Related papers: The Classification of Reversible Bit Operations
Optimal synthesis of reversible functions is a non-trivial problem. One of the major limiting factors in computing such circuits is the sheer number of reversible functions. Even restricting synthesis to 4-bit reversible functions results…
Loss of every bit in traditional logic circuits involves dissipation of power in the form of heat that evolve to the environment. Reversible logic is one of the alternatives that have capabilities to mitigate this dissipation by preventing…
Two different algorithms are presented for generating a quantum circuit realization of a matrix representing a permutation on $2^n$ letters. All circuits involve $n$ qubits and only use multi--controlled Toffoli gates. The first algorithm…
Most of the work on implementing arithmetic on a quantum computer has borrowed from results in classical reversible computing (e.g. [VBE95], [BBF02], [DKR04]). These quantum networks are inherently classical, as they can be implemented with…
The most general structure (in matrix form) of a single-qubit gate is presented. Subsequently, used that to obtain a set of conditions for testing (a) whether a given 2-qubit gate is genuinely a 2-qubit gate, i.e., not decomposable into two…
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 consider a stack sorting algorithm where only the appropriate output values are popped from the stack and then any remaining entries in the stack are run through the stack in reverse order. We identify the basis for the $2$-reverse pass…
The Fredkin three-bit gate is universal for computational logic, and is reversible. Classically, it is impossible to do universal computation using reversible two-bit gates only. Here we construct the Fredkin gate using a combination of six…
We present a general technique to implement products of many qubit operators communicating via a joint harmonic oscillator degree of freedom in a quantum computer. By conditional displacements and rotations we can implement Hamiltonians…
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…
Reversible computation has been proposed as a future paradigm for energy efficient computation, but so far few implementations have been realised in practice. Quantum circuits, running on quantum computers, are one construct known to be…
Many universal reversible libraries that contain more than one gate type have been proposed in the literature. Practical implementation of reversible circuits is much easier if a single gate type is used in the circuit construction. This…
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…
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…
For which sets A does there exist a mapping, computed by a total or partial recursive function, such that the mapping, when its domain is restricted to A, is a 1-to-1, onto mapping to $\Sigma^*$? And for which sets A does there exist such a…
We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of those gates. Specifically, we allow the standard circuit operations of composition and tensor product,…
Reversible computing basically means computation with less or not at all electrical power. Since the standard binary gates are not usually reversible we use the Fredkin gate in order to achieve reversibility. An algorithm for designing…
Homogeneous rotation symmetric Boolean functions have been extensively studied in recent years because of their applications in cryptography. Little is known about the basic question of when two such functions are affine equivalent. The…
The question of finding a lower bound on the number of Toffoli gates in a classical reversible circuit is addressed. A method based on quantum information concepts is proposed. The method involves solely concepts from quantum information -…
In this paper we consider circuit synthesis for n-wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms,…