Multi-qubit gates

4 Use of strongly modulated RF pulses for quantum gate implementation in NMRQIP 

RF field with amplitude co and phase j . The evolution of a spin system under the Hamiltonian (4.2.20) during a time interval t can be described by the unitary operator. 

Notice that the externally controllable parameters in this unitary operator are Aco, coi, and (/ . Now, let us consider another unitary operator composed by a product of M operators 

Quantum operation Gate fidelity F) Unitaiy propagator gate fidelity Fu) Process duration (Af,.) (ps) 

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Benjamin, S.C. (2004) Multi-qubit gates in arrays coupled by always-on interactions. New J. Phys., 6, 61, (1-17). 

Many algorithms start with an uniform superposition of states, produced by a multi-qubit Hadamard gate. Although such an operation can be formally written as a tensor product of one-qubit Hadamard gate, sometimes we have to regard it as a multi-qubit gate. This is the case, for instance, of quadrupole nuclei. 

Research on multi-qubit molecules starts with the synthesis and characterization of systems that seem to embody more than one qubit, for example, systems with weakly coupled electron spins. Indeed, many molecular structures include several weakly coupled magnetic ions [76-78]. On a smaller scale, the capability of implementing a Controlled-NOT quantum logic gate using molecular clusters... 

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