Synthesis and Optimization of Reversible Circuits - A Survey

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.Comment: 34 pages, 15 figures, 2 table

Efficient Algorithms for Optimal 4-Bit Reversible Logic System Synthesis

Owing to the exponential nature of the memory and run-time complexity, many methods can only synthesize 3-bit reversible circuits and cannot synthesize 4-bit reversible circuits well. We mainly absorb the ideas of our 3-bit synthesis algorithms based on hash table and present the efficient algorithms which can construct almost all optimal 4-bit reversible logic circuits with many types of gates and at mini-length cost based on constructing the shortest coding and the specific topological compression; thus, the lossless compression ratio of the space of n-bit circuits reaches near 2×n!. This paper presents the first work to create all 3120218828 optimal 4-bit reversible circuits with up to 8 gates for the CNT (Controlled-NOT gate, NOT gate, and Toffoli gate) library, and it can quickly achieve 16 steps through specific cascading created circuits

SQUARE: Strategic Quantum Ancilla Reuse for Modular Quantum Programs via Cost-Effective Uncomputation

Compiling high-level quantum programs to machines that are size constrained (i.e. limited number of quantum bits) and time constrained (i.e. limited number of quantum operations) is challenging. In this paper, we present SQUARE (Strategic QUantum Ancilla REuse), a compilation infrastructure that tackles allocation and reclamation of scratch qubits (called ancilla) in modular quantum programs. At its core, SQUARE strategically performs uncomputation to create opportunities for qubit reuse. Current Noisy Intermediate-Scale Quantum (NISQ) computers and forward-looking Fault-Tolerant (FT) quantum computers have fundamentally different constraints such as data locality, instruction parallelism, and communication overhead. Our heuristic-based ancilla-reuse algorithm balances these considerations and fits computations into resource-constrained NISQ or FT quantum machines, throttling parallelism when necessary. To precisely capture the workload of a program, we propose an improved metric, the "active quantum volume," and use this metric to evaluate the effectiveness of our algorithm. Our results show that SQUARE improves the average success rate of NISQ applications by 1.47X. Surprisingly, the additional gates for uncomputation create ancilla with better locality, and result in substantially fewer swap gates and less gate noise overall. SQUARE also achieves an average reduction of 1.5X (and up to 9.6X) in active quantum volume for FT machines.Comment: 14 pages, 10 figure

Heuristic Synthesis of Reversible Logic – A Comparative Study

Reversible logic circuits have been historically motivated by theoretical research in low-power, and recently attracted interest as components of the quantum algorithm, optical computing and nanotechnology. However due to the intrinsic property of reversible logic, traditional irreversible logic design and synthesis methods cannot be carried out. Thus a new set of algorithms are developed correctly to synthesize reversible logic circuit. This paper presents a comprehensive literature review with comparative study on heuristic based reversible logic synthesis. It reviews a range of heuristic based reversible logic synthesis techniques reported by researchers (BDD-based, cycle-based, search-based, non-search-based, rule-based, transformation-based, and ESOP-based). All techniques are described in detail and summarized in a table based on their features, limitation, library used and their consideration metric. Benchmark comparison of gate count and quantum cost are analysed for each synthesis technique. Comparing the synthesis algorithm outputs over the years, it can be observed that different approach has been used for the synthesis of reversible circuit. However, the improvements are not significant. Quantum cost and gate count has improved over the years, but arguments and debates are still on certain issues such as the issue of garbage outputs that remain the same. This paper provides the information of all heuristic based synthesis of reversible logic method proposed over the years. All techniques are explained in detail and thus informative for new reversible logic researchers and bridging the knowledge gap in this area

Heuristic synthesis of reversible logic - a comparative study

Reversible logic circuits have been historically motivated by theoretical research in low-power, and recently attracted interest as components of the quantum algorithm, optical computing and nanotechnology. However due to the intrinsic property of reversible logic, traditional irreversible logic design and synthesis methods cannot be carried out. Thus a new set of algorithms are developed correctly to synthesize reversible logic circuit. This paper presents a comprehensive literature review with comparative study on heuristic based reversible logic synthesis. It reviews a range of heuristic based reversible logic synthesis techniques reported by researchers (BDD-based, cycle-based, search-based, non-search-based, rule-based, transformation-based, and ESOP-based). All techniques are described in detail and summarized in a table based on their features, limitation, library used and their consideration metric. Benchmark comparison of gate count and quantum cost are analysed for each synthesis technique. Comparing the synthesis algorithm outputs over the years, it can be observed that different approach has been used for the synthesis of reversible circuit. However, the improvements are not significant. Quantum cost and gate count has improved over the years, but arguments and debates are still on certain issues such as the issue of garbage outputs that remain the same. This paper provides the information of all heuristic based synthesis of reversible logic method proposed over the years. All techniques are explained in detail and thus informative for new reversible logic researchers and bridging the knowledge gap in this area

Algorithms for the Optimization of Quantum Circuits

This thesis investigates techniques for the automated optimization of quantum circuits. In the first part we develop an exponential time algorithm for synthesizing minimal depth quantum circuits. We combine this with effective heuristics for reducing the search space, and show how it can be extended to different optimization problems. We then use the algorithm to compute circuits over the Clifford group and T gate for many of the commonly used quantum gates, improving upon the former best known circuits in many cases. In the second part, we present a polynomial time algorithm for the re-synthesis of CNOT and T gate circuits while reducing the number of phase gates and parallelizing them. We then describe different methods for expanding this algorithm to optimize circuits over Clifford and T gates

Logic Synthesis for Established and Emerging Computing

Logic synthesis is an enabling technology to realize integrated computing systems, and it entails solving computationally intractable problems through a plurality of heuristic techniques. A recent push toward further formalization of synthesis problems has shown to be very useful toward both attempting to solve some logic problems exactly--which is computationally possible for instances of limited size today--as well as creating new and more powerful heuristics based on problem decomposition. Moreover, technological advances including nanodevices, optical computing, and quantum and quantum cellular computing require new and specific synthesis flows to assess feasibility and scalability. This review highlights recent progress in logic synthesis and optimization, describing models, data structures, and algorithms, with specific emphasis on both design quality and emerging technologies. Example applications and results of novel techniques to established and emerging technologies are reported