Bob. The single operation of this "remote" CNOT computation, thus, consumes two EPR-Bell states (or ebits), and four classical bits (or cbits). Would it be possible to avoid such a complicated procedure, and instead conceive of quantum gates being capable of acting directly on remote qubits? The answer is yes, and the corresponding technique is called quantum gate teleportation. Within the scope of this chapter, we may not venture into the complex details of quantum gate teleportation, but I provide a generic example to show that it is possible, and also to show how this 18.6 Distributed quantum computing Alice Figure 18.12 (a) 4-qubit circuit used for quantum teleportation of CNOT gate; (b) equivalent distributed CNOT gate. can work. Here, I shall describe the quantum teleportation of a CNOT gate, 3 which we have learnt from Chapter 16, is one of the universal building blocks for quantum circuits. The principle of CNOT-gate teleportation is illustrated in Fig. 18.12. Locally, Alice and Bob have the control of two qubits each, which are labelled 1 and 2 for Alice (the first being called |a)), and 3 and 4 for Bob (the last being called /x)). As the figure indicates, the qubits 2 and 3 are entangled through the EPR-Bell state 1Boo), thus, qubits 3 and 4 represent a shared ebit. Both Alice and Bob have local CNOT gates, called C12 and C34, respectively. Furthermore, Alice first measures qubit 3 in the base {|0), |1)}, yielding a cbit m (namely, m=0 if the qubit is |0) and m' = 1 if the qubit is |1)); Bob then measures qubit 3 in the different base {|+), |-) yielding a cbit m' (namely, m' = 0 if the qubit is |+) and m' = 1 if the qubit is |-)). Alice and Bob then use a classical channel to communicate to each other their respective cbit measurement. To ensure the proper sequence order, Bob won't proceed with his own measurement until he has received cbit m from Alice. The cbit data m, m' are then used locally by Alice and Bob to control their Z or X gates placed on the 1 or 4 qubit paths, respectively, as indicated i