One-Qubit Manipulations

Lajos Diósi

Ming Zhang

For a multiple qubit system, the dimension of the system is exponentially large in the number of qubits, one may ask whether the cost of manipulating multiple qubit systems is exponentially large in the number of qubits or not? It has been found that only n(n + 3)/2 control Hamilton will guarantee open-loop controllability of n-qubit systems when only single qubit operators and two-qubit-interactive operators are permitted. Further more, the minimum cost of deterministically generating multiple-qubit GHZ entangled state will be at most linearly large in the number of qubits. To some extent, one may predict that the "cost" of manipulating multiple-qubit systems is tolerable.

Michel Le Bellac

Mathias S. Scheurer, Alexander Shnirman

We investigate the nonadiabatic processes occurring during the manipulations of Majorana qubits in one-dimensional semiconducting wires with proximity-induced superconductivity. Majorana qubits are usually protected by the excitation gap. Yet, manipulations performed at a finite pace can introduce both decoherence and renormalization effects. Although exponentially small for slow manipulations, these effects are important as they may constitute the ultimate decoherence mechanism. Moreover, as adiabatic topological manipulations fail to produce a universal set of quantum gates, nonadiabatic manipulations might be necessary to perform quantum computation.

Shao Xiao-Qiang, Chen Li, Zhang Shou +1 more

We present a scheme for implementing a three-qubit phase gate via manipulating rf superconducting quantum interference device (SQUID) qubits in the decoherence-free subspace with respect to cavity decay. Through appropriate changes of the coupling constants between rf SQUIDs and cavity, the scheme can be realized only in one step. A high fidelity is obtained even in the presence of decoherence.