Synthesis Of Reversible Circuits Research Articles

Design of reversible sequential circuits optimizing quantum cost, delay, and garbage outputs

Reversible logic has shown potential to have extensive applications in emerging technologies such as quantum computing, optical computing, quantum dot cellular automata as well as ultra low power VLSI circuits. Recently, several researchers have focused their efforts on the design and synthesis of efficient reversible logic circuits. In these works, the primary design focus has been on optimizing the number of reversible gates and the garbage outputs. The number of reversible gates is not a good metric of optimization as each reversible gate is of different type and computational complexity, and thus will have a different quantum cost and delay. The computational complexity of a reversible gate can be represented by its quantum cost. Further, delay constitutes an important metric, which has not been addressed in prior works on reversible sequential circuits as a design metric to be optimized. In this work, we present novel designs of reversible sequential circuits that are optimized in terms of quantum cost, delay and the garbage outputs. The optimized designs of several reversible sequential circuits are presented including the D Latch, the JK latch, the T latch and the SR latch, and their corresponding reversible master-slave flip-flop designs. The proposed master-slave flip-flop designs have the special property that they don't require the inversion of the clock for use in the slave latch. Further, we introduce a novel strategy of cascading a Fredkin gate at the outputs of a reversible latch to realize the designs of the Fredkin gate based asynchronous set/reset D latch and the master-slave D flip-flop. Finally, as an example of complex reversible sequential circuits, the reversible logic design of the universal shift register is introduced. The proposed reversible sequential designs were verified through simulations using Verilog HDL and simulation results are presented.

Synthesis of reversible circuits for large reversible functions

This paper presents a new algorithm MP (multiple pass) to synthesize large reversible binary circuits without ancilla bits. The well-known MMD algorithm for synthesis of reversible circuits requires to store a truth table (or a Reed-Muller - RM transform) as a 2n vector to represent a reversible function of n variables. This representation prohibits synthesis of large functions. However, in MP we do not store such an exponentially growing data structure. The values of minterms are calculated in MP dynamically, one-by-one, from a set of logic equations that specify the reversible circuit to be designed. This allows for synthesis of large scale reversible circuits (30-bits), which is not possible with any existing algorithm. In addition, our unique multi-pass approach where the circuit is synthesized with various, yet specific, minterm orders yields quasi-optimal solution. The algorithm returns a description of the quasi-optimal circuit with respect to gate count or to its 'quantum cost'. Although the synthesis process in MP is relatively slower, the solution is found in real-time for smaller circuits of 8 bits or less.

A Fast Algorithm for Synthesis of Quantum Reversible Logic Circuits

Reversible logic finds many applications,especially in the area of quantum computing. Quantum reversible logic circuits are basic elements in quantum computer construction. Synthesis of quantum reversible logic circuits means to automatically construct desired quantum reversible logic circuit with minimal quantum cost. The authors absorb different ideas of reversible logic circuits synthesis and present a novel and efficient algorithm which can automatically derive the positive polarity Reed-Muller expansion (RM). A solution space tree is constructed to create quantum reversible logic circuits. Firstly,floor traversal is applied globally,and depth-first search is used locally. Secondly,according to the technique of template optimization,the bound function is constructed,which can rapidly prune the branches with no or nonoptimal result. Thirdly,factors of RM are first considered,therefore the algorithm can effectively construct optimal result and saves computational cost significantly. Judging by the internationally recognized reversible functions of three variables,the proposed algorithm not only synthesizes all optimal reversible functions,but also runs extremely faster than others of the same kind.

Synthesis of reversible circuits with minimal costs

We present fast algorithms to synthesize exact minimal reversible circuits for various types of gate and cost. By reducing reversible logic synthesis problems to permutation group problems, we use the powerful algebraic software GAP to solve such problems. Our approach can minimize for arbitrary cost functions of gates. In addition, we show that Peres gates are a better choice than the standard Toffoli gates in libraries of universal reversible gates.

A recursive method for synthesizing quantum/reversible quaternary parallel adder/subtractor with look-ahead carry

Multiple-valued quantum logic circuits are a promising choice for future quantum computing technology since they have several advantages over binary quantum logic circuits. Adder/subtractor is the major component of the ALU of a computer and is also used in quantum oracles. In this paper, we propose a recursive method of hand synthesis of reversible quaternary full-adder circuit using macro-level quaternary controlled gates built on the top of ion-trap realizable 1-qudit quantum gates and 2-qudit Muthukrishnan–Stroud quantum gates. Based on this quaternary full-adder circuit we propose a reversible circuit realizing quaternary parallel adder/subtractor with look-ahead carry. We also show the way of adapting the quaternary parallel adder/subtractor circuit to an encoded binary parallel adder/subtractor circuit by grouping two qubits together into quaternary qudit values.

