Related papers: Synthesis of the Optimal 4-bit Reversible Circuits

We develop a framework for resource efficient compilation of higher-level programs into lower-level reversible circuits. Our main focus is on optimizing the memory footprint of the resulting reversible networks. This is motivated by the…

In this paper, a new non-search based synthesis algorithm for reversible circuits is proposed. Compared with the widely used search-based methods, our algorithm is guarantied to produce a result and can lead to a solution with much fewer…

Reversible logic has two main properties. First, the number of inputs is equal to the number of outputs. Second, it implements a one-to-one mapping; i.e., one can reconstruct the inputs from the outputs. These properties enable its…

Reversible circuits have been studied extensively and intensively, and have plenty of applications in various areas, such as digital signal processing, cryptography, and especially quantum computing. In 2003, the lower bound $\Omega(2^n…

We report optimal and asymptotically optimal reversible circuits composed of NOT, CNOT, and Toffoli (NCT) gates, keeping the count by the subsets of the gate types used. This study fine tunes the circuit complexity figures for the…

We use a random search technique to find quantum gate sequences that implement perfect quantum state preparation or unitary operator synthesis with arbitrary targets. This approach is based on the recent discovery that there is a large…

Optimizing the size and depth of CNOT circuits is an active area of research in quantum computing and is particularly relevant for circuits synthesized from the Clifford + T universal gate set. Although many techniques exist for finding…

We propose a linear-size synthesis of the multi-controlled Toffoli gate on qudits with at most one borrowed ancilla. This one ancilla can even be saved when the qudit dimension is odd. Our synthesis leads to improvements in various quantum…

We study the problem of finding the best approximate circuit that is the closest (in some pertinent metric) to a target circuit, and which satisfies a number of hardware constraints, like gate alphabet and connectivity. We look at the…

As quantum technology advances, the efficient design of quantum circuits has become an important area of research. This paper provides an introduction to the MCT quantum circuit design problem for reversible Boolean functions with the…

Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the…

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…

In this paper, a library-based synthesis methodology for reversible circuits is proposed where a reversible specification is considered as a permutation comprising a set of cycles. To this end, a pre-synthesis optimization step is…

Linear Nearest Neighbor (LNN) synthesis in reversible circuits has emerged as an important issue in terms of technological implementation for quantum computation. The objective is to obtain a LNN architecture with minimum gate cost. As…

Quantum oracles are widely adopted in problems, like query oracle in Grover's algorithm, cipher in quantum cryptanalytic and data encoder in quantum machine learning. Notably, the bit-flip oracle, capable of flipping the state based on a…

We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate…

In this paper, reversible circuits consisting of NOT, CNOT and 2-CNOT gates are studied. Several asymptotically optimal by the order of magnitude synthesis methods are described. Some circuit's complexity reduction approaches are…

We propose an approach to optimally synthesize quantum circuits from non-permutative quantum gates such as Controlled-Square-Root-of-Not (i.e. Controlled-V). Our approach reduces the synthesis problem to multiple-valued optimization and…

We consider the problem of the variational quantum circuit synthesis into a gate set consisting of the CNOT gate and arbitrary single-qubit (1q) gates with the primary target being the minimization of the CNOT count. First we note that…

Many synthesis approaches for reversible and quantum logic have been proposed so far. However, most of them generate circuits with respect to simple metrics, i.e. gate count or quantum cost. On the other hand, to physically realize…