A technology based complexity model for reversible Cuccaro ripple-carry adder

Reversible logic provides an alternative to classical computing, that may overcome many of the power dissipation problems. The paper presents a simple complexity model, from the study of a cascade of Cuccaro adders processed in standard 0.35 micrometer CMOS technology

RESOURCE EFFICIENT DESIGN OF QUANTUM CIRCUITS FOR CRYPTANALYSIS AND SCIENTIFIC COMPUTING APPLICATIONS

Quantum computers offer the potential to extend our abilities to tackle computational problems in fields such as number theory, encryption, search and scientific computation. Up to a superpolynomial speedup has been reported for quantum algorithms in these areas. Motivated by the promise of faster computations, the development of quantum machines has caught the attention of both academics and industry researchers. Quantum machines are now at sizes where implementations of quantum algorithms or their components are now becoming possible. In order to implement quantum algorithms on quantum machines, resource efficient circuits and functional blocks must be designed. In this work, we propose quantum circuits for Galois and integer arithmetic. These quantum circuits are necessary building blocks to realize quantum algorithms. The design of resource efficient quantum circuits requires the designer takes into account the gate cost, quantum bit (qubit) cost, depth and garbage outputs of a quantum circuit. Existing quantum machines do not have many qubits meaning that circuits with high qubit cost cannot be implemented. In addition, quantum circuits are more prone to errors and garbage output removal adds to overall cost. As more gates are used, a quantum circuit sees an increased rate of failure. Failures and error rates can be countered by using quantum error correcting codes and fault tolerant implementations of universal gate sets (such as Clifford+T gates). However, Clifford+T gates are costly to implement with the T gate being significantly more costly than the Clifford gates. As a result, designers working with Clifford+T gates seek to minimize the number of T gates (T-count) and the depth of T gates (T-depth). In this work, we propose quantum circuits for Galois and integer arithmetic with lower T-count, T-depth and qubit cost than existing work. This work presents novel quantum circuits for squaring and exponentiation over binary extension fields (Galois fields of form GF(2 m )). The proposed circuits are shown to have lower depth, qubit and gate cost to existing work. We also present quantum circuits for the core operations of multiplication and division which enjoy lower T-count, T-depth and qubit costs compared to existing work. This work also illustrates the design of a T-count and qubit cost efficient design for the square root. This work concludes with an illustration of how the arithmetic circuits can be combined into a functional block to implement quantum image processing algorithms

On the performance and programming of reversible molecular computers

If the 20th century was known for the computational revolution, what will the 21st be known for? Perhaps the recent strides in the nascent fields of molecular programming and biological computation will help bring about the ‘Coming Era of Nanotechnology’ promised in Drexler’s ‘Engines of Creation’. Though there is still far to go, there is much reason for optimism. This thesis examines the underlying principles needed to realise the computational aspects of such ‘engines’ in a performant way. Its main body focusses on the ways in which thermodynamics constrains the operation and design of such systems, and it ends with the proposal of a model of computation appropriate for exploiting these constraints. These thermodynamic constraints are approached from three different directions. The first considers the maximum possible aggregate performance of a system of computers of given volume, V, with a given supply of free energy. From this perspective, reversible computing is imperative in order to circumvent the Landauer limit. A result of Frank is refined and strengthened, showing that the adiabatic regime reversible computer performance is the best possible for any computer—quantum or classical. This therefore shows a universal scaling law governing the performance of compact computers of ~V^(5/6), compared to ~V^(2/3) for conventional computers. For the case of molecular computers, it is shown how to attain this bound. The second direction extends this performance analysis to the case where individual computational particles or sub-units can interact with one another. The third extends it to interactions with shared, non-computational parts of the system. It is found that accommodating these interactions in molecular computers imposes a performance penalty that undermines the earlier scaling result. Nonetheless, scaling superior to that of irreversible computers can be preserved, and appropriate mitigations and considerations are discussed. These analyses are framed in a context of molecular computation, but where possible more general computational systems are considered. The proposed model, the א-calculus, is appropriate for programming reversible molecular computers taking into account these constraints. A variety of examples and mathematical analyses accompany it. Moreover, abstract sketches of potential molecular implementations are provided. Developing these into viable schemes suitable for experimental validation will be a focus of future work

Time-space complexity of quantum search algorithms in symmetric cryptanalysis: applying to AES and SHA-2

Performance of cryptanalytic quantum search algorithms is mainly inferred from query complexity which hides overhead induced by an implementation. To shed light on quantitative complexity analysis removing hidden factors, we provide a framework for estimating time-space complexity, with carefully accounting for characteristics of target cryptographic functions. Processor and circuit parallelization methods are taken into account, resulting in the time-space trade-off curves in terms of depth and qubit. The method guides howto rank different circuit designs in order of their efficiency. The framework is applied to representative cryptosystems NIST referred to as a guideline for security parameters, reassessing the security strengths of AES and SHA-2