The computational power and fault tolerance of future large-scale quantum processors derive in large part from the connectivity between the qubits. One approach to increase connectivity is to engineer qubit–qubit interactions at a distance. Alternatively, the connectivity can be increased by physically displacing the qubits. For semiconductor spin qubits, several studies have investigated spin coherent shuttling of individual electrons, but high-fidelity transport over extended distances remains to be demonstrated. Here we report shuttling of an electron inside an isotopically purified Si/SiGe heterostructure using electric gate potentials. In a first set of experiments, we form static quantum dots and study how spin coherence decays during bucket-brigade shuttling, where we repeatedly move a single electron between up to five dots. Next, for conveyor-mode shuttling, we create a travelling-wave potential, formed with either one or two sets of sine waves, to transport an electron in a moving quantum dot. This method shows a spin coherence an order of magnitude better than the bucket-brigade shuttling. It allows us to displace an electron over an effective distance of 10 μm in under 200 ns while preserving the spin state with a fidelity of 99.5% on average. These results will guide future efforts to realize large-scale semiconductor quantum processors, making use of electron shuttling both within and between qubit arrays.

Randomized benchmarking techniques have been an essential tool for assessing the performance of contemporary quantum devices. The goal of this tutorial is to provide a pedagogical, self-contained, introduction to randomized benchmarking. With this intention, every chapter is also supplemented with an accompanying Python notebook, illustrating the essential steps of each protocol. In addition, we also introduce more recent trends in the field that bridge shadow tomography with randomized benchmarking, namely through the gate-set shadow protocol.

The advent of quantum technologies brought forward much attention to the theoretical characterization of the computational resources they provide. A method to quantify quantum resources is to use a class of functions called magic monotones and stabilizer entropies, which are, however, notoriously hard and impractical to evaluate for large system sizes. In recent studies, a fundamental connection between information scrambling, the magic monotone mana and 2-Renyi stabilizer entropy was established. This connection simplified magic monotone calculation, but this class of methods still suffers from exponential scaling with respect to the number of qubits. In this work, we establish a way to sample an out-of-time-order correlator that approximates magic monotones and 2-Renyi stabilizer entropy. We numerically show the relation of these sampled correlators to different non-stabilizerness measures for both qubit and qutrit systems and provide an analytical relation to 2-Renyi stabilizer entropy. Furthermore, we put forward and simulate a protocol to measure the monotonic behaviour of magic for the time evolution of local Hamiltonians.

Neuronal activity in the highly organized networks of the central nervous system is the vital basis for various functional processes, such as perception, motor control, and cognition. Understanding interneuronal connectivity and how activity is regulated in the neuronal circuits is crucial for interpreting how the brain works. Multi-electrode arrays (MEAs) are particularly useful for studying the dynamics of neuronal network activity and their development as they allow for real-time, high-throughput measurements of neural activity. At present, the key challenge in the utilization of MEA data is the sheer complexity of the measured datasets. Available software offers semi-automated analysis for a fixed set of parameters that allow for the definition of spikes, bursts and network bursts. However, this analysis remains time-consuming, user-biased, and limited by pre-defined parameters. Here, we present autoMEA, software for machine learning-based automated burst detection in MEA datasets. We exemplify autoMEA efficacy on neuronal network activity of primary hippocampal neurons from wild-type mice monitored using 24-well multi-well MEA plates. To validate and benchmark the software, we showcase its application using wild-type neuronal networks and two different neuronal networks modeling neurodevelopmental disorders to assess network phenotype detection. Detection of network characteristics typically reported in literature, such as synchronicity and rhythmicity, could be accurately detected compared to manual analysis using the autoMEA software. Additionally, autoMEA could detect reverberations, a more complex burst dynamic present in hippocampal cultures. Furthermore, autoMEA burst detection was sufficiently sensitive to detect changes in the synchronicity and rhythmicity of networks modeling neurodevelopmental disorders as well as detecting changes in their network burst dynamics. Thus, we show that autoMEA reliably analyses neural networks measured with the multi-well MEA setup with the precision and accuracy compared to that of a human expert.

Bilayer graphene is a nanomaterial that allows for well-defined, separated quantum states to be defined by electrostatic gating and, therefore, provides an attractive platform to construct tunable quantum dots. When a magnetic field perpendicular to the graphene layers is applied, the graphene valley degeneracy is lifted, and splitting of the energy levels of the dot is observed. Although bilayer graphene quantum dots have recently been realized in experiments, it is critically important to devise robust methods that can identify the observed quantum states from accessible measurement data. Here, we develop an efficient algorithm for extracting the model parameters needed to characterize the states of a bilayer graphene quantum dot. Specifically, we put forward a Hamiltonian-guided random search method and demonstrate robust identification of quantum states on both simulated and experimental data.

Topological properties of quantum systems are among the most intriguing emerging phenomena in condensed matter physics. A crucial property of topological systems is the symmetry-protected robustness towards local noise. Experiments have demonstrated topological phases of matter in various quantum systems. However, using the robustness of such modes to stabilize quantum correlations is still a highly sought-after milestone. In this work, we put forward a concept of using topological modes to stabilize fully entangled quantum states, and we demonstrate the stability of the entanglement with respect to parameter fluctuations. Specifically, we see that entanglement remains stable against parameter fluctuations in the topologically nontrivial regime, while entanglement in the trivial regime is highly susceptible to local noise. We supplement our scheme with an experimentally realistic and detailed proposal based on coupled superconducting resonators and qubits. Our proposal sets an approach for generating long-lived quantum modes with robustness towards disorder in the circuit parameters via a bottom-up experimental approach relying on easy-to-engineer building blocks.

