Periodic Reporting for period 1 - QuKiT (Quantum bits with Kitaev Transmons)
Okres sprawozdawczy: 2023-07-01 do 2024-09-30
Quantum computing will only reach its true potential if the quantum community develops hardware technology that is good enough to deal with errors that are intrinsic to any quantum technology. The strategy pursued by several leaders in the field is to incrementally increase the quality of the individual qubits, while at the same time trying to scale up to the millions of physical qubits needed for useful quantum applications. The requirement for such a large number of qubits makes practical quantum computing a daunting task. However, these millions of qubits are absolutely essential for the overhead required to correct quantum errors. To move beyond the current state of the art of mainstream approaches, it is therefore imperative to design a qubit that is protected from local sources of noise and, at the same time, is easy to control
Our approach is inspired by the field of topological qubits based on Majorana bound states (MBSs). The idea behind a topological qubit is to design a system where quantum information can be encoded in a manner whereby local noise sources cannot cause errors. The experimental realization of MBSs, based on previous proposals has however remained elusive due to large local variations in the microscopic properties of realistic materials. On the other hand, quantum dots (QDs) in semiconductors, when coupled via superconductors, can emulate the physical model of a topologically protected system [1,2], resulting in the formation of MBSs. This model is known as the Kitaev chain. Since such a realization of MBSs includes superconducting elements, it can readily be embedded into superconducting circuits, allowing one to perform circuit quantum electrodynamics (cQED) experiments. The cQED framework describes how qubits can be addressed and controlled using superconducting resonators and waveguides.
We propose to embed the Kitaev chain into a transmon qubit, the transmon being the most widespread qubit used worldwide. The key idea of QuKiT is to encode quantum information in the (nearly) degenerate states of a Kitaev chain, thus protecting it (by design) from the dominant error sources that currently limit transmon qubits. At the same time, integration into a transmon architecture will ensure the immediate availability of mature control techniques developed for superconducting qubits, allowing for high fidelity gate operations. Thus, our novel qubit, the Kitaev transmon (Kitmon), should enable significantly lower error rates.
[1] M. Leijnse, and K. Flensberg, Phys. Rev. B 86, 134528 (2012)
[2] Sau, Jay D., and S. Das Sarma, Nat. Comm. 3, 1 (2012)
Our approach is inspired by the field of topological qubits based on Majorana bound states (MBSs). The idea behind a topological qubit is to design a system where quantum information can be encoded in a manner whereby local noise sources cannot cause errors. The experimental realization of MBSs, based on previous proposals has however remained elusive due to large local variations in the microscopic properties of realistic materials. On the other hand, quantum dots (QDs) in semiconductors, when coupled via superconductors, can emulate the physical model of a topologically protected system [1,2], resulting in the formation of MBSs. This model is known as the Kitaev chain. Since such a realization of MBSs includes superconducting elements, it can readily be embedded into superconducting circuits, allowing one to perform circuit quantum electrodynamics (cQED) experiments. The cQED framework describes how qubits can be addressed and controlled using superconducting resonators and waveguides.
We propose to embed the Kitaev chain into a transmon qubit, the transmon being the most widespread qubit used worldwide. The key idea of QuKiT is to encode quantum information in the (nearly) degenerate states of a Kitaev chain, thus protecting it (by design) from the dominant error sources that currently limit transmon qubits. At the same time, integration into a transmon architecture will ensure the immediate availability of mature control techniques developed for superconducting qubits, allowing for high fidelity gate operations. Thus, our novel qubit, the Kitaev transmon (Kitmon), should enable significantly lower error rates.
[1] M. Leijnse, and K. Flensberg, Phys. Rev. B 86, 134528 (2012)
[2] Sau, Jay D., and S. Das Sarma, Nat. Comm. 3, 1 (2012)
The interdisciplinary nature of this project combines aspects of materials growth, mesoscopic transport, high frequency measurement techniques, theoretical modelling and full stack control of qubits. We describe below our progress thus far.
Materials development: to allow for proximity-induced superconductivity in InAs-Al two-dimensional electron gases (2DEGs) the quantum well (QW) must be located close enough to the surface to allow for wavefunction overlap between the superconductor and semiconductor. At the same time, electron mobility should be high enough to allow ballistic electronic transport. To find the optimal semiconductor heterostructure stack we have studied the effect of the quantum well depth on the mobility. Furthermore, we have developed techniques to grow Al in a controllable manner, resulting in clean interfaces and allowing for reliable fabrication of hybrid mesoscopic devices (Image 2).
Induced superconductivity in Ge: current studies reporting proximity-induced superconductivity in Germanium have used QWs which are buried at least about 20nm below the surface. Similar to works with III-V 2DEGs, we use shallow QWs (5nm below the surface). By depositing Al on top, we have demonstrated proximity-induced superconductivity with a gap exceeding 150µeV [1]. Furthermore we have optimized our fabrication protocols to create stable QDs (with induced superconductivity) in these shallow QWs (Image 3). These results are important first step for creating Kitaev chains in Ge.
Kitaev chains: we successfully created a 2-site chain in III-V 2DEGs (Image 3) by controlling the inter-dot couplings [2], and showd that Majoranas in these systems are protected from local perturbations. Building on this, we have successfully created a 3-site chain [3]. By probing all 3 sites simultaneously we were able to show that Majoranas in the chain are localized on the edges while the bulk (middle QD) is gapped. We also demonstrated that the extent to which the Majoranas are protected from local perturbations is inherently connected to size of this gap, in excellent agreement with theoretical simulations that we have performed. We expanded our theoretical understanding of these systems by studying different experimentally relevant conditions such as strong inter-dot coupling [4], strong coupling to normal leads [5], and the effects of having small floating superconductors [6]. These results provide insights into optimal device geometries for our Kitaev transmon.
