3,076 research outputs found
For Fixed Control Parameters the Quantum Approximate Optimization Algorithm's Objective Function Value Concentrates for Typical Instances
The Quantum Approximate Optimization Algorithm, QAOA, uses a shallow depth
quantum circuit to produce a parameter dependent state. For a given
combinatorial optimization problem instance, the quantum expectation of the
associated cost function is the parameter dependent objective function of the
QAOA. We demonstrate that if the parameters are fixed and the instance comes
from a reasonable distribution then the objective function value is
concentrated in the sense that typical instances have (nearly) the same value
of the objective function. This applies not just for optimal parameters as the
whole landscape is instance independent. We can prove this is true for low
depth quantum circuits for instances of MaxCut on large 3-regular graphs. Our
results generalize beyond this example. We support the arguments with numerical
examples that show remarkable concentration. For higher depth circuits the
numerics also show concentration and we argue for this using the Law of Large
Numbers. We also observe by simulation that if we find parameters which result
in good performance at say 10 bits these same parameters result in good
performance at say 24 bits. These findings suggest ways to run the QAOA that
reduce or eliminate the use of the outer loop optimization and may allow us to
find good solutions with fewer calls to the quantum computer.Comment: 16 pages, 1 figur
Indoor Navigation with MEMS sensors
AbstractAccurate positioning becomes extremely important for modern application like indoor navigation and location-based services. Standalone GPS cannot meet this accuracy. In this paper a method to couple GPS and a high resolution MEMS pressure sensor is presented to improve vertical as well as horizontal (in urban canyon environment) positioning. Further, a step counter based on an accelerometer is improved with an altimeter for stair detection and automatic step length adaptation for dead reckoning inside buildings. Finally, a stand-alone system accurately tracks floor levels inside buildings, using only a pressure sensor
Differences in daptomycin and vancomycin ex vivo behaviour can lead to false interpretation of negative blood cultures
AbstractIn clinical studies on bacteraemia, the negativity of blood cultures is an important endpoint for comparing the efficacy of different therapeutic regimens. In FAN° anaerobic blood culture medium (BacT/ALERT system), daptomycin displayed increased MIC against Staphylococcus aureus and improved abolishment of its carryover effect in charcoal when compared with vancomycin. Differences between these two drugs can lead to a false interpretation of negative blood cultures. To compare different antibiotic regimens for the treatment of bacteraemia, preliminary studies are mandatory to ensure that ex vivo antibiotic behaviour is similar in the blood-culture system used
Approximating Fractional Time Quantum Evolution
An algorithm is presented for approximating arbitrary powers of a black box
unitary operation, , where is a real number, and
is a black box implementing an unknown unitary. The complexity of
this algorithm is calculated in terms of the number of calls to the black box,
the errors in the approximation, and a certain `gap' parameter. For general
and large , one should apply a total of times followed by our procedure for approximating the fractional
power . An example is also given where for
large integers this method is more efficient than direct application of
copies of . Further applications and related algorithms are also
discussed.Comment: 13 pages, 2 figure
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