Cumulative balance testing of logic circuits
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Balance testing and balance-testable design of logic circuits
Journal of Electronic Testing: Theory and Applications
On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Quantum Information Processing
A new algorithm for fixed point quantum search
Quantum Information & Computation
Optimality proofs of quantum weight decision algorithms
Quantum Information Processing
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In two recent papers, a sure-success version of the Grover iteration has been applied to solve the weight decision problem of a Boolean function and it is shown that it is quadratically faster than any classical algorithm (Braunstein et al. in J Phys A Math Theor 40:8441, 2007; Choi and Braunstein in Quantum Inf Process 10:177, 2011). In this paper, a new approach is proposed to generalize the Grover's iteration so that it becomes exact and its application to the same problem is studied. The regime where a small number of iterations is applied is the main focus of this work. This task is accomplished by presenting the conditions on the decidability of the weights where the decidability problem is reduced to a system of algebraic equations of a single variable. Thus, it becomes easier to decide on distinguishability by solving these equations analytically and, if not possible, numerically. In addition, it is observed that the number of iterations scale as the square root of the iteration number of the corresponding classical probabilistic algorithms.