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Synthesis lectures on digital circuits and systems

Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits

Alexis De Vos, Stijn De Baerdemacker, Yvan Van Rentergem

Published Jan 1, 2018• 8 citations
Publisher
DOI
10.1007/978-3-031-79895-5

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A quantum oracle is a reversible quantum subroutine that implements a classical Boolean function within a quantum algorithm. Classical synthesis methods for quantum oracles typically involve two steps: reversible logic synthesis and quantum compilation. In the reversible logic synthesis phase, producing a compact reversible circuit is crucial to minimizing the quantum cost of the final quantum circuit. In this paper, we investigate Boolean functions that simultaneously exhibit two distinct XOR-based regularities: autosymmetry and D-reducibility. These regularities can be effectively utilized for efficient reversible circuit synthesis of Boolean functions. In particular, we propose and implement a new method for the quantum synthesis of autosymmetric and D-reducible Boolean functions. The experimental results demonstrate the effectiveness of our approach on the considered benchmarks, showing reductions in T-count and CNOT-count after Clifford+T quantum compilation.
The classical synthesis method for quantum oracles generally requires a reversible logic synthesis and a quantum compilation step. In the reversible logic synthesis it is important to obtain a compact reversible circuit in order to minimize the quantum cost of the final quantum circuit. In this paper, we exploit function regularities for enabling efficient reversible syn-thesis. In particular, we propose and implement a new method for the quantum synthesis of Dimension reducible Boolean functions. The experimental results validate the proposed approach showing relevant gains in area.
Novel quantum circuit synthesis, using reversible Davio expansions, is introduced. The new method uses two planes to synthesize the quantum circuits: (1) a reversible butterfly circuit plane; and (2) a plane of quantum gates to perform additions and multiplications. Since the reduction of power consumption is a major requirement for circuit design of future technologies, such as in quantum circuits, the main features of several future technologies must include reversibility, and thus the new synthesis method, using reversible butterfly circuits, can play an important role in the synthesis of circuits that consume minimal power.