We consider the class of constant depth AND/OR circuits augmented with a layer of modular counting gates at the bottom layer, i.e AC◦MODm circuits. We show that the following holds for several types of gates G: by adding a gate of type G at the output, it is possible to obtain an equivalent probabilistic depth 2 circuit of quasipolynomial size consisting of a gate of type G at the output and a ...

Reversible Peres gates with more than two all over binary-valued control signals are discussed. Methods are disclosed for the low cost realization of this kind of Peres gates without requiring ancillary lines. It is shown that Peres gates with n control signals may be obtained with a quantum cost of 2n+1 – n – 2, using Feynman gates and controlled gates realizing the κ-th root of NOT, where κ =...

A method of designing compact multiple-input combinational logic circuits is proposed. We show that i) fundamental logic gates can be constructed by a small number of collision-based fusion gates, ii) multiple-input logic gates are constructed in a systematic manner, iii) the number of transistors in specific logic gates constructed by the proposed method is significantly smaller than that of c...

Abstract By an explicit construction, we show that an arbitrary two-qubit gate can be implemented by using at most 16 elementary one-qubit gates and 3 CNOT gates. We show that this construction is optimal; in the sense that these numbers of gates is the minimal possible ones. Moreover, we show that if the two-qubit gate belongs to SO(4), then we need only 12 elementary one-qubit gates and 2 CNO...

We report herein a set of deoxyribozyme-based logic gates capable of generating any Boolean function. We construct basic NOT and AND gates, followed by the more complex XOR gate. These gates were constructed through a modular design that combines molecular beacon stem-loops with hammerhead-type deoxyribozymes. Importantly, as the gates have oligonucleotides as both inputs and output, they open ...

Shor’s algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a “classical” (macroscopic) signal resulting from the measurement of one bit (embodied in a twostate quantum system) is employed to determine the type of measuremen...

This paper describes the architecture, design & implementation of 2 bit ternary ALU (T-ALU) slice. The proposed ALU is designed for two-bit operation & can be used for n bit operations by cascading n/2 ALU slices. This ALU is implemented using C-MOS ternary logic gates (T-Gates) for ternary arithmetic & logic circuits. Ternary gates are implemented using enhancement / depletion MOSFET technolog...

This paper describes various techniques to reduce the number of logic gates needed to implement the DES S-boxes in bitslice software. Using standard logic gates, an average of 56 gates per S-box was achieved, while an average of 51 was produced when non-standard gates were utilized. This is an improvement over the previous best result, which used an average of 61 non-standard gates.

We give the optimal decomposition of a universal two-qubit circuit using Heisenberg exchange interactions and single qubit rotations. Tuning the strength and duration of the Heisenberg exchange allows one to implement SWAP gates. Our optimal circuit is constructed from only three SWAP gates and six single qubit gates. We show that three SWAP gates are not only sufficient, but necessary. Since s...