The simplicity of encoding a qubit in the state of a single electron spin and the potential for their integration into industry-standard microchips continue to drive the field of semiconductor-based quantum computing. After a series of key first-principles demonstrations validating universal gate operations, initialization and readout, three-qubit algorithms have already been realized with silicon-based quantum dots in past years. Devices containing more qubits have become available since then but experiments have not gone beyond meeting the DiVincenzo criteria. In this work, we fully exploit the capacity of a spin-qubit array and implement a six-qubit quantum circuit, the largest utilizing semiconductor quantum technology. By programming the quantum processor, we execute quantum circuits across all permutations of three, four, five, and six neighboring qubits, demonstrating successful programmable multi-qubit operation throughout the array. Using an error model that incorporates quasi-static noise allows us to qualitatively explain some key trends in our experimental results and highlight the necessity to minimize idling times through simultaneous operations, extending dephasing times, and consistently improving state preparation and measurement fidelities.

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.

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, crosstalk from densely packed electrodes poses a severe challenge. While crosstalk onto the quantum dot potentials is nowadays routinely compensated for, crosstalk 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 crosstalk on adjacent exchange interactions by following the singlet-triplet avoided crossing in Ge. We show that we can easily identify the barrier-to-barrier crosstalk element without knowledge of the particular exchange value in a 2×4 quantum dot array. We uncover striking differences among these crosstalk elements that can be linked to the geometry of the device and the barrier gate fan-out. We validate the method by tuning up four-spin Heisenberg chains. The same method 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 standout feature that can be easily tracked and directly returns the magnitude of the crosstalk.

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.

Micromagnet-enabled electric-dipole spin resonance (EDSR) is an established method for high-fidelity single-spin control in silicon, although so far experiments have been restricted to one-dimensional arrays. In contrast, qubit control based on hopping spins has recently emerged as a compelling alternative, with high-fidelity baseband control realized in sparse two-dimensional hole arrays in germanium. In this work, we commission a ²⁸Si/SiGe 2 × 2 quantum dot array both as a four-qubit device using EDSR and as a two-qubit device using baseband hopping control. We establish a lower bound on the fidelity of the hopping gate of 99.50(6)%, which is similar to the average fidelity of the resonant gate. The hopping gate also circumvents the transient pulse-induced resonance shift from heating observed during EDSR operation. To motivate hopping spins as an attractive means of scaling silicon spin-qubit arrays, we propose an extensible nanomagnet design that enables engineered baseband control of large spin arrays.

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.

As spin-based quantum processors grow in size and complexity, maintaining high fidelities and minimizing crosstalk will be essential for the successful implementation of quantum algorithms and error-correction protocols. In particular, recent experiments have highlighted pernicious transient qubit frequency shifts associated with microwave qubit driving. Work-Arounds for small devices, including prepulsing with an off-resonant microwave burst to bring a device to a steady state, wait times prior to measurement, and qubit-specific calibrations all bode ill for device scalability. Here, we make substantial progress in understanding and overcoming this effect. We report a surprising nonmonotonic relation between mixing chamber temperature and spin Larmor frequency which is consistent with observed frequency shifts induced by microwave and baseband control signals. We find that purposefully operating the device at 200 mK greatly suppresses the adverse heating effect while not compromising qubit coherence or single-qubit fidelity benchmarks. Furthermore, systematic non-Markovian crosstalk is greatly reduced. Our results provide a straightforward means of improving the quality of multispin control while simplifying calibration procedures for future spin-based quantum processors.

Semiconductor spin qubits have gained increasing attention as a possible platform to host a fault-tolerant quantum computer. First demonstrations of spin qubit arrays have been shown in a wide variety of semiconductor materials. The highest performance for spin qubit logic has been realized in silicon, but scaling silicon quantum dot arrays in two dimensions has proven to be challenging. By taking advantage of high-quality heterostructures and carefully designed gate patterns, we are able to form a tunnel coupled 2 × 2 quantum dot array in a ²⁸Si/SiGe heterostructure. We are able to load a single electron in all four quantum dots, thus reaching the (1,1,1,1) charge state. Furthermore, we characterize and control the tunnel coupling between all pairs of dots by measuring polarization lines over a wide range of barrier gate voltages. Tunnel couplings can be tuned from about 30 μ eV up to approximately 400 μ eV . These experiments provide insightful information on how to design 2D quantum dot arrays and constitute a first step toward the operation of spin qubits in ²⁸Si/SiGe quantum dots in two dimensions.

The efficient control of a large number of qubits is one of the most challenging aspects for practical quantum computing. Current approaches in solid-state quantum technology are based on brute-force methods, where each and every qubit requires at least one unique control line—an approach that will become unsustainable when scaling to the required millions of qubits. Here, inspired by random-access architectures in classical electronics, we introduce the shared control of semiconductor quantum dots to efficiently operate a two-dimensional crossbar array in planar germanium. We tune the entire array, comprising 16 quantum dots, to the few-hole regime. We then confine an odd number of holes in each site to isolate an unpaired spin per dot. Moving forward, we demonstrate on a vertical and a horizontal double quantum dot a method for the selective control of the interdot coupling and achieve a tunnel coupling tunability over more than 10 GHz. The operation of a quantum electronic device with fewer control terminals than tunable experimental parameters represents a compelling step forward in the construction of scalable quantum technology.

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.

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.

Future quantum computers capable of solving relevant problems will require a large number of qubits that can be operated reliably1. However, the requirements of having a large qubit count and operating with high fidelity are typically conflicting. Spins in semiconductor quantum dots show long-term promise2,3 but demonstrations so far use between one and four qubits and typically optimize the fidelity of either single- or two-qubit operations, or initialization and readout4-11. Here, we increase the number of qubits and simultaneously achieve respectable fidelities for universal operation, state preparation and measurement. We design, fabricate and operate a six-qubit processor with a focus on careful Hamiltonian engineering, on a high level of abstraction to program the quantum circuits, and on efficient background calibration, all of which are essential to achieve high fidelities on this extended system. State preparation combines initialization by measurement and real-time feedback with quantum-non-demolition measurements. These advances will enable testing of increasingly meaningful quantum protocols and constitute a major stepping stone towards large-scale quantum computers.

The prospect of building quantum circuits^1,2 using advanced semiconductor manufacturing makes quantum dots an attractive platform for quantum information processing^3,4. Extensive studies of various materials have led to demonstrations of two-qubit logic in gallium arsenide⁵, silicon^6–12 and germanium¹³. However, interconnecting larger numbers of qubits in semiconductor devices has remained a challenge. Here we demonstrate a four-qubit quantum processor based on hole spins in germanium quantum dots. Furthermore, we define the quantum dots in a two-by-two array and obtain controllable coupling along both directions. Qubit logic is implemented all-electrically and the exchange interaction can be pulsed to freely program one-qubit, two-qubit, three-qubit and four-qubit operations, resulting in a compact and highly connected circuit. We execute a quantum logic circuit that generates a four-qubit Greenberger−Horne−Zeilinger state and we obtain coherent evolution by incorporating dynamical decoupling. These results are a step towards quantum error correction and quantum simulation using quantum dots.