The Race To Make Better Qubits

One of the big challenges in quantum computing is getting qubits to last long enough to do something useful with them. After decades of research, there now appears to be tangible progress.

The challenge with any new semiconductor technology is to improve performance by one or more orders of magnitude without discarding a half-century of progress in other areas. Qubits based on silicon quantum dots are attractive in part because the semiconductor industry has developed mature industrial processes that can create large numbers of nearly identical devices. Similarly, the industry has a great deal of experience with the placement, manipulation, and characterization of dopant atoms.

In 1998, Bruce Kane, then a senior research associate at the University of New South Wales (and currently research staff at the University of Maryland), proposed the use of qubits based on dopant atom spins.[1] The most abundant isotope of phosphorous, ³¹P, features electron and nuclear spins of value 1/2. In 2009, researchers demonstrated the use of magnetic fields to initialize such qubits, achieving better than 99% electron spin polarization in ³¹P at low temperatures.[2]

Qubits based on phosphorous donor atoms potentially offer extremely high coherence times. In a comprehensive review, Gavin Morley, associate professor at the University of Warwick, observed that in isolated atoms, the electron spin persisted for up to 10 seconds, while nuclear spins were stable for up to 3 hours.[3] Though interactions with adjacent qubits reduce this value, donor-based qubits have the potential for much longer coherence times than many alternatives.

One proposed qubit design, based on the exchange interaction, places two donor atoms in close proximity, with a gate to control the interaction between them. Because the exchange interaction depends on the overlap between wave functions of two adjacent atoms, Andrea Morello, professor of quantum engineering, and his colleagues at the University of New South Wales explained that it is quite strong, but also very distance-dependent.[4] Exchange-based qubits require atoms that are less than 15 nm apart. Variability of even a few nanometers in the spacing between donor atoms, their neighbors, and the control gate will affect the behavior of the qubits. Benoit Voisin, researcher at the University of New South Wales, and his colleagues pointed out in a recent article in the MRS Bulletin that it has only recently become possible to examine such short-range interactions experimentally.[5] The implications of short-range order and disorder for quantum devices are not completely understood.

It is clear, though, that placing donor atoms, control electronics, and an appropriate readout mechanism in such close proximity is a challenging problem. In theory, it’s possible to organize control and readout elements vertically, using a crossbar arrangement to place readout transistors above their associated qubits. In practice, Sandia National Labs researchers Ezra Bussmann and colleagues noted that dramatic improvements to manufacturing capabilities will be needed to align devices to atomic tolerances and fabricate them in commercially plausible amounts of time.[6]

Devices based on longer-range interactions might allow simpler manufacturing. For instance, the Morello group described qubits that depend on the electron spin of a single donor atom, controlled by electron spin resonance. Displacing an electron relative to its donor atom creates a dipole, the orientation of which can be controlled by a magnetic field. These “flip-flop” qubits are simpler to manufacture than exchange-based qubits, but still require precise control of donor atom placement.

Commercial ion implantation tools place ions within a probability distribution defined by the edges of photoresist features. The photoresist dimensions depend on the variability of the lithographic process, and then Poisson statistics define the placement of ions within the lithographic features. Conventional ion implantation methods produce uncertainties of 3nm to 10nm in ion placement. Instead, researchers studying donor-based qubits typically use a process that Bussmann called atomic precision additive manufacturing (APAM).

APAM starts with a hydrogen-terminated silicon wafer. An STM tip selectively removes hydrogen atoms and places PH₃ molecules in the resulting openings. These molecules decompose to produce phosphorous atoms, which are frozen in place by an encapsulating silicon layer. While the accuracy of the technique is unsurpassed, it is extremely slow. Write speed is limited by the available current at the STM tip to only about 10 sq. nm/sec. Completing a single device might take several hours. Clearly any path to multi-qubit integration, much less commercial applications, will require more efficient fabrication tools.

Morello discussed possible approaches to deterministic ion implantation, such as by detecting the energy dissipated by an implanted ion and using an AFM tip to mark the location. Alternatively, arrays of STM tips could fabricate many devices in parallel.

Reading qubits for computation, memory, and sensors
Regardless of the specific qubit design, single electron transistors can serve as readout devices. In a magnetic field, carrier transport is spin-dependent. Carriers with the desired spin can tunnel into the transistor, producing a charge signal, while others cannot. This same mechanism can be used to collect data from quantum sensors.

For instance, ensembles of initialized donor spins could detect changes in an applied magnetic field. Lattice strain changes the distance between atoms, which could allow atomic-scale strain measurements based on changes in the interactions between adjacent qubits. Because these and other quantum sensors do not need to address individual qubits, they potentially are easier to build than quantum computers.

Along the same lines, Morello also proposed the use of arrays of donor qubits as memory elements in a general-purpose quantum computer. Writing a quantum state to an array of qubits does not require addressing each qubit individually. Such a memory, paired with a superconducting quantum processor, could allow useful calculations to be done with relatively small numbers of interacting qubits.

Conclusion
Nearly any clearly defined quantum system in theory can serve as the basis for a qubit device. Reading the literature, it’s sometimes hard to differentiate between proposals with commercial potential and interesting thought experiments for physicists. The long coherence times and well-characterized electronic behavior of common dopant atoms makes them worth watching as practical quantum computers begin to emerge.

References
[1] Kane, B. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998). https://doi.org/10.1038/30156
[2] van Tol, J., Morley, G.W., Takahashi, S. et al. High-Field Phenomena of Qubits. Appl Magn Reson 36, 259 (2009). https://doi.org/10.1007/s00723-009-0014-6
[3] Morley, G. W. (2014). Towards spintronic quantum technologies with dopants in silicon. In Electron Paramagnetic Resonance (pp. 62-76). https://doi.org/10.1039/9781782620280-00062
[4] Morello, A., Pla, J.J., Bertet, P. and Jamieson, D.N. (2020), Donor Spins in Silicon for Quantum Technologies. Adv. Quantum Technol., 3: 2000005. https://doi.org/10.1002/qute.202000005
[5] Voisin, B., Salfi, J., Rahman, R. et al. Novel characterization of dopant-based qubits. MRS Bulletin 46, 616–622 (2021). https://doi.org/10.1557/s43577-021-00136-x
[6] Bussmann, E., Butera, R.E., Owen, J.H.G. et al. Atomic-precision advanced manufacturing for Si quantum computing. MRS Bulletin 46, 607–615 (2021). https://doi.org/10.1557/s43577-021-00139-8

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