On the Geometry of the Moduli Space of Real Binary Octics

The moduli space of smooth real binary octics has five connected components. They parametrize the real binary octics whose defining equations have 0, 1, ..., 4 complex-conjugate pairs of roots respectively. We show that the GIT-stable completion of each of these five components admits the structure of an arithmetic real hyperbolic orbifold. The corresponding monodromy groups are, up to commensurability, discrete hyperbolic reflection groups, and their Vinberg diagrams are computed. We conclude with a simple proof that the moduli space of GIT-stable real binary octics itself cannot be a real hyperbolic orbifold.Comment: 23 page

High-fidelity trapped-ion quantum logic using near-field microwaves

We demonstrate a two-qubit logic gate driven by near-field microwaves in a room-temperature microfabricated ion trap. We measure a gate fidelity of 99.7(1)\%, which is above the minimum threshold required for fault-tolerant quantum computing. The gate is applied directly to $^{43}$Ca$^+$ "atomic clock" qubits (coherence time $T_2^*\approx 50\,\mathrm{s}$) using the microwave magnetic field gradient produced by a trap electrode. We introduce a dynamically-decoupled gate method, which stabilizes the qubits against fluctuating a.c.\ Zeeman shifts and avoids the need to null the microwave field

A microfabricated ion trap with integrated microwave circuitry

We describe the design, fabrication and testing of a surface-electrode ion trap, which incorporates microwave waveguides, resonators and coupling elements for the manipulation of trapped ion qubits using near-field microwaves. The trap is optimised to give a large microwave field gradient to allow state-dependent manipulation of the ions' motional degrees of freedom, the key to multiqubit entanglement. The microwave field near the centre of the trap is characterised by driving hyperfine transitions in a single laser-cooled 43Ca+ ion.Comment: 4 pages, 5 figure

How to wire a 1000-qubit trapped ion quantum computer

One of the most formidable challenges of scaling up quantum computers is that of control signal delivery. Today's small-scale quantum computers typically connect each qubit to one or more separate external signal sources. This approach is not scalable due to the I/O limitations of the qubit chip, necessitating the integration of control electronics. However, it is no small feat to shrink control electronics into a small package that is compatible with qubit chip fabrication and operation constraints without sacrificing performance. This so-called "wiring challenge" is likely to impact the development of more powerful quantum computers even in the near term. In this paper, we address the wiring challenge of trapped-ion quantum computers. We describe a control architecture called WISE (Wiring using Integrated Switching Electronics), which significantly reduces the I/O requirements of ion trap quantum computing chips without compromising performance. Our method relies on judiciously integrating simple switching electronics into the ion trap chip - in a way that is compatible with its fabrication and operation constraints - while complex electronics remain external. To demonstrate its power, we describe how the WISE architecture can be used to operate a fully connected 1000-qubit trapped ion quantum computer using ~ 200 signal sources at a speed of ~ 40 - 2600 quantum gate layers per second

Quantum Time and Spatial Localization: An Analysis of the Hegerfeldt Paradox

Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles and dependence of spatial localization on the motion of the observer, are analyzed in the context of Dirac's theory of constraints. A parametrization invariant formulation is obtained by introducing time and energy operators for the relativistic particle and then treating the Klein-Gordon equation as a constraint. The standard, physical Hilbert space is recovered, via integration over proper time, from an augmented Hilbert space wherein time and energy are dynamical variables. It is shown that the Newton-Wigner position operator, being in this description a constant of motion, acts on states in the augmented space. States with strictly positive energy are non-local in time; consequently, position measurements receive contributions from states representing the particle's position at many times. Apparent superluminal propagation is explained by noting that, as the particle is potentially in the past (or future) of the assumed initial place and time of localization, it has time to propagate to distant regions without exceeding the speed of light. An inequality is proven showing the Hegerfeldt paradox to be completely accounted for by the hypotheses of subluminal propagation from a set of initial space-time points determined by the quantum time distribution arising from the positivity of the system's energy. Spatial localization can nevertheless occur through quantum interference between states representing the particle at different times. The non-locality of the same system to a moving observer is due to Lorentz rotation of spatial axes out of the interference minimum.Comment: This paper is identical to the version appearing in J. Math. Phys. 41; 6093 (Sept. 2000). The published version will be found at http://ojps.aip.org/jmp/. The paper (40 page PDF file) has been completely revised since the last posting to this archiv

A measurement-based approach to quantum arrival times

For a quantum-mechanically spread-out particle we investigate a method for determining its arrival time at a specific location. The procedure is based on the emission of a first photon from a two-level system moving into a laser-illuminated region. The resulting temporal distribution is explicitly calculated for the one-dimensional case and compared with axiomatically proposed expressions. As a main result we show that by means of a deconvolution one obtains the well known quantum mechanical probability flux of the particle at the location as a limiting distribution.Comment: 11 pages, 4 figures, submitted to Phys. Rev.

High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit

We implement all single-qubit operations with fidelities significantly above the minimum threshold required for fault-tolerant quantum computing, using a trapped-ion qubit stored in hyperfine "atomic clock" states of $^{43}$Ca$^+$. We measure a combined qubit state preparation and single-shot readout fidelity of 99.93%, a memory coherence time of $T^*_2=50$ seconds, and an average single-qubit gate fidelity of 99.9999%. These results are achieved in a room-temperature microfabricated surface trap, without the use of magnetic field shielding or dynamic decoupling techniques to overcome technical noise.Comment: Supplementary Information included. 6 nines, 7 figures, 8 page

Microwave control electrodes for scalable, parallel, single-qubit operations in a surface-electrode ion trap

We propose a surface ion trap design incorporating microwave control electrodes for near-field single-qubit control. The electrodes are arranged so as to provide arbitrary frequency, amplitude and polarization control of the microwave field in one trap zone, while a similar set of electrodes is used to null the residual microwave field in a neighbouring zone. The geometry is chosen to reduce the residual field to the 0.5% level without nulling fields; with nulling, the crosstalk may be kept close to the 0.01% level for realistic microwave amplitude and phase drift. Using standard photolithography and electroplating techniques, we have fabricated a proof-of-principle electrode array with two trapping zones. We discuss requirements for the microwave drive system and prospects for scalability to a large two-dimensional trap array.Comment: 8 pages, 6 figure