Reversible logic is becoming more and more popular due to the fact that many novel technologies such as quantum computing, low power CMOS circuit design or quantum optical computing are becoming more and more realistic. In quantum computing, reversible computing is the main venue for the realization and design of classical functions and circuits. We present a new approach to synthesis of reversible circuits using Kronecker Functional Lattice Diagrams (KFLD). Unlike many of contemporary algorithms for synthesis of reversible functions that use n×n Toffoli gates, our method synthesizes functions using 3×3 Toffoli gates, Feynman gates and NOT gates. This reduces the quantum cost of the designed circuit but adds additional ancilla bits. The resulting circuits are always regular in a 4-neighbor model and all connections are predictable. Consequently resulting circuits can be directly mapped in to a quantum device such as quantum FPGA [14]. This is a significant advantage of our method, as it allows us to design optimum circuits for a given quantum technology.
Reversible logic is becoming more and more popular due to the fact that many novel technologies such as quantum computing, low power CMOS circuit design or quantum optical computing are becoming more and more realistic. In quantum computing, reversible computing is the main venue for the realization and design of classical functions and circuits. We present a new approach to synthesis of reversible circuits using Kronecker Functional Lattice Diagrams (KFLD). Unlike many of contemporary algorithms for synthesis of reversible functions that use n×n Toffoli gates, our method synthesizes functions using 3×3 Toffoli gates, Feynman gates and NOT gates. This reduces the quantum cost of the designed circuit but adds additional ancilla bits. The resulting circuits are always regular in a 4-neighbor model and all connections are predictable. Consequently resulting circuits can be directly mapped in to a quantum device such as quantum FPGA [14]. This is a significant advantage of our method, as it allows us to design optimum circuits for a given quantum technology.
Reversible logic is a circuit which has the ability to reduce the power dissipation. This type of logic circuit is used for the process of running the system both forward and backward.One of the main advantages of using any reversible logic is to get back the original data and to reduce the garbage output. Logic synthesis based on the Kronecker Functional Decision Diagram (KFDD) are generated for different reversible cascade methods both complemented and uncomplemented edge by using different reversible gates such as the CNOT (Controlled NOT), NOT, Toffoli gates, Peres gates, etc., and implemented in a quantum processor. In order to reduce the qubits which in turn reduces the quantum cost, it is implemented using reversible logic synthesis in KFDD method.The proposed method shows the implementation of these reversible circuits in an IBM quantum computer to find the probabilities, as it gives less quantum cost and also consumes less time when compared to other decision diagram. Reversible logic finds a wide range of applications in quantum computing and also in areas which deals with the low power design.This paper presents the implementation of KFDD using quantum circuits in IBM Quantum (IBM-Q) processor using different reversible logics and the output is discussed.
Reversible logic became a promising alternative to traditional circuits because of its applications in emerging technologies such as quantum computing, low-power design, DNA computing, or nanotechnologies. As a result, synthesis of the respective circuits is an intensely studied topic. However, most synthesis methods are limited, because they rely on a truth table representation of the function to be synthesized. In this paper, the authors present a synthesis approach that is based on Binary Decision Diagrams (BDDs). The authors propose a technique to derive reversible or quantum circuits from BDDs by substituting all nodes of the BDD with a cascade of Toffoli or quantum gates, respectively. Boolean functions containing more than a hundred of variables can efficiently be synthesized. More precisely, a circuit can be obtained from a given BDD using an algorithm with linear worst case behavior regarding run-time and space requirements. Furthermore, using the proposed approach, theoretical results known from BDDs can be transferred to reversible circuits. Experiments show better results (with respect to the circuit cost) and a significantly better scalability in comparison to previous synthesis approaches.
We present a new approach to the synthesis of quantum automata. In previous research, reversible quantum automata were designed from tabular specifications or state graphs, and minimum length codes, which lead to circuits with Toffoli gates with high numbers of inputs and thus to high quantum costs. This paper is the first to present a method to synthesize Sequential Quantum Circuits directly from flowcharts. In this paper, we directly map flowcharts to reversible/quantum circuits, using only inverters, 2*2 Feynman gates and 3*3 Toffoli gates, and thus reducing quantum costs. Our method has been confirmed by experiments on several benchmarks of practical flowcharts.
Quantum computers, more specifically quantum circuits, take on the eyes with their computational promises such as reversibility. In this paper, we perform synthesis and optimization of quantum circuits. In the first part, we propose a fast synthesis algorithm that implements any given reversible Boolean function with quantum gates. Instead of an exhaustive search on every given function, our algorithm creates a library of essential functions and performs sorting. As an example, to implement 4 bit circuits we only use 120 essential functions out of all 20922789888000 functions. In the second part, we optimize our circuits by using new templates. The proposed templates mainly consist of Toffoli gates with negative and positive controlling lines. These templates also show us that optimum area solutions proposed in the literature are not actually optimum; they can be improved.
In the last decade, the synthesis of reversible logic circuits has become a trending topic because of its future necessity and importance. Many methods have been studied and proposed, for instance, transformation-based, search-based, cycle-based, ESOP-based and BDD-based methods. Each of them has its limitation related to time processing, ancilla and garbage line, quantum cost. This study develops an algorithm that could synthesize quantum circuits based on mixed-polarity Toffoli gate and a variant of binary decision diagram (BDD) called reduced-ordered-complemented edge-bdd (ROCBDD). It is an optimized method of BDD to reduce nodes in the representation of Boolean functions, which leads to adding more lines and quantum gates in the reversible circuit. First, the differences between synthesis using ROCBDD, the traditional BDD and others methods are introduced. Then, we define a new structure consisting of mixed-polarity Toffoli gates relied on nodes of ROCBDD. An efficient algorithm to match BDD representation to the reversible logic circuit is also mentioned. Finally, the experimental results show that our algorithm has better synthesizing costs than previous BDD-based methods.
We present a logic synthesis method based on lattices that realize quantum arrays in One-Dimensional Ion Trap technology. This means that all gates are built from 2x2 quantum primitives that are located only on neighbor qubits in a one-dimensional space (called also vector of qubits or Linear Nearest Neighbor (LNN) architecture). The Logic circuits designed by the proposed method are realized only with 3*3 Toffoli, Feynman and NOT quantum gates and the usage of the commonly used multi-input Toffoli gates is avoided. This realization method of quantum circuits is different from most of reversible circuits synthesis methods from the literature that use only high level quantum cost based on the number of quantum gates. Our synthesis approach applies to both standard and LNN quantum cost models. It leads to entirely new CAD algorithms for circuit synthesis and substantially decreases the quantum cost for LNN quantum circuits. The drawback of synthesizing circuits in the presented LNN architecture is the addition of ancilla qubits.