by monitoring the ion's micromotion signal, which is related to the number of charges created on the trap. A wavelength and material dependence of the charging behavior is observed: lasers at lower wavelengths cause more charging, and aluminum exhibits more charging than copper or gold. We describe the charging dynamic based on a rate equation approach.Comment: 8 pages, 8 figure

Graph Concatenation for Quantum Codes

Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good quantum codes of relatively large block length, concatenated quantum codes and their generalizations play an important role. We develop a systematic method for constructing concatenated quantum codes based on "graph concatenation", where graphs representing the inner and outer codes are concatenated via a simple graph operation called "generalized local complementation." Our method applies to both binary and non-binary concatenated quantum codes as well as their generalizations.Comment: 26 pages, 12 figures. Figures of concatenated [[5,1,3]] and [[7,1,3]] are added. Submitted to JM

A microfabricated surface ion trap on a high-finesse optical mirror

A novel approach to optics integration in ion traps is demonstrated based on a surface electrode ion trap that is microfabricated on top of a dielectric mirror. Additional optical losses due to fabrication are found to be as low as 80 ppm for light at 422 nm. The integrated mirror is used to demonstrate light collection from, and imaging of, a single 88 Sr+ ion trapped $169\pm4 \mu$m above the mirror.Comment: 4 pages, 3 figure

Dynamics of a Quantum Phase Transition

We present two approaches to the dynamics of a quench-induced phase transition in quantum Ising model. The first one retraces steps of the standard approach to thermodynamic second order phase transitions in the quantum setting. The second one is purely quantum, based on the Landau-Zener formula for transition probabilities in avoided level crossings. We show that the two approaches yield compatible results for the scaling of the defect density with the quench rate. We exhibit similarities between them, and comment on the insights they give into dynamics of quantum phase transitions.Comment: 4 pages, 3 figures. Replaced by revised versio