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A dynamic programming approach to multi-objective logic synthesis of quantum circuits

Arezoo Rajaei, Mahboobeh Houshmand, Seyyed Abed Hosseini

Published Oct 18, 2023• 5 citations
Publisher
DOI
10.1007/s11128-023-04112-z

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The synthesis method of quantum reversible logic circuits based on the genetic algorithm was studied.The multi-objective optimal design of reversible logic circuit's function,the number of quantum gates,the number of garbage bits and quantum cost was achieved by new synthesis method.The mathematical model for quantum reversible logic circuit synthesis was established,the matrix encoding method of quantum reversible logic circuits was proposed,the evolution operations and the multi-objective evolutionary algorithm for quantum reversible logic circuit design were developed.The 8 bits reversible multiplier was designed as an example,the experimental results show that the proposed multi-objective evolutionary design method for quantum reversible logic circuit synthesis is correct and effective.
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.
The work starts with a general idea of how to realize a dynamic programming algorithm as a quantum circuit. This realization is not tied to a specific design model, technology or a class of dynamic algorithms, it shows an approach for such synthesis. As an illustration of the efficiency of this approach, the class of all multiple-output symmetric functions is realized in a dynamic programming algorithm manner as a reversible circuit of Toffoli type elements (NOT, CNOT, and Toffoli gates). The garbage and quantum cost (found based on Barenco et al. paper) of the presented implementation are calculated and compared to the costs of previously described reversible synthesis methods. The summary of results of this comparison is as follows. The quantum cost of the proposed method is less than the quantum cost of any other reported systematic approach. The garbage is usually lower, except for comparison with the synthesis methods, whose primary goal is synthesis with theoretically minimal garbage. The presented algorithm application to the symmetric function synthesis results in circuits suitable for quantum technology realizations.