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Can a quantum gate implement a reversible logic function?
For instance, the reversible Toffoli gate gate can implement all classical logic functions. The Toffoli gate has a quantum version too. Basically, all reversible classical logic operations can be directly mapped to quantum gate operations, which are unitary and reversible.
Is there a reversible version of the XOR gate?
Interestingly, the reversible quantum version of the XOR gate is the CNOT gate. However, there are exceptions like the classical NOT gate. For the NOT gate, if you’re given that the output state 1, then you can unambiguously say the initial state of A was 0.
How are quantum gates described as unitary matrices?
Quantum gates are unitary operators, and are described as unitary matrices relative to some basis. Usually we use the computational basis, which unless we compare it with something, just means that for a d -level quantum system (such as a qubit, a quantum register, or qutrits and qudits:22–23) we have labeled the orthogonal basis vectors
Is the Toffoli gate a direct quantum equivalent?
The Toffoli gate has a direct quantum equivalent, showing that quantum circuits can perform all operations performed by classical circuits. Quantum gates are unitary operators, and are described as unitary matrices relative to some basis.
How are quantum logic gates represented in matrices?
We represent quantum logic gates using matrices. All the gates are reversible means, if we multiply the same matrix twice we should get the identity matrix. Reversibility is an important concept in quantum computing due to the following reasons. Qubits are limited, short-lived and expensive resources.
How are quantum gates different from classical gates?
Classical gates are irreversible whereas, quantum gates are reversible. We have gates in quantum computing as well, perhaps logic is the basis for computing. The quantum gates we will be learning about today are — the Pauli operators (X, Y, Z), the Hadamard gate, and Controlled-NOT.
How are two qubits represented in a quantum circuit?
The controlled-Not gate or the CNOT gate is a 2 qubit quantum gate, wherein the second qubit gets flipped if the first qubit is SET, i.e, the first qubit is 1. Otherwise, it does nothing. It is represented in the quantum circuit as follows –