Symmetry-protected states of interacting qubits in superconducting quantum circuits

TL;DR

This paper addresses the fragility of quantum information by proposing a symmetry-protected decoherence-free subspace (DFS) built from a minimal four-spin system with nearest and next-nearest flip-flop couplings. By diagonalizing the finite spin-chain Hamiltonian, the authors show first-order cancellation of relaxation and dephasing within the ground–first excited subspace, robust to disorder up to ~15% and featuring a MajumdarGhosh point that yields degenerate protected states. They map this spin model to a superconducting circuit, design a four-qubit layout that realizes the required interactions, and analyze coherence properties including gap engineering to suppress quasiparticle tunneling, achieving millisecond-scale $T_1$ and $T_\phi$ under realistic noise. The study provides a practical, resource-efficient path toward intrinsically noise-tolerant quantum hardware, with potential applicability beyond superconducting platforms and guidance for DFS gate implementations.

Abstract

Superconducting circuits are one of the leading candidates for storing and manipulating quantum information. Among them, qubits embedded with intrinsic noise protection have seen rapid advancements in recent years. This noise protection is typically realized by isolating the computational states from local sources of noise. Here, we propose an interacting spin model that requires at least four spins with nearest-neighbor and next-nearest-neighbor couplings, where the two lowest eigenstates form a symmetry-protected qubit manifold, which is robust to both relaxation and dephasing from local perturbations. We map the spin model to a superconducting circuit and show that such a circuit can reach coherence times exceeding several milliseconds in the presence of realistic environmental noise. Our work opens a pathway to realizing qubits with long coherence times in a new generation of quantum devices.

Figures (13)

• Figure 1: (a) Interacting many-body spin model with the short-range (t, red arrow) and long-range ($\lambda$, green arrow) flip-flop couplings (b) The relaxation amplitudes $\text{R} = \sqrt{\sum_{w=x,y,z} |\langle 1|\sigma_m^w|0\rangle|^2}$ versus long-range flip-flop couplings $\lambda$ for different numbers of spins. (c) The dephasing amplitudes $\text{D} = \sqrt{\sum_{w=x,y,z} |\langle 1|\sigma_m^w|1\rangle-\langle 0|\sigma_m^w|0\rangle|^2}$ as a function of $\lambda$. In green rectangles in (b) and (c) the inversion and translation symmetries are satisfied, and the total excitation number is conserved. (d) A diagram of the finite-size spin model with a minimum of four spins. (e) The relative amplitude of the non-Bell component $\gamma$ in $|G^+\rangle$ from Eq. \ref{['Eq:state1']} as a function of $\lambda/t$.
• Figure 2: The combined decoherence sensitivity $\sqrt{R^2+D^2}$ as a function of long-range flip-flop coupling $\lambda$ and (a) all-to-all $\sigma^z\sigma^z$ coupling $\zeta$, (b) transverse field $\sigma^x$ amplitudes $\eta$, (c) longitudinal field $\sigma^z$ amplitudes $\omega$, (d) short-range counter-rotative terms $\mu$, (e) long-range counter-rotative terms $\nu$, and (f) amplitudes of disorder among the couplings for $M = 4$.
• Figure 3: (a) The circuit diagram of the superconducting qubit design with four radial Josephson junctions (blue) connected by four azimuthal junctions (green) and two diametric junctions (red). Each inner loop and outer loop is threaded by a magnetic flux with amplitudes $\Phi_{i}$, and the gate charges at each island are tuned at Q$_{g,i}$. The center is grounded. (b) The distribution of the qubit transition frequency $\omega_{01}$, broadened by the disorder introduced into circuit parameters. (c) The energy spectrum of the qubit device as a function of the offset of gate charges and external magnetic flux.
• Figure 4: (a) A schematic diagram of the Josephson junction structure formed by two layers of aluminum films with different thicknesses. The pink layer is thinner and has a higher superconducting gap. The quasiparticle can tunnel from both sides. (b) The direction of the gap engineering used for the Josephson junctions in our design. (c) The parity switching rates versus the gap difference $\delta \Delta$, while fixing the average superconducting gap of two layers at $\bar{\Delta}$ = 50 GHz, with the index i indicating the initial state of the qubit at the operation point, and the index j represents the final state after the quasiparticle tunneling. (d) The total rate $\Gamma^{\text{qp}}_{\text{tot}} = 0.5(\Gamma^{\text{qp}}_{0\rightarrow0}+\Gamma^{\text{qp}}_{0\rightarrow1}+\Gamma^{\text{qp}}_{1\rightarrow0}+\Gamma^{\text{qp}}_{1\rightarrow1})$ versus the gap difference $\delta \Delta$.
• Figure 5: (a-c) Qubit relaxation and excitation rates contributed by dielectric losses from Josephson junctions $(\Gamma^{\text{dl-jj}}_1)$, geometric capacitance $(\Gamma^{\text{dl-geom}}_1)$ and quasiparticle tunnelings $(\Gamma^{\text{qp}})$ as a function of the total offsets of gate charges and magnetic flux biases. Several gap differences are used: (a) $\delta\Delta = 0$; (b) $\delta\Delta = 5$ GHz; (c) $\delta\Delta = 10$ GHz. (d) Pure dephasing rates contributed by charge noise ($\Gamma_{\upphi}^{\text{c}}$), flux noise ($\Gamma_{\upphi}^{\text{f}}$) and critical current noise ($\Gamma_{\upphi}^{\text{cc}}$) on total offsets in gate charges and magnetic flux biases. The lower boundary is 1 Hz, and data smaller than 1 Hz is not shown in this figure.