Question

A controlled swap gate CSWAP is a gate acting on three systems: a control qubit (two dimensional), and two target systems (which, for this problem, may be of arbitrary, but equal, dimension). If the control qubit is the left-most system, then the CSWAP acts as follows:

CSWAP∣0,a,b⟩=∣0,a,b⟩
CSWAP∣1,a,b⟩=∣1,b,a⟩

Answer 1

The Controlled SWAP (CSWAP) gate is used in quantum computers to manipulate qubits, which can be in superpositions of states. It acts on three qubits and swaps the target qubits based on the state of the control qubit, showcasing the potential power of quantum computing.

Step-by-step explanation:

The Controlled SWAP gate (CSWAP), often discussed in the context of quantum mechanics and quantum computing, is an operation used in quantum computers to manipulate qubits. Unlike classical bits in a digital computer that exist in a definite state of zero or one, qubits can be in a superposition of both states simultaneously, which is called a mixed state. The CSWAP gate specifically acts on three qubits, with one acting as the control qubit. If this control qubit is in the state |0>, the CSWAP gate leaves the target qubits unchanged. If the control qubit is in the state |1>, the CSWAP gate swaps the states of the two target qubits. This unique behavior of qubits and their manipulation through quantum gates like CSWAP is vital for the operation of quantum computers and contributes to the belief that quantum computers are the future of the computer industry.