相关论文: Strong equivalence of reversible circuits is coNP-…
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…
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…
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…
The controlled-SWAP and controlled-controlled-NOT gates are at the heart of the original proposal of reversible classical computation by Fredkin and Toffoli. Their widespread use in quantum computation, both in the implementation of…
Atomic-scale logic and the minimization of heating (dissipation) are both very high on the agenda for future computation hardware. An approach to achieve these would be to replace networks of transistors directly by classical reversible…
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…
In recent years, reversible logic has emerged as a promising computing paradigm having its applications in low power computing, quantum computing, nanotechnology, optical computing and DNA computing. The classical set of gates such as AND,…
Boolean matching is an important problem in logic synthesis and verification. Despite being well-studied for conventional Boolean circuits, its treatment for reversible logic circuits remains largely, if not completely, missing. This work…
The circuit equivalence problem of a finite algebra $\mathbf A$ is the computational problem of deciding whether two circuits over $\mathbf A$ define the same function or not. This problem not just generalises the equivalence problem for…
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 define a problem "exact non-identity check": Given a classical description of a quantum circuit with an ancilla system, determine whether it is strictly equivalent to the identity or not. We show that this problem is NQP-complete. In a…
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…
We perform formal verification of quantum circuits by integrating several techniques specialized to particular classes of circuits. Our verification methodology is based on the new notion of a reversible miter that allows one to leverage…
Reversible circuits find applications in many areas of Computer Science including Quantum Computation. This paper examines the testability of an important subclass of reversible logic circuits that are composed of k-wire controlled NOT…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
We study Boolean circuits as a representation of Boolean functions and consider different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all…
Reversible computing has emerged as a possible low cost alternative to conventional computing in terms of speed, power consumption and computing capability. In order to achieve reliable circuits in reversible computing, provision for fault…
We describe a practical method of constructing quantum combinational logic circuits with basic quantum logic gates such as NOT and general $n$-bit Toffoli gates. This method is useful to find the quantum circuits for evaluating logic…
It is well known that most of the frequently used reversible logic gates (e.g., NOT, CNOT, SWAP, Toffoli, Fredkin) are self-inverse and are represented by square matrices that are unitary and Hermitian. However, with a simple minded…