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Carbon Nanotube Quantum Circuits

Periodic Reporting for period 3 - CNT-QUBIT (Carbon Nanotube Quantum Circuits)

Reporting period: 2018-09-01 to 2020-02-29

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 makes 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.
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. Measurement of carbon nanotube double quantum dot devices also allowed us to determine the amount of charge noise experienced by the electrons at low temperatures. 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 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. The equivalent noise temperature of the JPAs is about 0.1K which is an improvement by almost two orders of magnitude on previous work in our group.

Having strongly focussed on the technical aspects of the measurement set-up – i.e. optimizing our radio-frequency reflectometry readout and microwave control - the emphasis of the remainder of the project will be on the spin qubit measurements. That is, establishing spin coherence times and entanglement as well as exploring the interaction between electron and nuclear spins.
Aspects of the project (mid-term) that go beyond the state-of-the-art are (to the best of our knowledge) the high sensitivities demonstrated for carbon nanotube quantum dot charge sensors and the development and characterisation of a novel type of varactor that is compatible with mK temperature operation. Before the end of the project we expect to have demonstrated coherent control of the electron spins in carbon nanotubes, demonstrated measurement-based entanglement and explored the transfer of quantum information from an electron spin to a nuclear spin quantum memory in a carbon nanotube quantum dot.
Freestanding carbon nanotube double quantum dot