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Journal of Optics B Quantum and Semiclassical Optics

Triplet superconductors as the basis for solid-state quantum computing

ARMEN M. GULIAN, K. S. Wood

Published Oct 16, 2003• 1 citation
Publisher

Abstract

We propose triplet superconductors, such as ruthenates, as prospective materials for qubit construction. The vectorial nature of the order parameter in triplet superconductors makes it conceptually easy to estimate the performance of the qubits. The Cooper condensate of pairs in triplet superconductors has all the attributes of Bose–Einstein condensates and should facilitate long decoherence times for these qubits, relative to other vectorial schemes for qubits, such as small ferromagnets. There are other benefits, which the superconducting state provides for requirements such as entanglement between qubits via the proximity effect, etc. We consider these benefits in detail, although our consideration is only preliminary and further experimental and theoretical research will undoubtedly introduce correctives.

DOI
10.1088/1464-4266/5/6/012

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We propose triplet superconductors, such as ruthenates, as prospective materials for qubit construction. The vectorial nature of the order parameter in triplet superconductors makes it conceptually easy to estimate the performance of the qubits. The Cooper condensate of pairs in triplet superconductors has all the attributes of Bose–Einstein condensates and should facilitate long decoherence times for these qubits, relative to other vectorial schemes for qubits, such as small ferromagnets. There are other benefits, which the superconducting state provides for requirements such as entanglement between qubits via the proximity effect, etc. We consider these benefits in detail, although our consideration is only preliminary and further experimental and theoretical research will undoubtedly introduce correctives.
We discuss possibilities of utilizing superconductors with Cooper condensates in triplet pairing states (where the spin of condensate pairs is S=1) for practical realization of quantum computers. Superconductors with triplet pairing condensates have features that are unique and cannot be found in the usual (singlet pairing, S=0) superconductors. The symmetry of the order parameter in some triplet superconductors (e.g., ruthenates) corresponds to doubly-degenerate chiral states. These states can serve as qubit base states for quantum computing.
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Hybrid devices integrating quantum dots with Josephson junctions are gaining interest because they combine spin-based quantum computing with circuit quantum electrodynamics (circuit QED) methods. In particular, Andreev spin qubits have shown significant experimental progress including strong two-qubit coupling, and are predicted to exhibit all-to-all connectivity. Here we propose superconducting singlet-triplet (SST) qubits that rely on parallel-aligned double quantum dots in Josephson junctions. While Andreev spin qubits require spin-orbit interaction to unlock the spin degree-of-freedom, SST qubits do not require spin-orbit interaction, making the advantages of hybrid devices available to a wider range of materials. Similar to Andreev spin qubits, the qubit states couple to the superconducting phase across the junction, which allows for control and readout using circuit QED, and supports all-to-all connectivity. Only NNN flux lines are required to perform any single- and two-qubit gate among NNN qubits, and thus the overhead of control lines is small. Finally, linear protection from charge or flux noise makes these qubits interesting candidates for a future quantum processor.
Hybrid systems comprising superconducting and semiconducting materials are promising architectures for quantum computing. Superconductors induce long-range interactions between the spin degrees of freedom of semiconducting quantum dots. These interactions are widely anisotropic when the semiconductor material has strong spin-orbit interactions. We show that this anisotropy is tunable and enables fast and high-fidelity two-qubit gates between singlet-triplet (ST) spin qubits. Our design is immune to leakage of the quantum information into noncomputational states and removes always-on interactions between the qubits, thus resolving key open challenges for these architectures. Our ST qubits do not require additional technologically demanding components nor fine-tuning of parameters. They operate at low magnetic fields of a few millitesla and are fully compatible with superconductors. By suppressing systematic errors in realistic devices, we estimate infidelities below ${10}^{\ensuremath{-}3}$, which could pave the way toward large-scale hybrid superconducting-semiconducting quantum processors.
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We review the physical basis of and recent developments in ferromagnetic Josephson junctions with a focus on the π state, which is useful for applications to superconducting devices. Among various novel phenomena that emerge from the interaction between the superconductor and ferromagnet, the π state (junction) works as a phase shifter in superconducting devices, and several proposals and demonstrations of applications to quantum computing elements (qubits), classical superconducting logic circuits, and cryogenic memory have been presented. As a new research trend in superconducting spintronics, we also introduce recent interesting works on the long-range Josephson effect caused by spin-triplet Cooper pairs.