Quantum gates

Ray LaPierre

Zhiqiang Li, Xiaoyu Song B, Marek A. Perkowski +2 more

Since non-permutative quantum gates have more complex rules than permutative quantum gates, it is very hard to synthesize quantum logic circuits using non-permutative quantum gates, such as controlled-square-root-of-NOT gates (CV∕CV+ gates). In the efficient synthesis algorithm, direct use of quantum non-permutative gates should be avoided. Rather, the key method is to use quantum gates to create new permutative quantum gates that then replace non-permutative quantum gates. This method assumes the library of quantum gate primitives are constructed so as to have the lowest possible quantum cost. In this paper, we first propose some new CV∕CV+-like gates, i.e. controlled-kth-root-of-NOT gates where k = 2,4,8,…, and give all corresponding matrixes. Further, we also present a novel generic method to quickly and directly construct this new optimal quantum logic gate library using CNOT and these non-permutative quantum gates. Our method introduces new means to find permutative quantum gates with lower quantum cost.

Alice Flarend, Bob Hilborn

Abstract Quantum gates, equivalent to logic gates, modify the state vectors. Linear algebra calls these gates linear transformations. In quantum language, they are “operators.” These gates include the NOT gate, the Pauli gates, and the Hadamard gate. The operations of the gates are represented both as abstract symbols and by matrices multiplying state vectors (expressed as column vectors). Quantum computers use a series of gates called a quantum circuit. The chapter explains how to read a quantum circuit diagram and translate it into linear algebra mathematics. The mathematical requirements on the matrices allowed to be used is delineated. Gates are reversible by applying the same gate twice, but measurements are not reversible.

Ray LaPierre

Ropa Roy, Asoke Nath

A quantum gate or quantum logic gate is an elementary quantum circuit working on a small number of qubits. It means that quantum gates can grasp two primary feature of quantum mechanics that are entirely out of reach for classical gates : superposition and entanglement. In simpler words quantum gates are reversible. In classical computing sets of logic gates are connected to construct digital circuits. Similarly, quantum logic gates operates on input states that are generally in superposition states to compute the output. In this paper the authors will discuss in detail what is single and multiple qubit gates and scope and challenges in quantum gates.