Understanding collective phases of strongly correlated quantum magnets relies on theoretically tractable model systems with precise microscopic control. Antiferromagnetic spin ladders provide such a setting, hosting field-tunable gapped and gapless phases at half filling and unconventional pairing tendencies upon doping. Here, we realize a programmable Heisenberg spin ladder in a half-filled germanium quantum dot array featuring site-resolved, continuously tunable exchange interactions. Under a fixed magnetic field, we vary the rung and leg coupling to map the rung-singlet, canted antiferromagnetic, and fully polarized phases. Hamiltonian-learning protocols combining equilibrium and dynamical measurements quantitatively characterize the ladder, incorporating spin-orbit interactions to reproduce the observed crossover behavior. Measurements of higher-order spin correlators – including four-point correlations inaccessible to conventional bulk probes – reveal signatures of the underlying phase structure despite the finite size. Our results establish germanium quantum dot arrays as a controllable platform for quantum magnetism, opening routes to investigate unconventional superconductivity in doped ladders.

Quantum simulators enable studies of many-body phenomena, which are intractable with classical hardware. The manipulation of electronic spin states in devices based on semiconductor quantum dots promises precise electrical control and scalability advantages, but accessing many-body phenomena has so far been restricted by challenges in nanofabrication and simultaneous control of multiple interactions. In this study, we performed spectroscopy of up to eight interacting spins using a 2-×-4 array of gate-defined germanium quantum dots. The spectroscopy protocol is based on Ramsey interferometry and adiabatic mapping of many-body eigenstates to single-spin eigenstates, enabling complete energy spectrum reconstruction. As the interaction strength exceeds magnetic disorder, we observed signatures of the crossover from localization to a chaotic phase marking a step toward the observation of many-body phenomena in quantum dot systems.

Quasi-particle dynamics in interacting systems in the presence of disorder challenges the notion of internal thermalization, but proves difficult to investigate theoretically for large particle numbers. Engineered quantum systems may offer a viable alternative, as witnessed in experimental demonstrations in a variety of physical platforms, each with its own capabilities and limitations. Semiconductor gate-defined quantum dot arrays are of particular interest since they offer both a direct mapping of their Hamiltonian to Fermi-Hubbard and Heisenberg models and the in-situ tunability of (magnetic) interactions and onsite potentials. In this work, we use an array of germanium quantum dots to simulate the dynamics of both single-spin excitations (magnons) and two-spin excitations (triplons). We develop a methodology that combines digital spin qubit operations for state preparation and readout with analog evolution under the full system Hamiltonian. Using these techniques, we can reconstruct quantum walk plots for both magnons and triplons, and for various configurations of Heisenberg exchange couplings. We furthermore explore the effect of single-site disorder and its impact on the propagation of spin excitations. The obtained results can provide a basis for simulating disorder-based solid-state phenomena such as many-body localization.

Coupled spins in semiconductor quantum dots are a versatile platform for quantum computing and simulations of complex many-body phenomena. However, on the path of scale-up, cross-talk from densely packed electrodes poses a severe challenge. While cross-talk onto the dot potentials is nowadays routinely compensated for, cross-talk on the exchange interaction is much more difficult to tackle because it is not always directly measurable. Here we propose and implement a way of characterizing and compensating cross-talk on adjacent exchange interactions by following the singlet-triplet avoided crossing in Ge. We show that we can easily identify the barrier-to-barrier cross-talk element without knowledge of the particular exchange value in a 2x4 quantum dot array. We uncover striking differences among these cross-talk elements which can be linked to the geometry of the device and the barrier gate fan-out. We validate the methodology by tuning up four-spin Heisenberg chains. The same methodology should be applicable to longer chains of spins and to other semiconductor platforms in which mixing of the singlet and the lowest-energy triplet is present or can be engineered. Additionally, this procedure is well suited for automated tuning routines as we obtain a stand-out feature that can be easily tracked and directly returns the magnitude of the cross-talk.

