Dynamical decoupling is a central technique in quantum computing for actively suppressing decoherence and systematic imperfections through sequences of single-qubit operations. Conventional sequences typically aim to completely freeze system dynamics, often resulting in long protocols whose length scales exponentially with system size. In this work, we introduce a general framework for constructing time-optimal, selectively tailored sequences that remove only specific local interactions. By combining techniques from graph coloring and classical coding theory, our approach enables compact and hardware-tailored sequences across diverse qubit platforms, efficiently canceling undesired Hamiltonian terms while preserving target interactions. This opens up broad applications in quantum computing and simulation. At the core of our method is a mapping between dynamical decoupling sequence design and error-detecting codes, which allows us to leverage powerful coding-theoretic tools to construct customized sequences. To overcome exponential overheads, we exploit symmetries in colored interaction hypergraphs, extending graph-coloring strategies to arbitrary many-body Hamiltonians. We demonstrate the effectiveness of our framework through concrete examples, including compact sequences that suppress residual ZZ and ZZZ interactions in superconducting qubits and Heisenberg exchange coupling in spin qubits. We also show how it enables Hamiltonian engineering by simulating the anisotropic Kitaev honeycomb model using only isotropic Heisenberg interactions.

A fundamental challenge in quantum computing is to increase the number of operations within the qubit coherence time. While this can be achieved by decreasing the gate duration, the use of shorter signals increases their bandwidth and can cause leakage into energetically separated states. A common method to suppress leakage for short pulses is the Derivative Removal by Adiabatic Gate (DRAG) method, which, however, relies on IQ modulation of radio-frequency (RF) signals, thus cannot be applied to the baseband signals, e.g., for semiconductor spin qubits. This paper proposes a novel technique, Delayed Leakage Reduction (DLR), that suppresses leakage at targeted frequencies even for baseband control by using time-delayed repetitions of the control signal to enable rapid, high-fidelity operations. We apply DLR on the adiabatic CZ gate between two spin qubits and achieve fidelities exceeding 99.9% within 9.4 ns for a resonance frequency difference of only 100 MHz. Towards the experimental realization of the proposed control method, we also assess the impact on the fidelity of the sampling rate, noise, and signal quantization of the electronic hardware generating the control pulse, thus setting the minimum hardware requirements for any experimental demonstration.

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 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.

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.

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.

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.

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.

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.

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.

Coherent links between qubits separated by tens of micrometers are expected to facilitate scalable quantum computing architectures for spin qubits in electrically defined quantum dots. These links create space for classical on-chip control electronics between qubit arrays, which can help to alleviate the so-called wiring bottleneck. A promising method of achieving coherent links between distant spin qubits consists of shuttling the spin through an array of quantum dots. Here, we use a linear array of four tunnel-coupled quantum dots in a 28Si/SiGe heterostructure to create a short quantum link. We move an electron spin through the quantum dot array by adjusting the electrochemical potential for each quantum dot sequentially. By pulsing the gates repeatedly, we shuttle an electron forward and backward through the array up to 250 times, which corresponds to a total distance of approximately 80μm. We make an estimate of the spin-flip probability per hop in these experiments and conclude that this is well below 0.01% per hop.