Feedback-Driven Quantum Stabilization: Real-Time Two-Axis Control of Spin Qubits

Quantum computing has the potential to revolutionize the world through unprecedented computational power. However, the delicate nature of quantum states makes them susceptible to environmental fluctuations, posing a challenge to achieving optimal qubit control and stability. In a groundbreaking paper published in Nature Communications, titled “Two-Axis Real-Time Control of Spin Qubits” by Fabrizio Berritta et al. [1], researchers at the Niels Bohr Institute in Copenhagen unveiled a real-time control protocol tested on a two-electron singlet-triplet qubit. This innovative approach, powered by a full Quantum Machines quantum control setup, demonstrates the importance of feedback in enhancing the performance and stability of quantum devices. 

The Role of Feedback in Optimal Control for Semiconductor Spin Qubits

Feedback and feed-forward are crucial capabilities in stabilizing and optimizing quantum devices, allowing for real-time monitoring and control of quantum systems. The ability to continuously adapt to the ever-changing quantum environment is essential to achieve precise manipulation of quantum states and extend the lifetime of quantum systems. This is particularly relevant in the context of decoherence and relaxation. 

Semiconductor spin qubits stand out among various quantum information processing platforms for their long coherence times and foundry compatibility. Recent achievements in semiconductor spin qubits have demonstrated high qubit gate fidelities, making them promising candidates for quantum computing applications. However, achieving precise control of gated qubits remains challenging due to their sensitivity to environmental fluctuations, necessitating feedback-based corrections for stability and optimization. To correct for such environmental fluctuations, real-time adaptive control of a qubit has been demonstrated but limited to single-axis Hamiltonian estimation (e.g., noise from a nuclear spin bath). Here, the authors implement two-axis control of a singlet-triplet spin qubit with two fluctuating Hamiltonian parameters that are affected by nuclear and electrical noise. This has resulted in improved quality of coherent oscillations. 

Figure 1: Experimental setup. Quantum Machines OPX+ is used for RF reflectometry and fast gate control pulses with a bandwidth of less than 1 GHz. Additionally, the setup includes a Quantum Machines (QDevil) QDAC-II for generating low-frequency analog signals. A Quantum Machines (QDevil) QFilter-II suppresses noise and interference in the signal chain. Finally, the setup incorporates a Quantum Machines (QDevil) QBoard PCB sample holder with surface-mount tank circuits for multiplexed RF reflectometry.

The Real-Time Two-Axis Control Protocol 

The research conducted by the Spin Qubit Group, led by Prof. Ferdinand Kuemmeth at the Niels Bohr Institute, introduces a real-time control protocol for a singlet-triplet (ST0) spin qubit implemented in a gallium arsenide double quantum dot. The protocol leverages Quantum Machines’ OPX+ quantum controller to estimate the Overhauser field gradient and exchange interaction in real-time. This estimation enables controlled Overhauser-driven spin rotations without the need for micromagnets or nuclear polarization protocols. 

Get the OPX1000 spec sheet here

“ The OPX’s fast feedback and unique real-time processing capabilities were critical for our experiment. Combining these with the OPX’s intuitive programming and QM’s state-of-the-art cryogenic electronics allowed us to do something that we have dreamt of doing for years.” 

– Prof. Ferdinand Kuemmeth

Figure 2: Real-time Bayesian estimation of two control axes. (a) The two-axis estimation protocol cycle. After estimating the Larmor frequency ΩL, the OPX computes on-the-fly the pulse duration required to initialize the qubit near the equator of the Bloch sphere. After the ΩL(π/2) pulse, the qubit evolves under exchange interaction before another ΩL(π/2) pulse initiates readout. (b) Qubit evolution on the Bloch sphere during one exchange probe cycle.

Key Steps in the Protocol 

• Rapid Estimation of Fluctuating Fields: The protocol involves the rapid estimation of the instantaneous magnitude of one of the fluctuating fields, specifically the nuclear field gradient. This estimation creates one qubit control axis. How? ΔBz Is a control axis per se, but it fluctuates in time, so it cannot be really used for qubit control. If it is estimated fast enough, it is possible to use it as a control axis (but now its frequency is known) 

• Real-Time Qubit Frequency Probing: The control axis is then exploited to probe the qubit frequency across different operating points (higher detuning voltages) in real-time, where Heisenberg exchange coupling dominates. This step allows for counteracting fluctuations along both axes, resulting in an improved quality factor of coherent qubit rotations. More precisely, the estimated nuclear field is used to manipulate the qubit along one axis (X). For the Hadamard, the estimated J (exchange) fluctuations also need to be corrected, which depends on the difference between the chemical potentials of the two dots (detuning). Once J is estimated, it is corrected by adjusting the detuning accordingly (by pulsing with the OPX). 

QM’s OPX+ controller separates singlet-correlated electron pairs, performs single-shot readout classifications, and estimates the fluctuating nuclear field gradient within the double dot. The protocol allows for coherent qubit rotations between S and T0, adjusting baseband control pulses accordingly to correct for fluctuations along both axes. Beyond ST0 qubits, the following protocol can potentially improve the coherent control of any quantum systems manipulated by baseband pulses. 

Figure 3: Real-time universal ST0 control demonstrated by Hadamard rotations. The picture shows the Hadamard rotation protocol, where once the OPX estimates the nuclear field, it is used as a control axis to then estimate mostly J (affected by electrical noise).

Real-Time Control Protocols and Advanced Platforms Unveil Precision and Stability

This research represents a significant step forward in achieving precise control and stability of quantum devices, specifically spin qubits, in real time. The demonstrated protocol showcases how to use nuclear fluctuations as a control axis, as well as the importance of feedback in mitigating the effects of environmental fluctuations while highlighting its critical role in advancing various qubit implementations beyond spin qubits. As quantum computing continues to evolve, real-time control protocols like the one presented in this paper, together with advanced quantum control platforms such as the OPX+, contribute to unlocking the full potential of quantum devices for quantum technology applications.

Want to learn how to set up a similar experiment?  

Check out the setup employed by the Spin Qubit group at the Center for Quantum Devices at the Niels Bohr Institute using Quantum Machines’ OPX+, QDAC, QFilter, QBox, and QBoard, all seamlessly integrated to simplify spin qubit control, offering the highest performance (Figure1). 

Are you ready to join in on the excitement? Don’t miss out on the chance to explore something truly mind-blowing!  

Get in touch with us to discover more about OPX+ and his new big brother, the OPX1000.

Get a Personalized Demo

[1] Berritta, F., Rasmussen, T., Krzywda, J.A. et al. Real-time two-axis control of a spin qubit. Nat Commun 15, 1676 (2024). https://doi.org/10.1038/s41467-024-45857-0