Determining Hamiltonian parameters from noisy experimental measurements is a key task for the control of experimental quantum systems. An interesting experimental platform where precise knowledge of device parameters is useful is the quantum-dot-based Kitaev chain. In these systems, the fine tuning of Hamiltonian parameters is crucial in order to reach the desired regime with stable midgap modes. In this work, we demonstrate an adversarial machine-learning algorithm to determine the parameters of a quantum-dot-based Kitaev chain. We train a convolutional conditional generative adversarial neural network (CCGAN) with simulated differential conductance data and use the model to predict the parameters at which Majorana bound states are predicted to appear. In particular, the CCGAN model facilitates a rapid, numerically efficient exploration of the phase diagram describing the transition between elastic co-tunneling and crossed Andreev reflection regimes. We verify the theoretical predictions of the model by applying it to experimentally measured conductance obtained from a minimal Kitaev chain consisting of two spin-polarized quantum dots coupled by a superconductor-semiconductor hybrid. Our model accurately predicts, with an average success probability of 97%, whether the measurement was taken in the elastic co-tunneling or crossed Andreev reflection-dominated regime. Our work constitutes a stepping stone towards fast, reliable parameter prediction for tuning quantum dot systems into distinct Hamiltonian regimes. Ultimately, our results yield a strategy to support Kitaev-chain tuning that is scalable to longer chains.

Understanding the information processing in neuronal networks relies on the development of computational models that accurately reproduce their activity data. Machine learning techniques have shown promising results in generating synthetic neuronal data, but interpretability remains an issue due to a large number of parameters requiring fitting. Quantum machine learning models, particularly quantum generative learning, are emerging as more compact alternatives that offer similar outcomes. This study presents an efficient framework for generating synthetic neuronal data using a Quantum Generative Adversarial Network (QGAN), with a quantum generator and a classical discriminator. We tested the proposed framework for the minimal case of two neurons, considering the case of single time-steps. Preliminary results demonstrate the QGAN's capability to achieve reliable outcomes with a reduced number of trainable parameters, scaling efficiently for increasing neuronal network sizes. The model effectively captures spiking frequencies of real data, although further refinement is required to incorporate temporal correlations for more extended time-steps. Despite certain limitations, this study lays the foundation for future advancements in using quantum adversarial generative networks to model neuronal activity. The promising potential of QGANs in this domain highlights the possibility of gaining valuable insights into the functioning of complex biological systems through quantum-inspired computational methods.

Large-scale quantum devices provide insights beyond the reach of classical simulations. However, for a reliable and verifiable quantum simulation, the building blocks of the quantum device require exquisite benchmarking. This benchmarking of large-scale dynamical quantum systems represents a major challenge due to lack of efficient tools for their simulation. Here, we present a scalable algorithm based on neural networks for Hamiltonian tomography in out-of-equilibrium quantum systems. We illustrate our approach using a model for a forefront quantum simulation platform: ultracold atoms in optical lattices. Specifically, we show that our algorithm is able to reconstruct the Hamiltonian of an arbitrary sized bosonic ladder system using an accessible amount of experimental measurements. We are able to significantly increase the previously known parameter precision.

The prediction of measurement outcomes from an underlying structure often follows directly from fundamental physical principles. However, a fundamental challenge is posed when trying to solve the inverse problem of inferring the underlying source configuration based on measurement data. A key difficulty arises from the fact that such reconstructions often involve ill-posed transformations and that they are prone to numerical artifacts. Here, we develop a numerically efficient method to tackle this inverse problem for the reconstruction of magnetization maps from measured magnetic stray-field images. Our method is based on neural networks with physically inferred loss functions to efficiently eliminate common numerical artifacts. We report on a significant improvement in reconstruction over traditional methods and we show that our approach is robust to different magnetization directions, both in and out of plane, and to variations of the magnetic field measurement-axis orientation. While we showcase the performance of our method using magnetometry with nitrogen-vacancy center spins in diamond, our neural-network-based approach to solving inverse problems is agnostic to the measurement technique and thus is applicable beyond the specific use case demonstrated in this work.

Variational methods have proven to be excellent tools to approximate the ground states of complex many-body Hamiltonians. Generic tools such as neural networks are extremely powerful, but their parameters are not necessarily physically motivated. Thus, an efficient parametrization of the wave function can become challenging. In this Letter we introduce a neural-network-based variational ansatz that retains the flexibility of these generic methods while allowing for a tunability with respect to the relevant correlations governing the physics of the system. We illustrate the success of this approach on topological, long-range correlated, and frustrated models. Additionally, we introduce compatible variational optimization methods for the exploration of low-lying excited states without symmetries that preserve the interpretability of the ansatz.

With the lockdowns caused by the COVID-19 pandemic, researchers turn to online conferencing. While posing new challenges, this format also brings multiple advantages. We argue that virtual conferences will become part of our regular scientific communication and invite community members to join the movement.