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Carbon Nanotube Quantum Circuits

Periodic Reporting for period 4 - CNT-QUBIT (Carbon Nanotube Quantum Circuits)

Reporting period: 2020-03-01 to 2021-04-30

Aim: The aim of this proposal is to use spin qubits defined in carbon nanotube quantum dots to demonstrate measurement-based entanglement in an all-electrical and scalable solid-state architecture. The project aims to make use of spin-orbit interaction to drive spin rotations in the carbon nanotube host system and hyperfine interaction to store quantum information in the nuclear spin states. The proposal builds on techniques developed by the principal investigator for fast and non-invasive read-out of the electron spin qubits using radio-frequency reflectometry and spin-to-charge conversion.

Any quantum computer requires entanglement. One route to achieve entanglement between electron spin qubits in quantum dots is to use the direct interaction of neighbouring qubits due to their electron wavefunction overlap. This approach, however, becomes rapidly impractical for any large scale quantum processor, as distant qubits can only be entangled through the use of qubits in between. Here I propose an alternative strategy which makes use of an intriguing quantum mechanical effect by which two spatially separated spin qubits coupled to a single electrical resonator become entangled if a measurement cannot tell them apart. The quantum information encoded in the entangled electron spin qubits will be transferred to carbon-13 nuclear spins which are used as a quantum memory with coherence times that exceed seconds. Entanglement with further qubits then proceeds again via projective measurements of the electron spin qubits without risk of losing the existing entanglement. When entanglement of the electron spin qubits is heralded – which might take several attempts – the quantum information is transferred again to the nuclear spin states. This allows for the coupling of large numbers of physically separated qubits, building up so-called graph or cluster states in an all-electrical and scalable solid-state architecture.

Outcome: The project developed charge and spin qubits in double quantum dots in ultraclean freestanding carbon nanotubes. The devices were embedded in resonant LC circuits, achieving state-of-the art capacitance sensitivities for high-fidelity (>99.9%) qubit readout in sub-microsecond timescales and so-called video mode imaging of the charge stability diagrams. The record capacitance sensitivity (for any material platform) was achieved by developing novel quantum paraelectric strontium titanate varactors for impedance matching and frequency tuning at mK temperatures, as well as the incorporation of novel ultra-low noise sub-GHz Josephson parametric amplifiers in collaboration with VTT Finland. During the project we furthermore developed devices that incorporated micromagnets for electric - rather than magnetic - control of the quantum dot spin states, as well as the ability of carbon nanotube double quantum dots readout using a proximal single quantum dot carbon nanotube detector. We could furthermore control the devices using microwave signals applied to the device gate electrodes. We obtained Landau-Zener-Stuckelberg interferometry patterns that allowed us to probe orbital and valley dynamics in the double quantum dot devices. We furthermore developed code for the detection and coherent control of charge and spin states in the double quantum dots using FPGA based equipment, in collaboration with Zurich Instruments, Switzerland. This will allow us to herald entanglement on sub-microsecond timescales - that is, well within spin relaxation and coherence times - if two or more devices are measured simultaneously. This last step has not yet been demonstrated but the capabilities developed during the project has laid the groundwork to make this possible.
During the first part of the project our group has focussed on the installation of the low-temperature facilities and radio-frequency reflectometry techniques used for qubit readout. We demonstrated that the temperature of electrons in the carbon nanotube quantum dots that host the qubits is as low as 12 mK – much smaller than other relevant energy scales. We furthermore demonstrated significant improvements in the measurement readout of charge states of the quantum dots which – via spin-to-charge conversion – also allows fast spin-state readout. Fast readout is important as the measurement of the qubits has to be faster than the timescale on which entanglement is lost – estimated to be on the order of several tens of usec for realistic device parameters. We achieved this by introducing varactors (tunable capacitors) which allows us to impedance match the resonator-qubit circuits to the transmission lines that connect to them and to tune the resonator frequency. These varactors have been specifically designed and fabricated by our group such that they are compatible with the ultra-low temperatures at which the qubits are measured - in addition to being stable, low-loss and magnetic field insensitive. To further improve our measurement capabilities we have been collaborating with VTT Finland to incorporate frequency-tuneable ultra-low noise Josephson Parametric Amplifiers (JPAs) in our set-up. These JPA are made to operate in the frequency range of interested for our devices (tuneable around 600 MHz) and have sufficient magnetic shielding to apply magnetic fields up to 9 Tesla to our devices.

During the project, the quality of the devices were continuously improved. The carbon nanotubes quantum dots fabricated and measured at the final stages of the project were made completely freestanding and could be made free from contaminants and adsorbates, rendering them ultraclean, as confirmed by ultra-low device charge noise when measured at low temperatures. For electric spin control, rather than solely relying on spin-orbit coupling, we furthermore integrated micromagnets in our design. In addition, we could control the devices using microwave signals applied to the device gate electrodes. We obtained Landau-Zener-Stuckelberg interferometry patterns that allowed us to probe orbital and valley dynamics in the carbon nanotube double quantum dot devices. We furthermore developed code for the detection and coherent control of charge and spin states in the double quantum dots using FPGA based equipment, in collaboration with Zurich Instruments, Switzerland. Results were dissemination via research publications, patent applications, and workshops and conferences.
Progress beyond the state of the art include the development and demonstration of mK quantum paraelectric varactors in radio-frequency circuits. A varactor is simply a tunable capacitor which is widely used in everyday electronics. However, those standard components do not work at low temperatures as it relies on the mobility of charge carriers that freeze out. For the delivery of the ERC project, however, frequency tuning and impedance matching of quantum devices cooled down to mK temperatures is required. For this we developed novel mK varactors from a quantum paraelectric material – strontium titanate – that doesn’t undergo a ferroelectric phase transition due to quantum fluctuations persisting down to zero Kelvin, ensuring that the paraelectric material remains tunable. A further developed capability beyond the state of the art has been the demonstrated record capacitance sensitivities. This advance allows high-fidelity qubit readout, and ultimately the demonstration of measurement-based entanglement of spin qubits in quantum dot devices.
Freestanding carbon nanotube double quantum dot