1,019 research outputs found
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 Ca "atomic clock"
qubits (coherence time ) 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 Ca.
We measure a combined qubit state preparation and single-shot readout fidelity
of 99.93%, a memory coherence time of 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
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