Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos

by Seth Lloyd

Now look at interactions between qubits. Consider a two-qubit transformation that is a quantum analog of the controlled-NOT logic operation described earlier. Recall that the controlled-NOT operation flips one bit if and only if the other bit is 1. That is, the controlled-NOT takes 00 to 00, 01 to 01, 10 to 11, and 11 to 10. The controlled-NOT operation is one-to-one and can be reversed simply by applying it twice. The quantum controlled-NOT takes the quantum states |00> to |00>, |01> to |01>, |10> to |11>, and |11> to |10>. Here, the state |00> corresponds to the “joint wave” of the two quantum bits taken together, in which the first qubit is in the state |0> and the second qubit is also in the state |0>.