Towards the Kitmon: from the theoretical side, we have for the first time studied the proposed Kitmon qubit [7]. Importantly we demonstrate that by performing cQED spectroscopy on the Kitmon, one can observe distinct Majorana features in agreement with precise analytical predictions in terms of QD parameters only. On the experimental front, as a first step we have integrated high frequency coplanar waveguides for cQED experiments (Image 4), both in Ge [1] and InAs quantum wells [8]. These studies allowed for fast measurements of the current-phase relation of hybrid Josephson junctions. One of the observation in these studies was that superconducting resonators on these substrates have significant dielectric losses. As a step forward, we have also developed flip-chip techniques for the integration of Kitaev chain devices with high quality resonators.
[1] M. Valentini et al., Nat. Comm. 15, 169 (2024)
[2] S. L. D. ten Haaf et al., Nature 630, 329 (2024).
[3] S. L. D. ten Haaf et al., Nature in press (2025) arXiv:2410.00658
[4] M. Alvarado et al. arXiv:2407.07050 (2024)
[5] J. Cayao and R. Aguado arXiv:2406.18974 (2024)
[6] R. Seoane Souto et al., arXiv:2411.07068 (2024)
[7] D. M. Pino, R. Seoane Souto, and R. Aguado, Phys. Rev. B 109, 075101 (2024)
[8] Z. Scherübl et al., arXiv:2406.20059 (2024)
Materials development: to allow for proximity-induced superconductivity in InAs-Al two-dimensional electron gases (2DEGs) the quantum well (QW) must be located close enough to the surface to allow for wavefunction overlap between the superconductor and semiconductor. At the same time, electron mobility should be high enough to allow ballistic electronic transport. To find the optimal semiconductor heterostructure stack we have studied the effect of the quantum well depth on the mobility. Furthermore, we have developed techniques to grow Al in a controllable manner, resulting in clean interfaces and allowing for reliable fabrication of hybrid mesoscopic devices (Image 2).
Induced superconductivity in Ge: current studies reporting proximity-induced superconductivity in Germanium have used QWs which are buried at least about 20nm below the surface. Similar to works with III-V 2DEGs, we use shallow QWs (5nm below the surface). By depositing Al on top, we have demonstrated proximity-induced superconductivity with a gap exceeding 150µeV [1]. Furthermore we have optimized our fabrication protocols to create stable QDs (with induced superconductivity) in these shallow QWs (Image 3). These results are important first step for creating Kitaev chains in Ge.
Kitaev chains: we successfully created a 2-site chain in III-V 2DEGs (Image 3) by controlling the inter-dot couplings [2], and showd that Majoranas in these systems are protected from local perturbations. Building on this, we have successfully created a 3-site chain [3]. By probing all 3 sites simultaneously we were able to show that Majoranas in the chain are localized on the edges while the bulk (middle QD) is gapped. We also demonstrated that the extent to which the Majoranas are protected from local perturbations is inherently connected to size of this gap, in excellent agreement with theoretical simulations that we have performed. We expanded our theoretical understanding of these systems by studying different experimentally relevant conditions such as strong inter-dot coupling [4], strong coupling to normal leads [5], and the effects of having small floating superconductors [6]. These results provide insights into optimal device geometries for our Kitaev transmon.
Towards the Kitmon: from the theoretical side, we have for the first time studied the proposed Kitmon qubit [7]. Importantly we demonstrate that by performing cQED spectroscopy on the Kitmon, one can observe distinct Majorana features in agreement with precise analytical predictions in terms of QD parameters only. On the experimental front, as a first step we have integrated high frequency coplanar waveguides for cQED experiments (Image 4), both in Ge [1] and InAs quantum wells [8]. These studies allowed for fast measurements of the current-phase relation of hybrid Josephson junctions. One of the observation in these studies was that superconducting resonators on these substrates have significant dielectric losses. As a step forward, we have also developed flip-chip techniques for the integration of Kitaev chain devices with high quality resonators.
[1] M. Valentini et al., Nat. Comm. 15, 169 (2024)
[2] S. L. D. ten Haaf et al., Nature 630, 329 (2024).
[3] S. L. D. ten Haaf et al., Nature in press (2025) arXiv:2410.00658
[4] M. Alvarado et al. arXiv:2407.07050 (2024)
[5] J. Cayao and R. Aguado arXiv:2406.18974 (2024)
[6] R. Seoane Souto et al., arXiv:2411.07068 (2024)
[7] D. M. Pino, R. Seoane Souto, and R. Aguado, Phys. Rev. B 109, 075101 (2024)
[8] Z. Scherübl et al., arXiv:2406.20059 (2024)
We have realized the first artificial Kitaev chains in III-V 2DEGs, and shown how increasing the number of sites in the Kitaev chain results in stronger protection of Majoranas. We have developed new techniques to engineer superconductor-semiconductor hybrids in Germanium and shown the feasibility of performing hybrid cQED experiments in this platform. On the theoretical front, we performed the first studies of the Kitaev transmon, which serves as a foundation for more detailed work on expected coherence time in these qubits.