Controlling Spins in Quantum systems in an Online Setting

One of the most exciting quantum technologies proposed 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 important tasks, such as database searching and prime factorization, exponentially faster than a regular computer. Semiconducting spin qubits are among the most promising candidate systems for hosting quantum information. The idea is to localize single electrons in small potential traps created inside a semiconductor, and then use their spin state (which can only be "up" or "down") to encode the quantum information. Attractive features of spin qubits are their small size, fast operation speeds, and potential scalability due to their similarity to standard microchip transistors. The field is rapidly moving forward, and recent developments have pushed single-qubit performance parameters below the fault-tolerance threshold. In this project we will develop new algorithms for spin-qubit manipulation and stabilization and we will combine those with state-of-the-art control and read-out hardware. This will enable us to be the first to achieve "online" control of spin qubits, i.e., the ability to measure the state of one or more qubits followed by qubit manipulations that depend on the outcome of the measurements, all within the coherence time of the system. This will allow us (i) to dramatically improve the qubit coherence time, (ii) to obtain universal multi-qubit control in our system, and (iii) to be the first to perform unconditional quantum teleportation of a spin qubit, which depends on online control of the qubits. Furthermore, such online control is a crucial ingredient for most quantum error correction protocols and a successful realization would thus be a significant breakthrough for the field, potentially with a very large impact. In the first part of the project, we mainly focused on using fast read-out and control of qubits to enhance their coherence time, which led so far to four scientific publications in high-profile journals and two more manuscripts that are currently being finalized: (1) We developed an efficient Bayesian protocol for the online estimation of unknown slowly fluctuating parameters in the qubit's environment, which can be used to combat most common types of noise in electronic quantum devices. We explained how knowledge about the underlying physics of the noise source can be harnessed to make the estimation scheme much more efficient, and we presented an optimal memory-efficient "hybrid" estimation method that makes use of both analytic approaches and a neural network. (2,3) We were involved in the two first experiments where the estimation method we proposed was implemented, step by step. In the first breakthrough experiment, we showed how a very basic (non-adaptive) Bayesian method can be used to quickly estimate the value of the fluctuating environmental parameters in a spin qubit, and how the result can indeed be used to extend the qubit's coherence time significantly. In the second experiment, we added the ingredient of our understanding of the physics of the fluctuations, which indeed yielded much higher-quality and faster estimations. (4) Inspired by our successful implementation of such "machine-learning" methods for qubit control and stabilization, we proposed a scheme for the tuning of qubit devices involving also superconducting elements to special points where they could host special protected qubits. This tuning is a notoriously difficult task, and we presented a gradient-free optimization method that could successfully tune the system within a limited number of iterations. (5) We are currently finishing a paper where we use the same machine-learned tuning method to mitigate the unavoidable disorder in situ in a real experiment. We show how a simple protocol can be used to remove the detrimental effect of electrostatic randomness, the effects of which will become more and more important when scaling up to larger multi-qubit systems. (6) We are finalizing a paper where we show how also including the last ingredient of our proposed estimation protocol, i.e., true adaptivity of the probing sequence, leads to an even further increase of estimation speed and accuracy.

Semiconducting spin qubits have small sizes and incredible operation speeds, but using them for large-scale fault-tolerant applications has so far been prevented by material noise limiting qubit coherence and decreasing gate fidelity. However, their strong sensitivity to electric fields can be profited from if a sufficiently large number of gate voltages can be adjusted accurately (low-frequency control) and tuned quickly (high-frequency control) to cancel noise. By integrating low-noise control electronics with on-hardware real-time signal generation as well as fast qubit readout, and applying the resulting control pulses to multi-channel state-of-the-art spin-qubit processors, we will for the first time perform conditional quantum logic in which the control feedback happens faster than the coherence times associated with the qubits. We will demonstrate this “online control” by performing the world’s first unconditional quantum teleportation of a spin qubit. Since online qubit control is a crucial ingredient of quantum error correction in fault-tolerant architectures, our breakthrough will be an important stepping stone toward successful scaling up of spin-qubit quantum information processors. To achieve such online quantum control with high fidelities, we take advantage of the unique specializations of the ConSpiQuOS partners. Through the development of tailored quantum algorithms (NTNU, ranging from neural networks for multi-qubit classification to qubit stabilization based on real-time Hamiltonian estimation), their implementation on acquisition and control hardware (QM, based on advanced FPGA-based high-frequency digitizers and generators), and the fabrication of a quantum-classical interface (QDV, multi-channel high frequency cryogenic sample holders controlled with room temperature electronics), will allow us to employ the readily available spin-qubit devices (UCPH) as small scale quantum processors.