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.

The strong spin-orbit interaction in silicon and germanium hole quantum dots enables all-electric microwave control of single spins but is unsuited for multispin exchange-only qubits that rely on scalable discrete signals to suppress crosstalk and heating effects in large quantum processors. Here, we propose an exchange-only spin-orbit qubit that utilizes spin-orbit interactions to implement qubit gates and keeps the beneficial properties of the original encoding. Our encoding is robust to significant local variability in hole spin properties and, because it operates with two degenerate states, it eliminates the need for the rotating frame, avoiding the technologically demanding constraints of fast clocks and precise signal calibration. Unlike current exchange-only qubits, which require complex multistep sequences prone to leakage, our qubit design enables low-leakage two-qubit gates in a single step, addressing critical challenges in scaling spin qubits.

The scalability and power of quantum computing architectures depend critically on high-fidelity operations and robust and flexible qubit connectivity^{1, 2–3}. In this respect, mobile qubits are particularly attractive as they enable dynamic and reconfigurable qubit arrays. This approach allows quantum processors to adapt their connectivity patterns during operation, implement different quantum error correction codes on the same hardware and optimize resource use through dedicated functional zones for specific operations such as measurement or entanglement generation^{4, 5, 6–7}. Such flexibility also relieves architectural constraints, as recently demonstrated in atomic systems based on trapped ions^4,5 and neutral atoms manipulated with optical tweezers^6,7. In solid-state platforms, highly coherent shuttling of electron spins was recently reported^8,9. A key outstanding question is whether it may be possible to perform quantum gates directly on the mobile spins. Here we demonstrate two-qubit operations between two electron spins carried towards each other in separate travelling potential minima in a semiconductor device. We find that the interaction strength is highly tunable by their spatial separation. When we shuttle the two spins towards the centre by 120 nm each for a total displacement of 240 nm, we achieve an average two-qubit gate fidelity of about 99%. Furthermore, we implement conditional post-selected quantum state teleportation between qubits separated by 320 nm with an average gate fidelity of 87%, showcasing the potential of mobile spin qubits for non-local quantum information processing. We expect that operations on mobile qubits will become a universal feature of future large-scale semiconductor quantum processors.

Efficient adiabatic control schemes, where one steers a quantum system along an adiabatic path ensuring minimal excitations while achieving a desired final state, that enable fast, high-fidelity operations are essential for any practical quantum computation. However, current optimization protocols are not universally tractable due to stringent requirements imposed by the microscopic systems encoding the qubit, including complex energy level structures and unwanted transitions, and generally require a trade-off between speed and fidelity of the operation. Here, we address these challenges by developing a general framework for optimal control based on the quantum metric tensor. This framework allows for fast and high-fidelity adiabatic pulses, even for a dense energy spectrum, based solely on the Hamiltonian of the system instead of the time evolution propagator and independent of the size of the underlying Hilbert space. Furthermore, our framework suppresses diabatic transitions and state-dependent crosstalk effects without the need for additional control fields. As an example, we study the adiabatic charge transfer in a double quantum dot to find optimal control pulses with improved performance. We show that for the geometric protocol, the transfer fidelities are lower bounded F>99% for ultrafast 20ns pulses, regardless of the size of the anti-crossing, while being robust against miscalibration errors and quasistatic noise.

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.

Quantum computers require the systematic operation of qubits with high fidelity. For holes in germanium, the spin-orbit interaction allows for electric, fast and high-fidelity qubit gates. However, the strong g-tensor anisotropy of holes in germanium and their sensitivity to the operational and environmental conditions challenge the operation of large qubit arrays. Here, we investigate a two-dimensional 10-spin qubit array with single-qubit gate fidelities above 99%, and obtain surprisingly uniform qubit properties. By tuning the hole occupation, we demonstrate control over the spin susceptibility, enabling fast plunger gate driving with Rabi frequencies consistently above 1.45 MHz/ (mV ⋅ T). Moreover, we probe the locality of electric dipole spin resonance and find that the configuration with three-hole occupancy driven by the associated quantum dot plunger gate reduces crosstalk, lowering it by an average factor of 2.5 to nearest neighbours, compared to single-hole plunger driving. Theoretical modelling points towards the pronounced anisotropy of p-like orbitals as the main mechanism with significant contributions through Coulomb interactions, giving directions for reproducible control of large qubit arrays.

Electron-spin qubits in Si/SiGe quantum wells are limited by the small and variable energy separation of the conduction-band valleys. While sharp quantum-well interfaces are pursued to increase the valley-splitting energy deterministically, here we explore an alternative approach to enhancing the valley splitting on average. We grow increasingly thinner quantum wells with broad interfaces to controllably increase the electron wave function overlap with Ge atoms. Quantum Hall measurements of two-dimensional electron gases reveal a linear correlation between valley splitting and disorder-induced single-particle energy-level broadening, driven by increasing alloy scattering at the Si/SiGe interface. We demonstrate enhanced valley splitting while maintaining respectable electron mobility, indicating a low-disorder electrostatic potential environment. Simulations using experimental Ge concentration profiles predict an average valley splitting in quantum dots that matches the enhancement observed in two-dimensional systems. Our results motivate the experimental realization of quantum-dot spin qubits in these heterostructures.

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.

