4,092 research outputs found
Universal fault-tolerant gates on concatenated stabilizer codes
It is an oft-cited fact that no quantum code can support a set of
fault-tolerant logical gates that is both universal and transversal. This no-go
theorem is generally responsible for the interest in alternative universality
constructions including magic state distillation. Widely overlooked, however,
is the possibility of non-transversal, yet still fault-tolerant, gates that
work directly on small quantum codes. Here we demonstrate precisely the
existence of such gates. In particular, we show how the limits of
non-transversality can be overcome by performing rounds of intermediate
error-correction to create logical gates on stabilizer codes that use no
ancillas other than those required for syndrome measurement. Moreover, the
logical gates we construct, the most prominent examples being Toffoli and
controlled-controlled-Z, often complete universal gate sets on their codes. We
detail such universal constructions for the smallest quantum codes, the 5-qubit
and 7-qubit codes, and then proceed to generalize the approach. One remarkable
result of this generalization is that any nondegenerate stabilizer code with a
complete set of fault-tolerant single-qubit Clifford gates has a universal set
of fault-tolerant gates. Another is the interaction of logical qubits across
different stabilizer codes, which, for instance, implies a broadly applicable
method of code switching.Comment: 18 pages + 5 pages appendix, 12 figure
Symposium Review: \u3cem\u3eAmish and Old Order Mennonite Schools: A Concise History\u3c/em\u3e—Joseph Stoll; and The School by the Cornfield—Samuel Coon
Joseph Stoll, in Amish and Old Order Mennonite Schools: A Concise History, and Samuel Coon, in The School by the Cornfield, provide two very different perspectives on the struggle to establish Anabaptist schools. The books contrast primarily in their geographic and chronological scope. However, both write about parochial schools with a voice sympathetic to the vision of Amish and Mennonite school founders. They use similar sources, drawing on newspaper accounts, published Amish schools’ histories, and Amish and Mennonite periodicals, as well as personal recollections from individuals involved in school conflicts. [First paragraph.
Quantum imaging by coherent enhancement
Conventional wisdom dictates that to image the position of fluorescent atoms
or molecules, one should stimulate as much emission and collect as many photons
as possible. That is, in this classical case, it has always been assumed that
the coherence time of the system should be made short, and that the statistical
scaling defines the resolution limit for imaging time .
However, here we show in contrast that given the same resources, a long
coherence time permits a higher resolution image. In this quantum regime, we
give a procedure for determining the position of a single two-level system, and
demonstrate that the standard errors of our position estimates scale at the
Heisenberg limit as , a quadratic, and notably optimal, improvement
over the classical case.Comment: 4 pages, 4 figue
Quantum Inference on Bayesian Networks
Performing exact inference on Bayesian networks is known to be #P-hard.
Typically approximate inference techniques are used instead to sample from the
distribution on query variables given the values of evidence variables.
Classically, a single unbiased sample is obtained from a Bayesian network on
variables with at most parents per node in time
, depending critically on , the probability the
evidence might occur in the first place. By implementing a quantum version of
rejection sampling, we obtain a square-root speedup, taking
time per sample. We exploit the Bayesian
network's graph structure to efficiently construct a quantum state, a q-sample,
representing the intended classical distribution, and also to efficiently apply
amplitude amplification, the source of our speedup. Thus, our speedup is
notable as it is unrelativized -- we count primitive operations and require no
blackbox oracle queries.Comment: 8 pages, 3 figures. Submitted to PR
Fixed-point quantum search with an optimal number of queries
Grover's quantum search and its generalization, quantum amplitude
amplification, provide quadratic advantage over classical algorithms for a
diverse set of tasks, but are tricky to use without knowing beforehand what
fraction of the initial state is comprised of the target states. In
contrast, fixed-point search algorithms need only a reliable lower bound on
this fraction, but, as a consequence, lose the very quadratic advantage that
makes Grover's algorithm so appealing. Here we provide the first version of
amplitude amplification that achieves fixed-point behavior without sacrificing
the quantum speedup. Our result incorporates an adjustable bound on the failure
probability, and, for a given number of oracle queries, guarantees that this
bound is satisfied over the broadest possible range of .Comment: 4 pages plus references, 2 figure
Optimal arbitrarily accurate composite pulse sequences
Implementing a single qubit unitary is often hampered by imperfect control.
Systematic amplitude errors , caused by incorrect duration or
strength of a pulse, are an especially common problem. But a sequence of
imperfect pulses can provide a better implementation of a desired operation, as
compared to a single primitive pulse. We find optimal pulse sequences
consisting of primitive or rotations that suppress such errors
to arbitrary order on arbitrary initial states.
Optimality is demonstrated by proving an lower bound and
saturating it with solutions. Closed-form solutions for arbitrary
rotation angles are given for . Perturbative solutions for any
are proven for small angles, while arbitrary angle solutions are obtained by
analytic continuation up to . The derivation proceeds by a novel
algebraic and non-recursive approach, in which finding amplitude error
correcting sequences can be reduced to solving polynomial equations.Comment: 12 pages, 5 figures, submitted to Physical Review
Low-energy photoelectron transmission through aerosol overlayers
The transmission of low-energy (<1.8eV) photoelectrons through the shell of
core-shell aerosol particles is studied for liquid squalane, squalene, and DEHS
shells. The photoelectrons are exclusively formed in the core of the particles
by two-photon ionization. The total photoelectron yield recorded as a function
of shell thickness (1-80nm) shows a bi-exponential attenuation. For all
substances, the damping parameter for shell thicknesses below 15nm lies between
8 and 9nm, and is tentatively assigned to the electron attenuation length at
electron kinetic energies of ~0.5-1eV. The significantly larger damping
parameters for thick shells (> 20nm) are presumably a consequence of distorted
core-shell structures. A first comparison of aerosol and traditional thin film
overlayer methods is provided
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