Hole spin qubits are emerging as the workhorse of semiconducting quantum processors because of their large spin-orbit interaction, enabling fast, low-power, all-electric operations. However, this interaction also causes non-uniformities, resulting in site-dependent qubit energies and anisotropies. Although these anisotropies enable single-spin control, if not properly harnessed, they can hinder scalability. Here, we report on microwave-driven singlet-triplet qubits in planar germanium and use them to investigate spin anisotropies. For in-plane magnetic fields, the spins are largely anisotropic and electrically tunable, allowing access to all transitions and coherence times exceeding 3 μs are extracted. For out-of-plane fields they have an isotropic response. Even in this field direction, where the qubit lifetime is strongly affected by nuclear spins, we find 400 ns coherence times. Our work adds a valuable tool to investigate and harness the spin anisotropies, applicable to two-dimensional devices, facilitating the path towards scalable quantum processors.

The conversion of thermal energy into work is usually more efficient in the slow-driving regime, where the power output is vanishingly small. Efficient work extraction for fast-driving protocols remains an outstanding challenge at the nanoscale, where fluctuations play a significant role. In this Letter, we use a quantum-dot Szilard engine to extract work from thermal fluctuations with maximum efficiency over two decades of driving speed. We design and implement a family of optimized protocols ranging from the slow- to the fast-driving regime, and we measure the engine's efficiency as well as the mean and variance of its power output in each case. These optimized protocols exhibit significant improvements in power and efficiency compared to the naive approach. Our results also show that, when optimizing for efficiency, boosting the power output of a Szilard engine inevitably comes at the cost of increased power fluctuations.

We experimentally realize a quantum clock by using a charge sensor to count charges tunneling through a double quantum dot (DQD). Individual tunneling events are used as the clock's ticks. We quantify the clock's precision while measuring the power dissipated by the DQD and, separately, the charge sensor in both direct-current and radio-frequency readout modes. This allows us to probe the thermodynamic cost of creating ticks microscopically and recording them macroscopically. Our experiment is the first to explore the interplay between the entropy produced by a microscopic clockwork and its macroscopic measurement apparatus. We show that the latter contribution not only dwarfs the former but also unlocks greatly increased precision, because the measurement record can be exploited to optimally estimate time even when the DQD is at equilibrium. Our results suggest that the entropy produced by the amplification and measurement of a clock's ticks, which has often been ignored in the literature, is the most important and fundamental thermodynamic cost of timekeeping at the quantum scale.

Radio-frequency measurements could satisfy DiVincenzo’s readout criterion in future large-scale solid-state quantum processors, as they allow for high bandwidths and frequency multiplexing. However, the scalability potential of this readout technique can only be leveraged if quantum device tuning is performed using exclusively radio-frequency measurements, that is, without resorting to current measurements. We demonstrate an algorithm that performs automatic coarse tuning of double quantum dots with only radio-frequency measurements by exploiting their bandwidth and impedance matching. The tuning was completed within a few minutes with minimal prior knowledge about the device. Our results show that it is possible to eliminate the need for transport measurements for quantum-dot tuning, paving the way for more scalable device architectures.

The coherent control of interacting spins in semiconductor quantum dots is of strong interest for quantum information processing as well as for studying quantum magnetism from the bottom up. On paper, individual spin-spin couplings can be independently controlled through gate voltages, but nonlinearities and crosstalk introduce significant complexity that has slowed down progress in past years. Here, we present a 2×4 germanium quantum dot array with full and controllable interactions between nearest-neighbor spins. As a demonstration of the level of control, we define four singlet-triplet qubits in this system and show two-axis single-qubit control of each qubit and SWAP-style two-qubit gates between all neighbouring qubit pairs. Combining these operations, we experimentally implement a circuit designed to generate and distribute entanglement across the array. These results highlight the potential of singlet-triplet qubits as a competing platform for quantum computing and indicate that scaling up the control of quantum dot spins in extended bilinear arrays can be feasible.

Charge sensing is a sensitive technique for probing quantum devices, of particular importance for spin qubit readout. To achieve good readout sensitivities, the proximity of the charge sensor to the device to be measured is a necessity. However, this proximity also means that the operation of the device affects, in turn, the sensor tuning and ultimately the readout sensitivity. We present an approach for compensating for this cross-talk effect allowing for the gate voltages of the measured device to be swept in a 1 V x 1 V window while maintaining a sensor configuration chosen by a Bayesian optimiser. Our algorithm is a key contribution to the suite of fully automated solutions required for the operation of large quantum device architectures.

