Scalable architecture for quantum information processing with superconducting flux qubits based on purely longitudinal interactions

We devise a quantum register based on superconducting flux qubits that circumvents the impediments posed by the presence of fixed interactions. We describe a coupling scheme wherein two physical qubits are coupled to a third which acts as a coupler via their longitudinal degree of freedom (i.e., ${\sigma }_z$). This approach provides a solution to several issues such as residual interactions between physical qubits, deteriorations of the rotating wave approximation (RWA), and correlated errors, thereby expanding the opportunities for capitalizing on the large coupling strengths achievable with these systems.

Figure 1

(a) Schematic representation of three gradiometric flux qubits all coupled via their longitudinal degree of freedom [ZZZ configuration]. This type of interaction can be achieved in a configuration wherein all qubits are inductively coupled by means of their $\alpha$-loop. (b) Associated energy level diagram of the bare qubits ($J=0$, center), with symmetric couplings ($\rho =0$, left), and arbitrary couplings (right).

Figure 2

(a) Idealized evolution of the coupler in the Bloch sphere representation depending on the state of the physical qubits during a coupler drive pulse ($2\pi$ pulse) at the frequency $({\mathrm{\Delta }}_c+2J)/h$. We assume that $\mathrm{\Omega }\ll (1-|\rho \left|\right)\left(2J\right)$. (b) Schematic representation of an array of qubits on a 2D square lattice wherein each physical qubit is coupled via its longitudinal degree of freedom to its nearest neighbors through the intermediary of the longitudinal degree of freedom of a coupler.

Figure 3

Top: overall infidelity $(1-\mathcal{F})$ of the ${\mathrm{C}}_{\phi }$ gate against the microwave pulse duration $\sigma$ for different values of (a) the average coupling strength $J$ (${\mathrm{\Delta }}_c/h=6\mathrm{GHz}, \rho =0$, and $J/h$ ranges from 1.5 to $2.5\mathrm{GHz}$ in steps of $0.1\mathrm{GHz}$) and (b) the asymmetry parameter $\rho$ (${\mathrm{\Delta }}_c/h=6\mathrm{GHz}, J/h=2.5\mathrm{GHz}$, and $\rho$ ranges from 0 to 0.8 in steps of 0.1). Bottom: infidelity $(1-{\mathcal{F}}_c)$ with which the coupler is brought back in its ground state against the average coupling strength $J$ for different values of (c) the pulse length $\sigma$ (${\mathrm{\Delta }}_c/h=6\mathrm{GHz}, \rho =0$, and $\sigma$ ranges from 0.4 to $2.2\mathrm{ns}$ in steps of $0.2\mathrm{ns}$) and (d) the asymmetry parameter $\rho$ (${\mathrm{\Delta }}_c/h=6\mathrm{GHz}$ and $\sigma =2\mathrm{ns}$). For comparison, we plot the fidelity associated with a Rabi flop for an isolated qubit with the same resonant frequency $({\mathrm{\Delta }}_c+2J)/h$, and a Gaussian pulse with the same length [dashed curves in (c)].