Synthesis of reversible circuits using a moving forward strategy

Reversible circuits have applications in various research areas including signal processing, cryptography and quantum computation. In this paper, a non-search based moving forward synthesis algorithm (MOSAIC) for Boolean reversible circuits is proposed to convert an arbitrary well-formed matrix into an identity matrix using a set of reversible gates. In contrast with the widely used search-based methods, MOSAIC is guaranteed to produce a result and can lead to a solution in much fewer algorithmic steps. To evaluate the proposed algorithms, different circuits and benchmarks were used that show the efficiency of the proposed algorithm to lead a result.

Bi-Directional Synthesis of 4-Bit Reversible Circuits

Reversible circuits play an important role in quantum computing, which is one of the most promising emerging technologies. In this paper, we investigate the problem of optimally synthesizing 4-bit reversible circuits. We present an enhanced bi-directional synthesis approach. Owing to the exponential nature of the memory and run-time complexity, all existing methods can only perform four steps for the Controlled-Not gate NOT gate, and Peres gate library. Our novel method can achieve 12 steps. As a result, we augment the number of circuits that can optimally be synthesized by over 5 × 106 times. We synthesized 1000 random 4-bit reversible circuits. The statistical analysis result supports our estimation. The quantum cost of our result is also better than the quantum cost of other approaches. The promising experimental results demonstrate the effectiveness of our approach.

Synthesis of reversible logic for nanoelectronic circuits

AbstractReversible logic circuits can be synthesized hierarchically by dividing them into smaller, more manageable blocks. As all reversible circuits of a certain width w form a group, this problem relates to the partitioning of a group into (double) cosets. In this article, we propose three different strategies for the synthesis of reversible circuits, all based on group theory. We will compare these different methods and will determine which is the most efficient. Copyright © 2007 John Wiley & Sons, Ltd.

Universality of 2-qudit ternary reversible gates

In this paper, we investigate the synthesis of ternary reversible circuits in the absence of ancilla bits. We demonstrated that 2-qudit ternary Swap, NOT and 1-controlled-NOT gates are universal for realization of arbitrary ternary n-qudit reversible circuits without ancilla qudits, and all even ternary n-qudit reversible circuits can be constructed by ternary NOT and ternary 1-controlled-NOT gates without ancilla qudits. The realization approach is constructive. This result is significantly different from the binary case.

Majority-based reversible logic gates

Reversible logic plays an important role in the synthesis of circuits for quantum computing. In this paper, we introduce families of reversible gates based on the majority Boolean function (MBF) and we prove their properties in reversible circuit synthesis. These gates can be used to synthesize reversible circuits of minimum “scratchpad register width” for arbitrary reversible functions. We show that, given a MBF f with 2 k + 1 inputs, f can be implemented by a reversible logic gate with 2 k + 1 inputs and 2 k + 1 outputs, i.e., without any constant inputs. We also demonstrate new gates from this family with very efficient quantum realizations for majority-based applications. They can be used to synthesize any reversible function of the same width in conjunction with inverters and Feynman (2-qubit controlled-NOT) gates. The gate universality problem is formulated in terms of elementary group theory and solved using the algebraic software GAP.

Evolutionary Approach to Quantum and Reversible Circuits Synthesis

The paper discusses the evolutionary computation approach to the problem of optimal synthesis of Quantum and Reversible Logic circuits. Our approach uses standard Genetic Algorithm (GA) and its relative power as compared to previous approaches comes from the encoding and the formulation of the cost and fitness functions for quantum circuits synthesis. We analyze new operators and their role in synthesis and optimization processes. Cost and fitness functions for Reversible Circuit synthesis are introduced as well as local optimizing transformations. It is also shown that our approach can be used alternatively for synthesis of either reversible or quantum circuits without a major change in the algorithm. Results are illustrated on synthesized Margolus, Toffoli, Fredkin and other gates and Entanglement Circuits. This is for the first time that several variants of these gates have been automatically synthesized from quantum primitives.

Synthesis of reversible logic circuits

Reversible or information-lossless circuits have applications in digital signal processing, communication, computer graphics, and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We investigate the synthesis of reversible circuits that employ a minimum number of gates and contain no redundant input-output line-pairs (temporary storage channels). We prove constructively that every even permutation can be implemented without temporary storage using NOT, CNOT, and TOFFOLI gates. We describe an algorithm for the synthesis of optimal circuits and study the reversible functions on three wires, reporting the distribution of circuit sizes. We also study canonical circuit decompositions where gates of the same kind are grouped together. Finally, in an application important to quantum computing, we synthesize oracle circuits for Grover's search algorithm, and show a significant improvement over a previously proposed synthesis algorithm.