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A Hierarchical Approach to Computer-Aided Design of Quantum Circuits

Marek A. Perkowski, Martin Lukáč, Paweł Kerntopf, Mikhail Pivtoraiko, Michele Folgheraiter, Yong Woo Choi, Jung-wook Kim, Dongsoo Lee, Woong Hwangbo, Hyungock Kim

Published Jan 1, 2003• 60 citations
OpenAlex

Abstract

A new approach to synthesis of quantum logic circuits has been presented in this paper. This approach produces better results than the previous approaches based on classical reversible logic and can be easier tuned to any particular quantum technology such as nuclear magnetic resonance (NMR). The approach is based on the following principles: (1) design of (complex) gates using approach that links evolutionary, combinatorial and human interaction approaches, (2) design of circuits with these gates using evolutionary and search methods, (3) macro-generation of complex gates to lower level quantum primitives, (4) applying technology-related optimizing tautological transforms that take realistic quantum layout constraints, (5) calculating realistic costs related to quantum realization, (6) synthesis of incompletely specified functions. 1.

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•Jan 1, 2008•3 citations
A new approach to synthesis of quantum logic circuits has been presented in this paper. This approach produces better results than the previous approaches based on classical reversible logic and can be easier tuned to any particular quantum technology such as nuclear magnetic resonance (NMR). The approach is based on the following principles: (1) design of (complex) gates using approach that links evolutionary, combinatorial and human interaction approaches, (2) design of circuits with these gates using evolutionary and search methods, (3) macro-generation of complex gates to lower level quantum primitives, (4) applying technology-related optimizing tautological transforms that take realistic quantum layout constraints, (5) calculating realistic costs related to quantum realization, (6) synthesis of incompletely specified functions. 1.
Reversible quantum logic plays an important role in quantum computing. In this paper, we propose an approach to optimally synthesize quantum circuits by symbolic reachability analysis where the primary inputs are purely binary. we use symbolic reachability analysis, a technique most commonly used in model checking (a way of formal verification), to synthesize the optimum quantum circuits. We present an exact synthesis method with optimal quantum cost and a speedup method with non-optimal quantum cost. Both our methods guarantee the synthesizeability of all reversible circuits. Unlike previous works which use permutative reversible gates, we use a lower level library which includes non-permutative quantum gates. For the first time, problems in quantum logic synthesis have been reduced to those of multiple-valued logic synthesis thus reducing the search space and algorithm complexity. We synthesized quantum circuits for gate, half-adder, full-adder, etc. with the smallest cost.. Our approach obtains the minimum cost quantum circuits for Miller's gate, half-adder, and full-adder, which are better than previous results. In addition, we prove the minimum quantum cost (using our elementary quantum gates) for Fredkin, Peres, and Toffoli gates. Our work constitutes the first successful experience of applying satisfiability with formal methods to quantum logic synthesis.
Two questions have been addressed here: how many logic levels are necessary to synthesise a specific instance of a reversible circuit, and how much better to have large gate libraries, and what gates should be required in libraries. Group theory is applied to 3-bit reversible gate synthesis to create a library useful in hierarchical design. It has been shown that arbitrary 3-bit reversible circuit can be synthesised with four-logic levels, using this new gate library. The respective universal library for the four-level synthesis is constructed and optimised it on the level of nuclear magnetic resonance pulses. A very fast algorithm to synthesise arbitrary 3-bit reversible function to gates from our library is also presented. The algorithm demonstrates dramatic speed benefit and results in a maximum of four-level circuit for arbitrary 3-bit reversible function. The gates are optimised on the level of pulses to decrease their cost and allow for objective comparison with standard CNOT, NOT, Toffoli gates (CNT) circuits. This library guarantees a four-level circuit for any 3-qubit reversible function and is also intended to be used in a hierarchical design of larger circuits.
Reversible quantum logic synthesis is to study given quantum gates and quantum circuits of the constraints and limitations and find the smallest or smaller quantum cost to achieve the desired quantum logic circuits.The quantum logic gate functions of the matrix is indicated by the mathematical model. The synthesis and optimization are achieved simultaneously by the genetic algorithm as global search tool. Genetic algorithm is applied to quantum reversible logic synthesis.The fourth-order quantum circuit experiment has achieved good results,and further analysis of this method in high-level synthesis of quantum circuits and its application is completed.
