Bayram Ashyrmyradovich Jumayev
ABSTRACT
Quantum gates are building blocks of quantum circuits and they are used to carry out corresponding operations on quantum bits or qubits. The distinguishing feature of multi-qubit quantum control-gates is that they act on target qubits according to the state of control qubit(s). In this sense, there exist 2- and 3-qubit quantum gates such as Controlled-NOT, Toffoli (Controlled-Controlled-NOT), Controlled-Hadamard, Controlled-Swap and so on. In order to make complex quantum circuits easier and control more qubits, it is necessary to work out mathematical models of new control gates acting on more than three qubits depending on the state of control qubit. Therefore, in this work, mathematical model of multi-qubit universal control gate is worked out and some control gates are formulated in accordance with the proposed model, moreover the tests of these novel control gates are carried out using online open resource or virtual laboratory that is called “Quirk”. Existing 2- and 3-qubit control gates can also be derived using this model. Matrix representations of Controlled-NOT-NOT, Controlled-Hadamard-Hadamard, Controlled-NOT-NOT-Hadamard, Controlled-Hadamard-Swap and Controlled-Hadamard-SWAP-NOT gates are derived using the proposed mathematical model. These quantum gates are unitary and reversible gates. Using the proposed model and novel quantum gates will help to reduce complexity of quantum circuits and develop new cryptographic algorithms.
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