Evolutionary quantum logic synthesis of Boolean reversible logic circuits embedded in ternary quantum space using structural restrictions

Abstract

It has been experimentally proven that realizing universal quantum gates using higher-radices logic is practically and technologically possible. We developed a Parallel Genetic Algorithm that synthesizes Boolean reversible circuits realized with a variety of quantum gates on qudits with various radices. In order to allow synthesizing circuits of medium sizes in the higher radix quantum space we performed the experiments using a GPU accelerated Genetic Algorithm. Using the accelerated GA we compare heuristic improvements to the mutation process based on cost minimization, on the adaptive cost of the primitives and improvements due to Baldwinian vs. Lamarckian GA. We also describe various fitness function formulations that allowed for various realizations of well known universal Boolean reversible or quantum-probabilistic circuits. *

On Some Basic Aspects of Ternary Reversible and Quantum Computing

“…This is one important reason why evolutionary approaches for the design of binary and MV reversible circuits are receiving increasing attention (see e.g. [5,6,13,14]). …”

“…Using the idea of heterogeneous quantum gates disclosed in [14], it is straight forward to realize an isolated ternary Toffoli gate over a processing unitary matrix U, working on qutrits, using non-embedded binary controlling signals and a 2-qubit XOR gate. In the "ternary part", the controlled gates would be specified by complex-valued unitary matrices realizing the and its adjoint.…”

Automatic Synthesis of Reversible Circuits

“…Lukac et al proposed automated synthesis of reversible circuits using GA. Their emphasis is on better problem encoding which results in providing better solutions. They have also developed a Parallel Genetic Algorithm for constructing Boolean reversible circuits using several Quantum gates on qudits with various radices [16]. Datta et al [4] introduced a PSO (Particle Swarm Optimization) based search technique for synthesis of a reversible logic circuit.…”

Design of a Ternary Reversible/Quantum Adder using Genetic Algorithm

“…In a reversible circuit, the number of inputs must be equal to the number of outputs, thus, every output can be used only once (i.e., no fan-out is permitted), and must be acyclic. Multiple valued quantum logic synthesis, and ternary logic in particular, has become popular in the recent years [7][8][9][10][11]. Previous works [10,11] used cascades of ternary reversible gates, like Feynman and Toffoli gates, to realize ternary logic functions.…”

“…Multiple valued quantum logic synthesis, and ternary logic in particular, has become popular in the recent years [7][8][9][10][11]. Previous works [10,11] used cascades of ternary reversible gates, like Feynman and Toffoli gates, to realize ternary logic functions. The advantage of this approach is that ternary logic functions having many input variables can be easily expressed as a ternary Galois field sum of products and can be realized using a cascade of ternary Feynman and Toffoli gates.…”