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IEEE Congress on Evolutionary Computation (CEC)

Evolutionary approach to quantum symbolic logic synthesis

Martin Lukac, Marek A. Perkowski

Published Jun 1, 2008• 11 citations
Publisher

Abstract

In this paper we present an evolutionary approach to the quantum symbolic logic synthesis. We use a genetic algorithm to synthesize quantum circuits from examples, allowing to synthesize functions that are both completely and incompletely specified. The symbolic synthesis is implemented in the GA so as to verify our approach. The Occam Razor principle, fundamental to inductive learning as well as to logic synthesis, is satisfied in this approach by seeking circuits of reduced complexity. The GA is tested on a set of benchmark functions representing single output quantum circuits as well as multiple entangled-qubit state generators.

DOI
10.1109/cec.2008.4631254

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In this paper we present an evolutionary approach to the quantum symbolic logic synthesis. We use a genetic algorithm to synthesize quantum circuits from examples, allowing to synthesize functions that are both completely and incompletely specified. The symbolic synthesis is implemented in the GA so as to verify our approach. The Occam Razor principle, fundamental to inductive learning as well as to logic synthesis, is satisfied in this approach by seeking circuits of reduced complexity. The GA is tested on a set of benchmark functions representing single output quantum circuits as well as multiple entangled-qubit state generators.
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In this paper studied are new concepts of robotic behaviors - deterministic and quantum probabilistic. In contrast to classical circuits, the quantum circuit can realize both of these behaviors. When applied to a robot, a quantum circuit controller realizes what we call quantum robot behaviors. We use automated methods to synthesize quantum behaviors (circuits) from the examples (examples are cares of the quantum truth table). The don't knows (minterms not given as examples) are then converted not only to deterministic cares as in the classical learning, but also to output values generated with various probabilities. The Occam Razor principle, fundamental to inductive learning, is satisfied in this approach by seeking circuits of reduced complexity. This is illustrated by the synthesis of single output quantum circuits, as we extended the logic synthesis approach to Inductive Machine Learning for the case of learning quantum circuits from behavioral examples.
A new approach to synthesis of quantum logic circuits has been presented in this paper. This approach produces better results than the previous approaches based on classical reversible logic and can be easier tuned to any particular quantum technology such as nuclear magnetic resonance (NMR). The approach is based on the following principles: (1) design of (complex) gates using approach that links evolutionary, combinatorial and human interaction approaches, (2) design of circuits with these gates using evolutionary and search methods, (3) macro-generation of complex gates to lower level quantum primitives, (4) applying technology-related optimizing tautological transforms that take realistic quantum layout constraints, (5) calculating realistic costs related to quantum realization, (6) synthesis of incompletely specified functions. 1.
Reversible quantum logic synthesis is to study given quantum gates and quantum circuits of the constraints and limitations and find the smallest or smaller quantum cost to achieve the desired quantum logic circuits.The quantum logic gate functions of the matrix is indicated by the mathematical model. The synthesis and optimization are achieved simultaneously by the genetic algorithm as global search tool. Genetic algorithm is applied to quantum reversible logic synthesis.The fourth-order quantum circuit experiment has achieved good results,and further analysis of this method in high-level synthesis of quantum circuits and its application is completed.
We present a comparative study in the Evolutionary Quantum Logic Synthesis (EQLS) of Quantum Circuits (QC). The objective of this paper focuses on the high speed Evolutionary Algorithms for the synthesis of Quantum circuits. In particular, we describe the comparison between an efficient representation of the synthesized quantum circuit as Quantum Multi-valued Decision Diagram (QMDD) and a low level parallelized evaluation method using the hardware accelerated matrix manipulation. As it is shown in the experiments, each approach has its limits and advantages, and an appropriate choice of each of them yield better results for a subset of the QLS.