In recent years qubit designs such as transmons have approached fidelities of up to 0.999. However, even these devices are still insufficient for realizing quantum error correction requiring better than 0.9999 fidelity. Topologically protected superconducting qubits are arguably the most prospective for building a realistic quantum computer as they are intrinsically protected from noise and leakage errors that occur in transmons. We propose a topologically protected qubit design based on a $\ensuremath{\pi}$-periodic Josephson element and a universal set of gates: A protected Clifford group and highly robust (with infidelity $\ensuremath{\lesssim}{10}^{\ensuremath{-}4}$) nondiscrete holonomic phase gate. The qubit is controlled via charge $Q$ and flux $\mathrm{\ensuremath{\Phi}}$ biases. The holonomic gate is realized by quickly, but adiabatically, going along a particular closed path in the two-dimensional ${\mathrm{\ensuremath{\Phi}},Q}$ space---a path where computational states are always degenerate but Berry curvature is localized inside the path. This gate is robust against currently achievable noise levels. This qubit architecture allows building a realistic scalable superconducting quantum computer with leakage and noise-induced errors below ${10}^{\ensuremath{-}4}$, which allows performing realistic error correction codes with currently available fabrication techniques.In recent years qubit designs such as transmons have approached fidelities of up to 0.999. However, even these devices are still insufficient for realizing quantum error correction requiring better than 0.9999 fidelity. Topologically protected superconducting qubits are arguably the most prospective for building a realistic quantum computer as they are intrinsically protected from noise and leakage errors that occur in transmons. We propose a topologically protected qubit design based on a $\ensuremath{\pi}$-periodic Josephson element and a universal set of gates: A protected Clifford group and highly robust (with infidelity $\ensuremath{\lesssim}{10}^{\ensuremath{-}4}$) nondiscrete holonomic phase gate. The qubit is controlled via charge $Q$ and flux $\mathrm{\ensuremath{\Phi}}$ biases. The holonomic gate is realized by quickly, but adiabatically, going along a particular closed path in the two-dimensional ${\mathrm{\ensuremath{\Phi}},Q}$ space---a path where computational states are always degenerate but Berry curvature is localized inside the path. This gate is robust against currently achievable noise levels. This qubit architecture allows building a realistic scalable superconducting quantum computer with leakage and noise-induced errors below ${10}^{\ensuremath{-}4}$, which allows performing realistic error correction codes with currently available fabrication techniques.

arXiv:1907.04379Physical review. B./Physical review. BOct 6, 202114 citations

Majorana Superconducting Qubit

Constantin Schrade, Liang Fu

We propose a platform for universal quantum computation that uses conventional s-wave superconducting leads to address a topological qubit stored in spatially separated Majorana bound states in a multiterminal topological superconductor island. Both the manipulation and readout of this "Majorana superconducting qubit" are realized by tunnel couplings between Majorana bound states and the superconducting leads. The ability of turning on and off tunnel couplings on demand by local gates enables individual qubit addressability while avoiding cross-talk errors. By combining the scalability of superconducting qubit and the robustness of topological qubits, the Majorana superconducting qubit may provide a promising and realistic route towards quantum computation.We propose a platform for universal quantum computation that uses conventional s-wave superconducting leads to address a topological qubit stored in spatially separated Majorana bound states in a multiterminal topological superconductor island. Both the manipulation and readout of this "Majorana superconducting qubit" are realized by tunnel couplings between Majorana bound states and the superconducting leads. The ability of turning on and off tunnel couplings on demand by local gates enables individual qubit addressability while avoiding cross-talk errors. By combining the scalability of superconducting qubit and the robustness of topological qubits, the Majorana superconducting qubit may provide a promising and realistic route towards quantum computation.

arXiv:1803.01002Physical Review LettersDec 27, 201850 citations

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and flux $\mathrm{\ensuremath{\Phi}}$ biases. The holonomic gate is realized by quickly, but adiabatically, going along a particular closed path in the two-dimensional ${\mathrm{\ensuremath{\Phi}},Q}$ space---a path where computational states are always degenerate but Berry curvature is localized inside the path. This gate is robust against currently achievable noise levels. This qubit architecture allows building a realistic scalable superconducting quantum computer with leakage and noise-induced errors below ${10}^{\ensuremath{-}4}$, which allows performing realistic error correction codes with currently available fabrication techniques.