All-electrical baseband control of qubits facilitates scaling up quantum processors by removing issues of crosstalk and heat generation. In semiconductor quantum dots, this is enabled by multispin qubit encodings, such as the exchange-only qubit. However, their performance is limited by unavoidable leakage states that are energetically close to the computational subspace. In this Letter, we introduce an alternative, scalable spin qubit architecture that leverages strong spin-orbit interactions of hole nanostructures for baseband qubit operations while completely eliminating leakage channels and reducing the overall gate overhead. This encoding is intrinsically robust to local variability in hole spin properties and operates with two degenerate states, removing the need for precise calibration and mitigating heat generation from fast signal sources. Finally, our architecture is fully compatible with current technology, utilizing the same initialization, readout, and multiqubit protocols of state-of-The-Art spin-1/2 systems. By addressing critical scalability challenges, our design offers a robust and scalable pathway for semiconductor spin qubit technologies.

Qubits that can be efficiently controlled are essential for the development of scalable quantum hardware. Although resonant control is used to execute high-fidelity quantum gates, the scalability is challenged by the integration of high-frequency oscillating signals, qubit cross-talk, and heating. Here, we show that by engineering the hopping of spins between quantum dots with a site-dependent spin quantization axis, quantum control can be established with discrete signals. We demonstrate hopping-based quantum logic and obtain single-qubit gate fidelities of 99.97%, coherent shuttling fidelities of 99.992% per hop, and a two-qubit gate fidelity of 99.3%, corresponding to error rates that have been predicted to allow for quantum error correction. We also show that hopping spins constitute a tuning method by statistically mapping the coherence of a 10-quantum dot system. Our results show that dense quantum dot arrays with sparse occupation could be developed for efficient and high-connectivity qubit registers.

Direct interactions between quantum particles naturally fall off with distance. However, future quantum computing architectures are likely to require interaction mechanisms between qubits across a range of length scales. In this work, we demonstrate a coherent interaction between two semiconductor spin qubits 250 μm apart using a superconducting resonator. This separation is several orders of magnitude larger than for the commonly used direct interaction mechanisms in this platform. We operate the system in a regime in which the resonator mediates a spin–spin coupling through virtual photons. We report the anti-phase oscillations of the populations of the two spins with controllable frequency. The observations are consistent with iSWAP oscillations of the spin qubits, and suggest that entangling operations are possible in 10 ns. These results hold promise for scalable networks of spin qubit modules on a chip.

Micromagnet-based electric dipole spin resonance offers an attractive path for the near-term scaling of dense arrays of silicon spin qubits in gate-defined quantum dots while maintaining long coherence times and high control fidelities. However, accurately controlling dense arrays of qubits using a multiplexed drive will require an understanding of the cross-talk mechanisms that may reduce operational fidelity. We identify an unexpected cross-talk mechanism whereby the Rabi frequency of a driven qubit is drastically changed when the drive of an adjacent qubit is turned on. These observations raise important considerations for scaling single-qubit control.

Practical Quantum computing hinges on the ability to control large numbers of qubits with high fidelity. Quantum dots define a promising platform due to their compatibility with semiconductor manufacturing. Moreover, high-fidelity operations above 99.9% have been realized with individual qubits, though their performance has been limited to 98.67% when driving two qubits simultaneously. Here we present single-qubit randomized benchmarking in a two-dimensional array of spin qubits, finding native gate fidelities as high as 99.992(1)%. Furthermore, we benchmark single qubit gate performance while simultaneously driving two and four qubits, utilizing a novel benchmarking technique called N-copy randomized benchmarking, designed for simple experimental implementation and accurate simultaneous gate fidelity estimation. We find two- and four-copy randomized benchmarking fidelities of 99.905(8)% and 99.34(4)% respectively, and that next-nearest neighbor pairs are highly robust to cross-talk errors. These characterizations of single-qubit gate quality are crucial for scaling up quantum information technology.

Semiconductor spin qubits demonstrated single-qubit gates with fidelities up to 99.9 % benchmarked in the single-qubit subspace. However, tomographic characterizations reveal non-negligible crosstalk errors in a larger space. Additionally, it was long thought that the two-qubit gate performance is limited by charge noise, which couples to the qubits via the exchange interaction. Here, we show that coherent error sources such as a limited bandwidth of the control signals, diabaticity errors, microwave crosstalk, and non-linear transfer functions can equally limit the fidelity. We report a simple theoretical framework for pulse optimization that relates erroneous dynamics to spectral concentration problems and allows for the reuse of existing signal shaping methods on a larger set of gate operations. We apply this framework to common gate operations for spin qubits and show that simple pulse shaping techniques can significantly improve the performance of these gate operations in the presence of such coherent error sources. The methods presented in the paper were used to demonstrate two-qubit gate fidelities with F > 99.5 % in Xue et al (2022 Nature 601 343). We also find that single and two-qubit gates can be optimized using the same pulse shape. We use analytic derivations and numerical simulations to arrive at predicted gate fidelities greater than 99.9% with duration less than, 4 / ( Δ E z ) where Δ E z is the difference in qubit frequencies.

We report observations of transitions between excited states in the Jaynes-Cummings ladder of circuit quantum electrodynamics with electron spins (spin circuit QED). We show that unexplained features in recent experimental work correspond to such transitions and present an input-output framework that includes these effects. In new experiments, we first reproduce previous observations and then reveal both excited-state transitions and multiphoton transitions by increasing the probe power and using two-tone spectroscopy. This ability to probe the Jaynes-Cummings ladder is enabled by improvements in the coupling-to-decoherence ratio, and shows an increase in the maturity of spin circuit QED as an interesting platform for studying quantum phenomena.