Controlled Coupling of Qubits

Yu-xi Liu, Franco Nori

After a brief review on superconducting qubits, we overview our recent studies on controllable couplings in superconducting flux qubits via a variable frequency (ac) magnetic flux. In particular: (i) we describe how to use a variable frequency magnetic flux to control the coupling between two inductively coupled flux qubits, (ii) Based on this approach, using a variable frequency controlled coupling, we present a proposal on how to achieve scalable quantum computing circuits with flux qubits. We also explain why superconducting qubits can be coupled and addressed as trapped ions, as well as describe how to utilize dressed states to couple and decouple qubits and the data bus.

Fernando Gago-Encinas, M. Leibscher, Christiane P. Koch

Abstract The ability to implement any desired quantum logic gate on a quantum processing unit is equivalent to evolution-operator controllability of the qubits. Conversely, controllability analysis can be used to minimize the resources, i.e. the number of external controls and qubit–qubit couplings, required for universal quantum computing. Standard controllability analysis, consisting in the construction of the dynamical Lie algebra, is, however, impractical already for a comparatively small number of qubits. Here, we show how to leverage an alternative approach, based on a graph representation of the Hamiltonian, to determine controllability of arrays of coupled qubits. We provide a complete computational framework and exemplify it for arrays of five qubits, inspired by the ibmq_quito architecture. We find that the number of controls can be reduced from five to one for complex qubit–qubit couplings and to two for standard qubit–qubit couplings.

Yuriy Makhlin, Gerd Scöhn, Alexander Shnirman

Michel Le Bellac

Zhongyuan Zhou, Shih‐I Chu, Siyuan Han

We demonstrate that in a coupled two-qubit system any single-qubit gate can be decomposed into \ensuremath{\mid}0⟩-controlled and \ensuremath{\mid}1⟩-controlled two-qubit gates which can be implemented by manipulations analogous to that used for a controlled NOT (CNOT) gate. Based on this we present a unified approach to implement universal single-qubit and two-qubit gates in a coupled two-qubit system with fixed always-on coupling. This approach requires neither supplementary circuit or additional physical qubits to control the coupling nor extra hardware to adjust the energy level structure. The feasibility of this approach is demonstrated by numerical simulation of single-qubit gates and creation of two-qubit Bell states in rf-driven inductively coupled two superconducting quantum interference device flux qubits with realistic device parameters and constant always-on coupling.