Related papers: Multi-output, multi-level, multi-gate design using…
Nonlinear phase gates are essential to achieve the universality of continuous-variable quantum processing and its applications. We present a deterministic protocol for generating nonlinear phase gates in trapped ion systems using…
The multiplicative depth of a logic network over the gate basis $\{\land, \oplus, \neg\}$ is the largest number of $\land$ gates on any path from a primary input to a primary output in the network. We describe a dynamic programming based…
The minimum number of NOT gates in a Boolean circuit computing a Boolean function is called the inversion complexity of the function. In 1957, A. A. Markov determined the inversion complexity of every Boolean function and proved that…
We prove lower bounds on the number of product gates in bilinear and quadratic circuits that compute the product of two $n \cross n$ matrices over finite fields. In particular we obtain the following results: 1. We show that the number of…
Scaling up quantum computing hardware is hindered by the narrow operating margins of current quantum components. Here, we introduce a composite qubit and gate scheme that achieves wide margins by use of transistor-like nonlinearities to…
Due to the scarcity of quantitative details about biological phenomena, quantitative modeling in systems biology can be compromised, especially at the subcellular scale. One way to get around this is qualitative modeling because it requires…
The nonlinear filter model is an old and well understood approach to the design of secure stream ciphers. Extensive research over several decades has shown how to attack stream ciphers based on this model and has identified the security…
Now a day reversible logic is an attractive research area due to its low power consumption in the area of VLSI circuit design. The reversible logic gate is utilized to optimize power consumption by a feature of retrieving input logic from…
We explore the possibilities of designing classical logic gates at nano-scale level using magnetic quantum rings. A single ring is used for designing OR, NOT, XOR, XNOR and NAND gates, while AND and NOR gate responses are achieved using two…
Nonlinear programming targets nonlinear optimization with constraints, which is a generic yet complex methodology involving humans for problem modeling and algorithms for problem solving. We address the particularly hard challenge of…
Maximal monotonicity is explored as a generalization of the linear theory of passivity, aiming at an algorithmic input/output analysis of physical models. The theory is developed for maximal monotone one-port circuits, formed by the series…
Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in…
We propose a method for exact circuit synthesis using a discrete gate set, as required for fault-tolerant quantum computing. Our approach translates the problem of synthesizing a gate specified by its unitary matrix into a boolean…
The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is…
Logic gates can be written in terms of complex differential operators, where the inputs and outputs are holomorphic functions with several variables. Using the polar representation of complex numbers, we arrive at an immediate connection…
We study learnable logic gate networks that stack layers of 2-input Boolean gates to build combinational circuits. Every 2-input gate has a unique multilinear polynomial with 4 coefficients, so the 16 Boolean gates form a codebook of…
Residue number systems (RNS) represent numbers by their remainders modulo a set of relatively prime numbers. This paper pro- poses an efficient hardware implementation of modular multiplication and of the modulo function (X(mod P)), based…
Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…
The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with…
We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the…