Reversible Logic Circuit Synthesis

We propose the theory of Cayley graphs as a framework to analyse gate counts and quantum costs resulting from reversible circuit synthesis. Several methods have been proposed in the reversible logic synthesis literature by considering different libraries whose gates are associated to the generating sets of certain Cayley graphs. In a Cayley graph, the distance between two vertices corresponds to the optimal circuit size. The lower bound for the diameter of Cayley graphs is al...

In this paper we discuss an efficient technique that can implement any given Boolean function as a quantum circuit. The method converts a truth table of a Boolean function to the corresponding quantum circuit using a minimal number of auxiliary qubits. We give examples of some circuits synthesized with this technique. A direct result that follows from the technique is a new way to convert any classical digital circuit to its classical reversible form.

A rotation-based synthesis framework for reversible logic is proposed. We develop a canonical representation based on binary decision diagrams and introduce operators to manipulate the developed representation model. Furthermore, a recursive functional bi-decomposition approach is proposed to automatically synthesize a given function. While Boolean reversible logic is particularly addressed, our framework constructs intermediate quantum states that may be in superposition, he...

Reversible circuits for SR flip flop, JK flip flop, D flip flop, T flip flop, Master Slave D flip flop and Master Slave JK flip flop have been provided with three different logical approaches. All the circuits have been optimized with the help of existing local optimization algorithms (e.g. template matching, moving rule and deletion rule) and the optimized sequential circuits have been compared with the earlier proposals for the same. It has been shown that the present propo...

In this paper, simultaneous reduction of circuit depth and synthesis cost of reversible circuits in quantum technologies with limited interaction is addressed. We developed a cycle-based synthesis algorithm which uses negative controls and limited distance between gate lines. To improve circuit depth, a new parallel structure is introduced in which before synthesis a set of disjoint cycles are extracted from the input specification and distributed into some subsets. The cycle...

This paper presents models for transforming standard reversible circuits into Linear Nearest Neighbor (LNN) architecture without inserting SWAP gates. Templates to optimize the transformed LNN circuits are proposed. All minimal LNN circuits for all 3-qubit functions have been generated to serve as benchmarks to evaluate heuristic optimization algorithms. The minimal results generated are compared with optimized LNN circuits obtained from the post synthesis algorithm --- templ...

We describe a family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity. Two objectives are of importance: circuit size and depth. In each case we combine a scalable heuristic with a non-scalable, yet exact, synthesis. Our algorithms are applicable to generic connectivity constraints, scale favorably, and achieve close-to-optimal performance in many cases. We demonstrate the utility of these algorithms by optimizi...

Reversible circuits form the backbone for many promising emerging technologies such as quantum computing, low power/adiabatic design, encoder/decoder devices, and several other applications. In the recent years, the scalable synthesis of such circuits has gained significant attention. In this work, we present the SyReC Synthesizer, a synthesis tool for reversible circuits based on the hardware description language SyReC. SyReC allows to describe reversible functionality at a ...

The paper discusses the gate complexity of reversible circuits consisting of NOT, CNOT and 2-CNOT gates. The Shannon gate complexity function $L(n, q)$ for a reversible circuit, implementing a Boolean transformation $f\colon \mathbb Z_2^n \to \mathbb Z_2^n$, is defined as a function of $n$ and the number of additional inputs $q$. The general lower bound $L(n,q) \geq \frac{2^n(n-2)}{3\log_2(n+q)} - \frac{n}{3}$ for the gate complexity of a reversible circuit is proved. An uppe...

In this paper we present a method for minimizing reversible quantum circuits using the Quantum Operator Form (QOF); a new representation of quantum circuit and of quantum-realized reversible circuits based on the CNOT, CV and CV$^\dagger$ quantum gates. The proposed form is a quantum extension to the well known Reed-Muller but unlike the Reed-Muller form, the QOF allows the usage of different quantum gates. Therefore QOF permits minimization of quantum circuits by using prope...