Related papers: Strongly Universal Reversible Gate Sets
It is well-known that the Toffoli gate and the negation gate together yield a universal gate set, in the sense that every permutation of $\{0,1\}^n$ can be implemented as a composition of these gates. Since every bit operation that does not…
Reversible logic has attracted much research interest over the last few decades, especially due to its application in quantum computing. In the construction of reversible gates from basic gates, ancilla bits are commonly used to remove…
We present a complete classification of all possible sets of classical reversible gates acting on bits, in terms of which reversible transformations they generate, assuming swaps and ancilla bits are available for free. Our classification…
We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values $(x,y)$ to $(x,x \oplus y)$) is universal in the sense that all unitary operations on arbitrarily many…
We present numerical results which show how two-bit logic gates can be used in the design of a quantum computer. We show that the Toffoli gate, which is a universal gate for all classical reversible computation, can be implemented using a…
We give some optimal size generating sets for the group generated by shifts and local permutations on the binary full shift. We show that a single generator, namely the fully asynchronous application of the elementary cellular automaton 57…
We present a collection of results concerning the structure of reversible gate classes over non-binary alphabets, including (1) a reversible gate class over non-binary alphabets that is not finitely generated (2) an explicit set of…
The quantum Toffoli gate allows universal reversible classical computation. It is also an important primitive in many quantum circuits and quantum error correction schemes. Here we demonstrate the realization of a Toffoli gate with three…
Universal gate sets for quantum computation, when single and two qubit operations are accessible, include both Hermitian and non-Hermitian gates. Here we utilize the fact that any single-qubit operator may be implemented as two Hermitian…
A single-shot Toffoli, or controlled-controlled-NOT, gate is desirable for classical and quantum information processing. The Toffoli gate alone is universal for reversible computing and, accompanied by the Hadamard gate, forms a universal…
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…
It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions…
An algorithm for reversible logic synthesis is proposed. The task is, for a given $n$-bit substitution map $P_n: \{0,1\}^n \rightarrow \{0,1\}^n$, to find a sequence of reversible logic gates that implements the map. The gate library…
Say a collection of $n$-qu$d$it gates $\Gamma$ is eventually universal if and only if there exists $N_0 \geq n$ such that for all $N \geq N_0$, one can approximate any $N$-qu$d$it unitary to arbitrary precision by a circuit over $\Gamma$.…
We generalise clones, which are sets of functions $f:A^n \rightarrow A$, to sets of mappings $f:A^n \rightarrow A^m$. We formalise this and develop language that we can use to speak about it. We then look at bijective mappings, which have…
It is not a problem to complement a classical bit, i.e. to change the value of a bit, a 0 to a 1 and vice versa. This is accomplished by a NOT gate. Complementing a qubit in an unknown state, however, is another matter. We show that this…
A problem of universality in simulation of evolution of quantum system and in theory of quantum computations is related with the possibility of expression or approximation of arbitrary unitary transformation by composition of specific…
In this paper, we have introduced the notion of UselessGate and ReverseOperation. We have also given an algorithm to implement a sorting network for reversible logic synthesis based on swapping bit strings. The network is constructed in…
An $(n+1)$-bit Toffoli gate is mainly utilized to construct other quantum gates and operators, such as Fredkin gates, arithmetical adders, and logical comparators, where $n \geq 2$. Several researchers introduced different methods to…
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…