Taking Transmons Out For a Quantum Spin
Coupling spin and superconducting qubits via a resonator opens up opportunities for hybrid quantum architectures.
In the race to create a viable quantum computer, each competing implementation has its own strengths and weaknesses. Instead of just one winner, however, future systems could take advantage of multiple qubit types, reaping the benefits of each. In 2019 in Nature Communications, Andreas Landig and colleagues from ETH Zürich and the University of Wisconsin-Madison successfully coupled a spin qubit to a distant superconducting qubit using a microwave resonator [1]. This is the first demonstration of its kind and is an important step towards large-scale hybrid quantum architectures using spins.
In 1998, Loss and DiVincenzo [2] (and in related fashion, Kane [3]) proposed a qubit made from the spins of single electrons trapped in tiny regions of semiconductors, called “quantum dots”. Unlike charge, which interacts with both electric and magnetic fields, spins are relatively resilient againt electric fields. These qubits can therefore remain in a given state, or remain “coherent”, for desirably long times. In 2014, researchers demonstrated coherence lasting 0.5 seconds [4], several orders of magnitude longer than superconducting qubits.
Unfortunately, spin qubits are far from perfect. The resilience to electric fields means they are difficult to manipulate for quantum computation. The qubit-qubit interactions between neighbouring dots are also intrinsically short-range. Accordingly, it is challenging to design large-scale systems that place many qubits in proximity while minimising crosstalk.
As researchers work to overcome these challenges, one might look to more mature technologies such as superconducting qubits. Already used in world-leading quantum computers like at Google and IBM Q, these involve nonlinear superconducting circuits and promise high speeds and accuracies. Indeed, researchers used superconducting qubits to achieve the first qubit-qubit interactions accurate enough to potentially be fault- tolerant [5]. However, with this interactivity comes an increased susceptibility to noise, reducing their coherence times. One way forward is to consider a hybrid system using superconducting qubits for computation and spin qubits for information storage. In 2011, researchers demonstrated this using nitrogen-vacancy centres [6], but it had yet to be achieved with spins in quantum dots.
In their paper, Landig and colleagues coupled a spin qubit to a distant superconducting qubit for the first time. To do this, they coupled both qubits to a shared superconducting microwave resonator: a transmission line that confines photons and carries information between the two qubits. This approach was very successful in past works using superconducting qubits, achieving distant coupling even in 2007 [7]. It was only in 2018, however, that Landig and colleagues succeeded in coupling a particular type of spin qubit, a “resonant exchange” (RX) qubit, to these resonators [8].
Proposed by Medford et al. [9], RX qubits use three electrons shared between three quantum dots (Fig. 1). They rely on the “exchange interaction”, a consequence of Pauli’s exclusion principle that causes energy levels to split based on the arrangement of electrons. Importantly, an applied voltage precisely determines this splitting, enabling control over the quantum states without the magnetic fields normally required for spin qubits. This was crucial for the success of Landig’s paper [1], since superconducting phases are notoriously vulnerable to strong magnetic fields.
In their experiment, they formed the triple quantum dot in a gallium arsenide structure with aluminium electrodes. One electrode connected to a coupling resonator, enabling electric dipole interactions with the photons. The same end of the resonator also capacitively coupled to an aluminium superconducting qubit. To maximise the coupling, the resonators had an enhanced characteristic impedance and they used a novel quantum dot design that increased the overlap between the resonator gates and the qubit itself.
Using this, Landig and colleagues demonstrated the crucial result of coherent coupling between the two qubits, which were separated by several hundred micrometres. Specifically, coupling resulted in a shift to the superconducting qubit’s energy, dependent on the state of the RX qubit. They detected this by measuring the amplitude of light reflected from a waveguide coupled to the superconductor.
Importantly, to achieve these results they first had to fine-tune the RX qubit, reaching a “sweet spot” that maximised coupling to the resonator while minimising loss. By varying the energy splitting ∆ using voltages (Fig. 1), they shifted the qubit’s behaviour to be more charge-like (stronger coupling) or spin-like (longer coherence times). The optimum was near ∆/h ≃ −3.3 GHz, which produced a ratio of coupling strength to decay rate that was 1.7 times larger than previous RX qubits [8]. Notably, they achieved this while operating at magnetic fields of order 100 times weaker.
This result is a critical step towards realising hybrid quantum architectures, opening the door for future designs that combine spins and superconducting qubits. The next challenge will be improving the properties of the system to a point where they can be used for quantum computation. In their experiment, the coherence time was limited by the hyperfine interaction, where the electron spin has unwanted coupling to the nuclear spin of the gallium. An essential next step would be replicating these results in materials without nuclear spin, such as isotopically purified silicon. Indeed, 2020 saw the successful coupling of two spin qubits in silicon double quantum dots, also using a superconducting resonator [10].
Ultimately, the success of this hybrid architecture rides on its scalability: it remains a pivotal question how to turn two coupled qubits into ten, a thousand, or a million. It may be a while before researchers solve these challenges, but the results from experiments such as Landig’s are vital, promising steps towards creating a hybrid future for quantum computation.
References
[1] A. J. Landig et al., “Virtual-photon-mediated spin-qubit–transmon coupling”, Nature Communications 10, 5037 (2019).
[2] D. Loss and D. P. DiVincenzo, “Quantum computation with quantum dots”, Physical Review A 57, 120 (1998).
[3] B. E. Kane, “A silicon-based nuclear spin quantum computer”, Nature 393, 133 (1998).
[4] J. T. Muhonen et al., “Storing quantum information for 30 seconds in a nanoelectronic device”, Nature Nanotechnology 9, 986 (2014).
[5] R. Barends et al., “Superconducting quantum circuits at the surface code threshold for fault tolerance”, Nature 508, 500 (2014).
[6] Y. Kubo et al., “Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble”, Physical Review Letters 107, 220501 (2011).
[7] J. Majer et al., “Coupling superconducting qubits via a cavity bus”, Nature 449, 443 (2007).
[8] A. J. Landig et al., “Coherent spin–photon coupling using a resonant exchange qubit”, Nature 560, 179 (2018).
[9] J. Medford et al., “Quantum-Dot-Based Resonant Exchange Qubit”, Physical Review Letters 111, 050501 (2013).
[10] F. Borjans, X. G. Croot, X. Mi, M. J. Gullans, and J. R. Petta, “Resonant microwave-mediated interactions between distant electron spins”, Nature 577, 195 (2020).
