Performing joint measurements and transformations on several qubits by operating on a single “control” qubit
Dominik Janzing, Thomas Decker, Thomas Beth · Physical Review A · 2003
An n-qubit quantum register can in principle be completely controlled by operating on a single qubit that interacts with the register via an appropriate fixed interaction. In this paper, we consider a hypothetical system consisting of n spin-1/2 nuclei that interact magnetically with an electron spin (control and probe particle). We describe control algorithms that implement premeasurements on nontrivial joint observables. We then devote a section to the implementation of unitary gates for the register by acting only on the control spin. Although this model of universal quantum computation is not efficient for large n, it can become efficient if we allow n possible positions for the control particle. This ``toy'' model of premeasurements shows how specific interactions between the register and the probe particle would support specific types of joint measurements. This means that some joint observables can be measured by performing a simple sequence of operations on the probe particle. In our model, some measurements of joint observables are simpler to perform than for one-qubit observables.