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 $2^n$ 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