Quantum systems with engineered Hamiltonians can be used as simulators of many-body physics problems to provide insights beyond the capabilities of classical computers. Semiconductor gate-defined quantum dot arrays have emerged as a versatile platform for quantum simulation of generalized Fermi-Hubbard physics, one of the richest playgrounds in condensed matter physics. In this work, we employ a germanium 4$\times$2 quantum dot array and show that the naturally occurring long-range Coulomb interaction can lead to exciton formation and transport. We tune the quantum dot ladder into two capacitively-coupled channels and exploit Coulomb drag to probe the binding of electrons and holes. Specifically, we shuttle an electron through one leg of the ladder and observe that a hole is dragged along in the second leg under the right conditions. This corresponds to a transition from single-electron transport in one leg to exciton transport along the ladder. Our work paves the way for the study of excitonic states of matter in quantum dot arrays.

The potential of Si and SiGe-based devices for the scaling of quantum circuits is tainted by device variability. Each device needs to be tuned to operation conditions and each device realisation requires a different tuning protocol. We demonstrate that it is possible to automate the tuning of a 4-gate Si FinFET, a 5-gate GeSi nanowire and a 7-gate Ge/SiGe heterostructure double quantum dot device from scratch with the same algorithm. We achieve tuning times of 30, 10, and 92 min, respectively. The algorithm also provides insight into the parameter space landscape for each of these devices, allowing for the characterization of the regions where double quantum dot regimes are found. These results show that overarching solutions for the tuning of quantum devices are enabled by machine learning.

The spin-orbit interaction permits to control the state of a spin qubit via electric fields. For holes it is particularly strong, allowing for fast all electrical qubit manipulation, and yet an in-depth understanding of this interaction in hole systems is missing. Here we investigate, experimentally and theoretically, the effect of the cubic Rashba spin-orbit interaction on the mixing of the spin states by studying singlet-triplet oscillations in a planar Ge hole double quantum dot. Landau-Zener sweeps at different magnetic field directions allow us to disentangle the effects of the spin-orbit induced spin-flip term from those caused by strongly site-dependent and anisotropic quantum dot g tensors. Our work, therefore, provides new insights into the hole spin-orbit interaction, necessary for optimizing future qubit experiments.

Spin qubits are considered to be among the most promising candidates for building a quantum processor. Group IV hole spin qubits are particularly interesting owing to their ease of operation and compatibility with Si technology. In addition, Ge offers the option for monolithic superconductor–semiconductor integration. Here, we demonstrate a hole spin qubit operating at fields below 10 mT, the critical field of Al, by exploiting the large out-of-plane hole g-factors in planar Ge and by encoding the qubit into the singlet-triplet states of a double quantum dot. We observe electrically controlled g-factor difference-driven and exchange-driven rotations with tunable frequencies exceeding 100 MHz and dephasing times of 1 μs, which we extend beyond 150 μs using echo techniques. These results demonstrate that Ge hole singlet-triplet qubits are competing with state-of-the-art GaAs and Si singlet-triplet qubits. In addition, their rotation frequencies and coherence are comparable with those of Ge single spin qubits, but singlet-triplet qubits can be operated at much lower fields, emphasizing their potential for on-chip integration with superconducting technologies. A singlet-triplet spin qubit using holes in a Ge quantum well is demonstrated, and can be operated at low magnetic fields of a few millitesla.

Hole gases in planar germanium can have high mobilities in combination with strong spin-orbit interaction and electrically tunable g-factors, and are therefore emerging as a promising platform for creating hybrid superconductor-semiconductor devices. A key challenge towards hybrid Ge-based quantum technologies is the design of high-quality interfaces and superconducting contacts that are robust against magnetic fields. In this work, by combining the assets of aluminum, which provides good contact to the Ge, and niobium, which has a significant superconducting gap, we demonstrate highly transparent low-disordered JoFETs with relatively large \IcRn \ products that are capable of withstanding high magnetic fields. We furthermore demonstrate the ability of phase-biasing individual JoFETs, opening up an avenue to explore topological superconductivity in planar Ge. The persistence of superconductivity in the reported hybrid devices beyond 1.8 Tesla paves the way towards integrating spin qubits and proximity-induced superconductivity on the same chip.