37,112 research outputs found
On fault-tolerance with noisy and slow measurements
It is not so well-known that measurement-free quantum error correction
protocols can be designed to achieve fault-tolerant quantum computing. Despite
the potential advantages of using such protocols in terms of the relaxation of
accuracy, speed and addressing requirements on the measurement process, they
have usually been overlooked because they are expected to yield a very bad
threshold as compared to error correction protocols which use measurements.
Here we show that this is not the case. We design fault-tolerant circuits for
the 9 qubit Bacon-Shor code and find a threshold for gates and preparation of
(30% of the best known result for the
same code using measurement based error correction) while admitting up to 1/3
error rates for measurements and allocating no constraints on measurement
speed. We further show that demanding gate error rates sufficiently below the
threshold one can improve the preparation threshold to .
We also show how these techniques can be adapted to other
Calderbank-Shor-Steane codes.Comment: 11 pages, 7 figures. v3 has an extended exposition and several
simplifications that provide for an improved threshold value and resource
overhea
Three Puzzles on Mathematics, Computation, and Games
In this lecture I will talk about three mathematical puzzles involving
mathematics and computation that have preoccupied me over the years. The first
puzzle is to understand the amazing success of the simplex algorithm for linear
programming. The second puzzle is about errors made when votes are counted
during elections. The third puzzle is: are quantum computers possible?Comment: ICM 2018 plenary lecture, Rio de Janeiro, 36 pages, 7 Figure
A repetition code of 15 qubits
The repetition code is an important primitive for the techniques of quantum
error correction. Here we implement repetition codes of at most qubits on
the qubit \emph{ibmqx3} device. Each experiment is run for a single round
of syndrome measurements, achieved using the standard quantum technique of
using ancilla qubits and controlled operations. The size of the final syndrome
is small enough to allow for lookup table decoding using experimentally
obtained data. The results show strong evidence that the logical error rate
decays exponentially with code distance, as is expected and required for the
development of fault-tolerant quantum computers. The results also give insight
into the nature of noise in the device.Comment: 7 page
Experiments in fault tolerant software reliability
The reliability of voting was evaluated in a fault-tolerant software system for small output spaces. The effectiveness of the back-to-back testing process was investigated. Version 3.0 of the RSDIMU-ATS, a semi-automated test bed for certification testing of RSDIMU software, was prepared and distributed. Software reliability estimation methods based on non-random sampling are being studied. The investigation of existing fault-tolerance models was continued and formulation of new models was initiated
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