Quantum Circuits for Toom-Cook Multiplication

In this paper, we report efficient quantum circuits for integer multiplication using Toom-Cook algorithm. By analysing the recursive tree structure of the algorithm, we obtained a bound on the count of Toffoli gates and qubits. These bounds are further improved by employing reversible pebble games through uncomputing the intermediate results. The asymptotic bounds for different performance metrics of the proposed quantum circuit are superior to the prior implementations of multiplier circuits using schoolbook and Karatsuba algorithms

Reversible Pebble Games For Reducing Qubits In Hierarchical Quantum Circuit Synthesis

Hierarchical reversible logic synthesis can find quantum circuits for large combinational functions. The price for a better scalability compared to functional synthesis approaches is the requirement for many additional qubits to store temporary results of the hierarchical input representation. However, implementing a quantum circuit with large number of qubits is a major hurdle. In this paper, we demonstrate and establish how reversible pebble games can be used to reduce the number of stored temporary results, thereby reducing the qubit count. Our proposed algorithm can be constrained with number of qubits, which is aimed to meet. Experimental studies show that the qubit count can be significantly reduced (by up to 63.2%) compared to the slate-of-the-art algorithms, at the cost of additional gate count

A MANUSH or HUMANS Characterisation of the Human Development Index

Proposing a set of axioms MANUSH (Monotonicity, Anonymity, Normalisation, Uniformity, Shortfall sensitivity, Hiatus sensitivity to level), this paper evaluates three aggregation methods of computing Human Development Index (HDI). The old measure of HDI, which is a linear average of the three dimensions, satisfies monotonicity, anonymity, and normalisation (or MAN) axioms. The current geometric mean approach additionally satisfies the axiom of uniformity, which penalises unbalanced development across dimensions. We propose ℋα measure, which for α ≥ 2 also satisfies axioms of shortfall sensitivity (emphases on the worse-off to better-off dimensions should be at least in proportion to their shortfalls) and hiatus sensitivity to level (higher overall attainment must simultaneously lead to a reduction in gap across dimensions). Special cases of ℋα are the linear average (α = 1), the displaced ideal (α = 2), and the leximin ordering (α → ∞) methods. For its axiomatic advantages, we propose to make use of the displaced ideal (α = 2) method in the computation of HDI replacing the current geometric mean