381 research outputs found
Quantum Coins
One of the earliest cryptographic applications of quantum information was to
create quantum digital cash that could not be counterfeited. In this paper, we
describe a new type of quantum money: quantum coins, where all coins of the
same denomination are represented by identical quantum states. We state
desirable security properties such as anonymity and unforgeability and propose
two candidate quantum coin schemes: one using black box operations, and another
using blind quantum computation.Comment: 12 pages, 4 figure
Exact quantum Fourier transforms and discrete logarithm algorithms
We show how the quantum fast Fourier transform (QFFT) can be made exact for
arbitrary orders (first for large primes). For most quantum algorithms only the
quantum Fourier transform of order is needed, and this can be done
exactly. Kitaev \cite{kitaev} showed how to approximate the Fourier transform
for any order. Here we show how his construction can be made exact by using the
technique known as ``amplitude amplification''. Although unlikely to be of any
practical use, this construction e.g. allows to make Shor's discrete logarithm
quantum algorithm exact. Thus we have the first example of an exact non black
box fast quantum algorithm, thereby giving more evidence that ``quantum'' need
not be probabilistic. We also show that in a certain sense the family of
circuits for the exact QFFT is uniform. Namely the parameters of the gates can
be calculated efficiently.Comment: 10 pages Late
The lifetime gender gap in Italy. Do the pension system countervails labour market outcomes?
In Italy large work career gender gaps currently exists, particularly regarding wages and activity rates. The paper investigates the issue looking at lifetime incomes, where from the one side all the career gaps tend to accumulate, from the other the redistribution acted by the pension system may mitigate the differences. Exploiting an original database on the entire work careers, we document how the pay gap constantly opens with age and how women tend to cumulate lower seniority. Both gaps have an impact in the pension calculation, so that the day after retirement gender differences are even higher. By means of a microsimulation model we show that the pension system partially countervails labour market outcomes, implying lower differences in lifetime incomes. However, due to the current transition to an actuarially neutral system, the effect is going to vanish in following decades, posing some concerns about future prospects of gender income inequality.
Polynomial-time T-depth Optimization of Clifford+T circuits via Matroid Partitioning
Most work in quantum circuit optimization has been performed in isolation
from the results of quantum fault-tolerance. Here we present a polynomial-time
algorithm for optimizing quantum circuits that takes the actual implementation
of fault-tolerant logical gates into consideration. Our algorithm
re-synthesizes quantum circuits composed of Clifford group and T gates, the
latter being typically the most costly gate in fault-tolerant models, e.g.,
those based on the Steane or surface codes, with the purpose of minimizing both
T-count and T-depth. A major feature of the algorithm is the ability to
re-synthesize circuits with additional ancillae to reduce T-depth at
effectively no cost. The tested benchmarks show up to 65.7% reduction in
T-count and up to 87.6% reduction in T-depth without ancillae, or 99.7%
reduction in T-depth using ancillae.Comment: Version 2 contains substantial improvements and extensions to the
previous version. We describe a new, more robust algorithm and achieve
significantly improved experimental result
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