We observe an enormous increase in the computational power of digital computers. This was due to the revolution in manufacturing processes and controlling semiconductor structures on submicron scale, ultimately leading to the control of individual atoms. Eventually, the classical electric circuits encountered the barrier of quantum mechanics and its effects. However, the laws of quantum mechanics can be also used to produce computational devices that lead to extraordinary speed increases over classical computers. Thus quantum computing becomes a very promising and attractive research area. The Computer Aided Design for Quantum circuits becomes an essential ingredient for such emerging research which may lead to these powerful computers to be realized—an era of Quantum computing. This thesis presents an integrated theoretical study of software algorithms to design circuits of quantum oracles as well as methods for designing quantum oracles for Grover algorithm to solve combinatorial problems. An implementation of quantum algorithm involves the initialization of the input state and its manipulation with quantum gates followed by the measurements. In Grover algorithm the problem to be solved is specified by a permutative logic oracle – the fundamental problem is then how to build this oracle from quantum logic circuits and how to optimize these circuits. These problems are NP-hard and require search algorithms. In future, the search will be also done in quantum and this thesis leads to quantum algorithms to design quantum circuits more efficiently.
Quantum information processing is of interest as it offers the potential for a new generation of very powerful computers supporting novel computational paradigms. Over the last couple of decades, different aspects of quantum computers ranging from quantum algorithms to quantum physical design have received growing attention. One of the most important research areas is the synthesis and post-synthesis optimization of reversible and quantum circuits. Many synthesis and optimization approaches can be found in the literature, yet, due to the complexity of the problem, finding approaches leading to optimal, or near optimal, results is still an open problem. The synthesized circuits are usually evaluated based on quantum cost models. Therefore, they are often technology mapped to circuits of more primitive gates. To this end, various technology mapping approaches have also been proposed in the past few years. Related work shows an existing gap in optimized technology mapping for reversible and quantum circuits. In this dissertation, an optimized technology mapping design flow is introduced for mapping reversible circuits to quantum circuits. The contributions of this dissertation are classified as follows: - New reversible circuit optimization methods. - Optimized reversible to quantum mapping approaches. - New quantum gate libraries and new cost models for reversible gates based on the new libraries. - Quantum circuit optimization approaches. The steps above, form an optimized flow for mapping reversible circuits to quantum circuits. At each step of the design flow optimized and consistent approaches are suggested with the goal of reducing the quantum cost of the synthesized reversible circuits. The evaluations show that the proposed mapping methodology leads to significant improvement in the quantum cost of the existing benchmark circuits.
Emerging quantum computing technologies are poised to replace standard CMOS logic when the exponential size reduction reaches sub-atomic dimensions. Quantum circuits are reversible and therefore promise the potential of computation without energy loss. This research considers computer aided design (CAD) methods for all major aspects of quantum computing circuit design including logic synthesis, simulation, verification, and testing. The technologies we investigate include quantum cell automata (QCA) and general quantum circuits (QC), with significantly more emphasis on the later. The recently introduced quantum multi-valued decision diagram (QMDD) provides an efficient method to represent and simulate quantum (and other classical reversible) circuits. A major contribution of this dissertation is the development of a sift-like minimization as well as structure metrics based minimization techniques for QMDD. We have used the enhanced QMDD to efficiently simulate quantum circuits as well as quantum vectors. Our early investigation of reversible logic is concerned with a virtual implementation that uses a direct translation of relatively complex binary functions into circuits composed of Fredkin reversible gates. This allowed us to project size and speed complexity of complex reversible circuits, although this direct translation approach fails to minimize garbage inputs and outputs. To achieve proper garbage minimization, one must synthesize reversible logic using gate cascades with appropriate optimization methods embedded that attempt to minimize the total number of lines in the circuit. To that end, we developed a novel QMDD-based tool for cascade logic synthesis that utilizes the QMDD minimized variable order for lexicographical synthesis with garbage minimization included as an optimization criterion. We developed a synthesis tool that investigates the QCA native 3-input majority gates ability to implement complex logic circuits. In particular, we explore the benefit of transforming the logic description into exclusive sum of products (ESOP) forms prior to implementation in the majority gates. We survey recent efforts in establishing the foundation for QC testing and fault tolerant QC. We project the potential use of random tests as well as built in self test (BIST) techniques for future QC. A major contribution of this dissertation is the investigation of partially redundant reversible logic. Detection of partially redundant logic within any design, reversible or irreversible, has ramifications for logic synthesis, for design verification, and for design for test (DFT) issues.