The way forward for exchange-only multi-spin qubits in semiconductor quantum dots

Several aspects of quantum mechanics are hard to understand intuitively, such as the principle that particles can be in a superposition of multiple, mutually exclusive states. It turned out, however, that these absurd concepts can in fact be exploited to create new revolutionizing quantum technologies. One of the most exciting ones is quantum computation, where information is coded in quantum bits (qubits), instead of classical bits. Since these qubits can be in a superposition of 0 and 1 and can be entangled with each other, a quantum computer could perform certain tasks exponentially faster than a regular computer, such as database searching and prime factorization. The quest for the optimal physical qubit is at full speed, and by now it has been narrowed down to a handful of approaches. The quantum-dot-based spin qubit is one of the most feasible and scalable qubits proposed so far: The idea is to trap single electrons inside a semiconductor and then use their spin state (which can only be "up" or "down") to encode the quantum information. There has been enormous progress in this field over the past two decades. One of the main obstacles has been the influence from the atoms that constitute the host semiconductor. These atoms also carry (nuclear) spin, which couples to the electrons' spin via so-called hyperfine coupling, and thereby destabilizes the qubits. The main objective of my project is to find the optimal way to overcome this problem. We made several promising discoveries, which has led so far to eight publications in high-profile journals: (1) Using more than one spin to encode a qubit has important advantages in terms of qubit control. We discovered a way to construct a qubit using six spins in a linear array of three quantum dots that has all these benefits, but in addition is intrinsically insensitive to the nuclear spins. In June 2021 we were contacted by two world-leading experimental groups that have started to attempt an experimental realization of our idea. (2) The popular three-dot three-spin qubit is not well protected against nuclear spin noise. We discovered that running an electric current through the three dots in a specific way can give rise to a feedback process that can be tuned such that the overall effect is a suppression of the harmful nuclear spin fluctuations, which will then stay suppressed for several seconds. This provides a practical procedure to "clean" the polarization on the dots before using them to host a qubit. (3) Another way to mitigate the effect of the nuclear spins is to encode the qubits in spins of electrons that are *removed* from the semiconductor. It turns out that, due to their underlying wave function, these so-called holes couple very weakly to nuclear spins. This notion led to a very recent surge in interest for hole spin qubits. However, their different wave function also comes with several complications that make the way hole spins couple to magnetic fields (which is a crucial ingredient for qubit definition and control) much more intricate. We worked out a material-independent theory to understand all details of this coupling. (4) The residual interaction of holes with the nuclear spins depends on choice of material, but is also qualitatively different from the coupling between electron spins and nuclear spins. Understanding the details of the coupling is crucial for assessing the quality of the resulting qubits. We developed a theory to connect transport measurements that have been reported recently to the details of the hyperfine coupling, thereby providing a tool to gain direct insight in the exact nature of the coupling. (5) We teamed up with an experimental group from IST Austria to investigate the detailed properties of a Ge-based hole system, accessing several material parameters that are relevant for spin-qubit implementations. (6) With experimental collaborators from ETH Zürich we developed a new type of system to host spin qubits. We analyzed their data and proved that the system has very weak spin-orbit interaction. This interaction is detrimental for spin qubits in several ways, and is usually strong in the material that was used (InAs). Our discovery of how to suppress this interaction in InAs thus introduces a whole new material platform for hosting spin qubits, with several significant advantages in terms of sensitivity to heat and noise. (7) We presented a unified theory for understanding different resonant line shapes that are typically observed when spin qubits are driven with an oscillating electric field (which is a common tool for control and spectroscopy). We were able to connect several distinctive features to different underlying physical mechanisms, thereby providing a new tool for investigating relevant material parameters. (8) We contributed to a short review article explaining how the protection against nuclear spin noise works in the six-spin qubit we proposed.

The objective of this project was to solve the main challenges in the further development of multi-spin exchange-only spin qubits. All three lines of research we performed revolved around the question how one can mitigate the qubit decoherence caused by the randomly fluctuating nuclear spins of the host semiconductor in which the qubits are defined; the most important outcomes in the three directions were as follows: (1) We discovered a practical way in which running an electric current through the system suppresses the harmful fluctuations. (2) We proposed new ways to encode exchange-only spin qubits in so-called decoherence-free subspaces, where they are insensitive to magnetic noise, such as caused by the nuclear spins. (3) We developed advanced theories to understand the detailed spin physics of hole spin qubits hosted in nuclear-spin-free materials such as Si-28. The short-term impacts of our findings will be mostly within the research field of spin-based quantum information processing. Especially the results mentioned under (2) and (3) generated much attention: Our main proposal of the decoherence-free spin qubit has been picked up by several experimental groups around the world, who actually started efforts to try to implement our idea. Our detailed understanding of several aspects of hole-spin physics in Si- and Ge-based structures quickly became well-cited and has thus been recognized by the community as a resource for designing the optimal hole spin qubit in nuclear-spin-free materials. Another, more abstract, impact of the results is that they put Norway more visibly on the map in the area of quantum computing and quantum technologies in a broader sense. Based on the expertise we demonstrated through the scientific dissemination channels, world-leading experimental groups in the field started contacting us for assistance with the interpretation of their data. More concretely, this led so far to two collaborations in both of which we revealed the potential of a completely new material platform for hosting spin qubits. Finally, in a broader picture, one can say that our results contribute to the global efforts to develop a quantum computer, which will have a disruptive impact on society as a whole. The specific strength of a quantum computer lies in solving problems that require some type of “optimization,” in other words, identifying the right answer in a large set of possible answers. Envisioned applications range from drug development and image recognition to battery research and 100% secure communication, and could thus have a significant impact on health care, safety, and the green energy transition.

One of the more promising qubits proposed so far is the quantum-dot-based exchange-only qubit, which encodes quantum information in multi-particle spin states of electrons localized inside quantum dots created in a semiconductor structure. These qubits are conceptually simple and scalable, they rely on well developed experimental techniques, and can be operated fully electrically. The first attempts to create and operate such a qubit were promising, but also identified obstacles to further progress: Apart from being relatively sensitive to charge noise, exchange-only qubits couple to the fluctuating spins of the atomic nuclei of the host semiconductor. This coupling leads to decoherence, typically on the scale of tens of nanoseconds. I want to solve the intrinsic problem of the nuclear spins and identify the optimal way forward for the exchange-only qubit. Roughly speaking, I will investigate two approaches: (1) I want to find a way to suppress or circumvent the effect of nuclear spin fluctuations in the commonly used III-V semiconductors, while keeping the qubit as much protected from charge noise as possible. (2) I want to determine the optimal implementation of such a qubit in (nuclear-spin-free) Si. Here, understanding the role of the multi-valley structure of the conduction band edge in Si is crucial. If this indeed provides a solution to the problems, the exchange-only qubit will become a qubit of unprecedented quality with a high potential to win the race.