# Research

The focus of our group is on the experimental study of solid-state quantum devices for quantum information processing applications. We make use of the excellent fabrication facilities of the London Centre for Nanotechnology, such as its class 6 cleanroom, to develop nanoscale devices such as spin qubits in carbon and silicon-based materials or topological qubits in semiconductor nanowires. Our lab is equiped with a number of dilution refrigerators that allow us to investigate these quantum devices at mK temperatures - using high-frequency measurement techniques for readout and control at the level of individual electrons. We work closely with other groups within the UCL Quantum Science and Technology Institute as well as many other groups worldwide. A short overview of our current research is given below.

- Carbon nanotube spin qubits
In our group we investigate carbon nanotube quantum dots for application in solid-state quantum information processing. Carbon nanotubes have unique potential as a host material for charge and spin-based qubits: carbon nanotubes provide natural spatial confinement, allow accurate control of electron charge, spin and valley degrees of freedom, are atomically perfect and can be made isotopically pure. In our group we already developed techniques for spin-to-charge conversion and fast readout of charge states [1]. Our current efforts focus on understanding and mitigating charge noise and developing techniques to create entanglement between spatially separated qubits using a measurement-based approach.

In our most recent work, we examined charge coherence in carbon nanotube quantum dots. The use of quantum dots to define charge and spin qubits is well established in the field of quantum information processing. Quantum dot charge qubits are attractive because of the possibility of fast qubit control but are sensitive to charge noise which can result in rapid decoherence. Spin qubits can have much longer coherence times but are susceptible to charge noise as well since fast manipulation, or the coupling of two or more spin qubits, often relies on mixing of charge and spin degrees of freedom. As a result, two-qubit quantum gate fidelities are still relatively low even for spin qubits. Scalability therefore depends critically on an understanding of charge noise and on developing techniques to lower the susceptibility of quantum dot devices to this source of decoherence.

To examine charge coherence, we used a carbon nanotube device consisting of two quantum dots in series: a charge qubit in which quantum information is encoded in the spatial position of an electron. To read out the quantum states, we developed a technique based on radio-frequency reflectometry measurements of the quantum capacitance of the device: a measure of how easy, or difficult, it is for an electron to move between the quantum dots, as illustrated in the figure above. In combination with microwave manipulation of the qubit, our group could measure the degree of charge noise experienced by the device and determine charge coherence [2]. Moreover, by operating the qubit at an optimal point (or sweet spot) coherence could be extended by more than an order of magnitude. This work is in collaboration with the Quantum and Nanoelectronics group Basel, Swizerland, the group of Prof. Takis Kontos, LPA, France, and C12 Quantum Electronics.

[1] Chorley et al, Physical Review Letters 108, 036802 (2012) [2] Penfold-Fitch et al, Physical Review Applied 7, 054017 (2017) - Donor spin qubits in silicon
The elementary unit of quantum information is the quantum bit or qubit. Like the classical bit, the qubit is a two-level system but with the intriguing ability to exist in a superposition of states. This means it can be in the on and off state at the same time which has profound implications if we consider quantum systems of more than one qubit. Instead of each qubit carrying any well-defined information of its own, the information is encoded in their joint properties. In quantum mechanics, the qubits are described as being entangled. The challenge is to find ways to harness quantum phenomena such as superposition and entanglement to construct a quantum computer that is able to perform tasks that are unaittainable in a classical context.

A very natural qubit is the electron spin. The energy difference between spin states of an electron can be precisely controlled by magnetic fields and, using the electron's charge, it is also possible to isolate and manipulate individual spins electrically. One route to achieve entanglement between spin qubits is to use the interaction of their wavefunction overlap by placing them in close proximity [1]. While such an approach is feasible for a small number of qubits, a large-scale quantum processor which relies on direct nearest neighbour coupling becomes rapidly impractical. In our group we therefore follow an alternative strategy which makes use of an intriguing quantum mechanical effect by which two spatially separated quantum bits become entangled if a measurement cannot tell them apart.

As has been shown theoretically, measurement-based entanglement can be used to couple large numbers of physically separated qubits, building up so-called graph states. Computation is then achieved by a sequence of measurements on individual qubits that consumes the entanglement - known as one-way quantum computation - which is entirely different from the standard circuit-based approach [3]. In practise this also requires the presence of a quantum memory where quantum information is stored to allow graph-state growth without the risk of losing existing entanglement. In our group we use a solid-state implementation which is ideally suited to this task: single As-dopants in isotopically pure Si-28.

The devices are fabricated by the groups of Prof. Neil Curson and Dr. Taylor Stock at the LCN using the most precise silicon dopant incorporation technique available: scanning tunnelling microscopy (STM) hydrogen resist lithography [3]. The atomically precise incorporation of individual As-dopants is essential in satisfying a key requirement of the measurement-based entanglement protocol: qubit indistinguishability. To manipulate the electron spins of the As-dopants and create entanglement between remote qubits using projective measurements we exploit radio-frequency reflectometry techniques which allows us to perform these tasks on a timescale significantly faster than electron spin lifetimes. We furthermore aim to use hyperfine coupling to transfer the quantum information from the electron to the As nuclear spin states. This approach takes advantage of record nuclear spin coherence, in the 10-100 second range, of dopants in Si and allows us to grow the entangled spin qubit network. This work is in collaboration with VTT, Finland and Zurich Instruments, Switzerland and the group of Prof. Sougato Bose at UCL who is working on the theory of measurement-based entanglement of donor spin qubits.

[1] Loss and Divincenzo, Physical Review A 57, 120 (1998) [2] Briegel et al, Nature Physics 5, 19 (2009) [3] Stock et al, ACS Nano 14, 3316 (2020) - Topological qubits
There is a strong current interest in solid-state manifestations of Majorana physics – a Majorana particle being a fermion which is its own antiparticle. Apart from the fundamental aspects of this phenomenon, Majorana qubits have been proposed that are extremely well protected against decoherence due to their topological nature. So far, the study of Majorana fermions has mainly focussed on topological insulators or materials with strong spin-orbit interaction coupled to s-wave superconductors to stabilize the Majorana particles [1]. More recent theories have shown that the requirement for strong intrinsic spin-orbit interaction can be relaxed if this can be engineered using external magnetic fields such as those of magnets of submicron size - opening up the field to a whole new set of material platforms [2,3]. In collaboration with groups at Imperial College London (Dr. Malcolm Connolly and Dr. Will Branford) and the Niels Bohr Institute, Denmark (Prof. Jesper Nygard) we aim to take these novel ideas in to the lab by developing and characterising nanomagnets and coupled them to quasi one-dimensional systems such as carbon nanotubes and InAs/Al heterostructures.

[1] Mourik et al, Science 336, 1003 (2012) [2] Kjaergaard et al, Physical Review B 85, 020503 (2012) [3] Klinovaja et al, Physical Review Letters 109, 236801 (2012)