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Quantum Information Processing

Heuristic methods to use don’t cares in automated design of reversible and quantum logic circuits

Majid Mohammadi, Mohammad Eshghi

Published Aug 1, 2008• 43 citations
Publisher
DOI
10.1007/s11128-008-0081-x

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Various synthesis methods have been proposed in the literature for reversible and quantum logic circuits. However, there are few algorithms to optimize an existing circuit with multiple constraints simultaneously. In this paper, some heuristics in genetic algorithms (GA) to optimize a given circuit in terms of quantum cost, number of gates, location of garbage outputs, and delay, are proposed. The proposed methods can optimize an existing circuit with a given truth table, including don’t care values, for different aspects of optimality. The results show good enhancements in the optimization of benchmark circuits compared to the previously published methods.

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The majority of work in reversible logic circuits has been limited to combinational logic. Researchers are now beginning to suggest designs for sequential circuits. In this paper we propose a new method to design and optimize feedback reversible logic circuits and a specific group of quantum logic circuits based on the reversible state transition table and genetic algorithms (GA). To show the efficiency of the proposed method, some reversible sequential elements such as D and T flip-flops (FFs), with and without clock and reset, and edge triggered FFs are designed. We have also extended our method to multiple loop feedback circuits. The proposed circuits are highly optimized using a GA synthesis tool that allows don't care values. Some of the designs in this paper are presented in other papers; however, the comparisons show that the quantum cost and number of garbage inputs/outputs are reduced efficiently by our method.

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Abstract In classical logic design, there are machine learning methods based on converting a set of input-output traces to non-deterministic automata that are then converted to deterministic automata and synthesized using logic gates. This approach has not yet been extended to quantum automata. In this paper, we present a method to convert a set of input-output traces to a non-deterministic automaton, which is then converted to an incompletely specified multi-output Boolean function. The existing logic synthesis approaches for designing quantum circuits are insufficient to handle incompletely specified functions. So, we present a novel algorithm to synthesize logic functions with don’t cares using permutative quantum gates. The original MMD (D.M.Miller, D. Maslov, and G.W.Dueck) algorithm minimizes only completely specified reversible functions using cascades of reversible gates. In this paper, this algorithm is modified to allow for the inclusion of don’t cares within the given function’s truth table (reversible or irreversible). The distinguishing property of our presented algorithm QAS, is that it does not add any ancilla qubits if it is not necessary. This algorithm solves the problem of synthesizing deterministic and non-deterministic quantum state machines, both completely specified and incompletely specified.

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Various synthesis methods have been proposed in the literature for reversible and quantum logic circuits. However, there are few algorithms to optimize an existing circuit with multiple constraints simultaneously. In this paper, some heuristics in genetic algorithms (GA) to optimize a given circuit in terms of quantum cost, number of gates, location of garbage outputs, and delay, are proposed. The proposed methods can optimize an existing circuit with a given truth table, including don’t care values, for different aspects of optimality. The results show good enhancements in the optimization of benchmark circuits compared to the previously published methods.
The majority of work in reversible logic circuits has been limited to combinational logic. Researchers are now beginning to suggest designs for sequential circuits. In this paper we propose a new method to design and optimize feedback reversible logic circuits and a specific group of quantum logic circuits based on the reversible state transition table and genetic algorithms (GA). To show the efficiency of the proposed method, some reversible sequential elements such as D and T flip-flops (FFs), with and without clock and reset, and edge triggered FFs are designed. We have also extended our method to multiple loop feedback circuits. The proposed circuits are highly optimized using a GA synthesis tool that allows don't care values. Some of the designs in this paper are presented in other papers; however, the comparisons show that the quantum cost and number of garbage inputs/outputs are reduced efficiently by our method.
Abstract In classical logic design, there are machine learning methods based on converting a set of input-output traces to non-deterministic automata that are then converted to deterministic automata and synthesized using logic gates. This approach has not yet been extended to quantum automata. In this paper, we present a method to convert a set of input-output traces to a non-deterministic automaton, which is then converted to an incompletely specified multi-output Boolean function. The existing logic synthesis approaches for designing quantum circuits are insufficient to handle incompletely specified functions. So, we present a novel algorithm to synthesize logic functions with don’t cares using permutative quantum gates. The original MMD (D.M.Miller, D. Maslov, and G.W.Dueck) algorithm minimizes only completely specified reversible functions using cascades of reversible gates. In this paper, this algorithm is modified to allow for the inclusion of don’t cares within the given function’s truth table (reversible or irreversible). The distinguishing property of our presented algorithm QAS, is that it does not add any ancilla qubits if it is not necessary. This algorithm solves the problem of synthesizing deterministic and non-deterministic quantum state machines, both completely specified and incompletely specified.