Synthesis and Optimization of Reversible Circuits - A Survey (1110.2574v2)

Abstract: Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.

• The paper surveys key methodologies for reversible circuit synthesis, including algorithmic paradigms, specific exact and heuristic algorithms, and post-synthesis optimization techniques.
• It highlights that while optimal synthesis works for small functions, scalable heuristic approaches are necessary for larger circuits due to computational complexity.
• The work emphasizes the relevance of reversible circuits for quantum computing and identifies challenges in synthesizing large-scale functions and incorporating new physical constraints.

Overview of "Synthesis and Optimization of Reversible Circuits - A Survey"

The paper "Synthesis and Optimization of Reversible Circuits - A Survey" by Mehdi Saeedi and Igor L. Markov presents a comprehensive analysis of reversible circuit synthesis and optimization. Reversible logic circuits, motivated historically by their potential to mitigate power consumption in electronics, are increasingly relevant due to their applications in quantum computing, cryptography, and nano-computing technologies. These circuits ensure that no information is lost during computation, a property that is analogous to quantum computing where unitary transformations are inherently reversible.

The main goal of reversible circuit synthesis is to create a compact representation of a reversible function while minimizing the number of gates, depth, and ancillary bits, which are critical resources in quantum implementations. The authors explore several methodologies for reversible circuit synthesis, namely:

1. Algorithmic Paradigms: These include search-based, cycle-based, transformation-based, and BDD-based methods. Each paradigm offers unique trade-offs between scalability, optimality, and resource utilization.
2. Specific Algorithms: The survey explores both exact and heuristic algorithms. Exact methods aim to find provably optimal solutions but are limited by their computational complexity. In contrast, heuristic methods provide scalable solutions that are often suboptimal.
3. Post-synthesis Optimization: This involves refining the circuit produced by synthesis algorithms to further decrease gate count or circuit depth. Techniques such as template matching and local reordering are highlighted.

The paper discusses a variety of optimization strategies that address different facets of the synthesis problem:

• Optimal and Asymptotic Synthesis: These methods are valuable for either yielding absolute minimal solutions or for providing upper bounds that are close to the theoretical limits.
• Heuristic Synthesis Techniques: These are practical for handling larger circuits and involve intelligent approximation methods to achieve near-optimal results.
• Technology Mapping: This phase adapts the logical circuit to a specific technology, taking into account the physical constraints and the availability of certain gate sets.

Numerical results demonstrated in the survey suggest that while constructing optimal circuits for small-scale functions is feasible, larger functions necessitate heuristic approaches to manage complexity effectively. Moreover, the survey emphasizes the importance of benchmark circuits and software tools such as RevLib and RevKit, which facilitate testing and verification of synthesis algorithms.

The practical implications of this research are profound, particularly in quantum computing where reversibility is a critical factor for implementing quantum algorithms. The theoretical implications also provide extensive insight into the relationship between reversible logic and computational complexity.

In conclusion, the paper illustrates that while significant progress has been made, challenges remain, particularly concerning the synthesis of efficient circuits for large-scale and arithmetic-intensive reversible functions. Future research directions include developing scalable synthesis techniques that can handle growing function sizes without excessive resource utilization and exploring novel cost functions that capture emerging physical constraints in quantum and nano technologies. The work serves as a foundational resource for researchers aiming to advance the design and optimization of reversible and quantum circuits.