Topology-Enhanced Superconducting Qubit Networks for In-Sensor Quantum Information Processing

Abstract

We investigate the influence of topology on the magnetic response of inductively coupled superconducting flux-qubit networks. Using exact diagonalization methods and linear response theory, we compare the magnetic response of linear and cross-shaped array geometries, used as paradigmatic examples. We find that the peculiar coupling matrix in cross-shaped arrays yields a significant enhancement of the magnetic flux response compared to linear arrays, this network-topology effect arising from cooperative coupling among the central and the peripheral qubits. These results establish quantitative design criteria for function-oriented superconducting quantum circuits, with direct implications for advancing performance in both quantum sensing and quantum information processing applications. Concerning the latter, by exploiting the non-linear and high-dimensional dynamics of such arrays, we demonstrate their suitability for quantum reservoir computing technology. This dual functionality suggests a novel platform in which the same device serves both as a quantum-limited electromagnetic sensor and as a reservoir capable of signal processing, enabling integrated quantum sensing and processing architectures.

Figures (11)

• Figure 1: (a) Schematic of a flux qubit realized by means of the four Josephson junctions technology Qiu2016. The red crosses denote the weak links between superconducting regions (blue lines). (b) Circulating currents in the qubit loop: counterclockwise and clockwise currents correspond to the current states $|\uparrow\rangle$ and $|\downarrow\rangle$, respectively. (c) Energy spectrum of the effective Hamiltonian $H_{\text{eff}}$ as a function of the normalized magnetic flux $f$. (d) Expectation value of the current operator on the energy eigenstates, normalized to the maximum loop current $I_s$ and plotted as a function of $f$.
• Figure 2: Schematic of a five-qubit array with inductive coupling: (a) linear configuration and (b) cross-shaped configuration. (c)-(e) Different coupling conditions with a transmission line, biased by the current $I(t)$.
• Figure 3: (a) Energy eigenvalues $E_n$ of a linear array of five identical qubits, labeled by the index $n$, and sorted in ascending order. Energy eigenvalues are expressed in units of $\hbar \omega_0=I_s \Phi_0$. (b) Loop currents of the linear array normalized to the maximum current $I_s$ as a function of the qubit index $i$ for the ground state and the first excited state. (c) Current-current correlations, in units of $I_S^2$, between the first qubit and the $i$-th qubit.
• Figure 4: (a) Energy eigenvalues $E_n$ of a cross-shaped array of five identical qubits, labeled by the index $n$, and sorted in ascending order. Energy eigenvalues are expressed in units of $\hbar \omega_0=I_s \Phi_0$. (b) Loop currents of the cross-shaped array normalized to the maximum current $I_s$ as a function of the qubit index $i$ for the ground state and the first excited state.
• Figure 5: (a) Qubit array embedded in a dc SQUID, used as a flux sensor. (b) Magnetic flux $\Phi$ generated by the qubit network as a function of the normalized external flux $f$ threading each qubit. A comparison is performed among three different qubit configurations: isolated, linear- and cross-shaped array.