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Efficient scaling and flexible control are key aspects of useful quantum computing hardware. Spins in semiconductors combine quantum information processing with electrons, holes or nuclei, control with electric or magnetic fields, and scalable coupling via exchange or dipole interaction. However, accessing large Hilbert space dimensions has remained challenging, due to the short-distance nature of the interactions. Here, we present an atom-based semiconductor platform where a 16-dimensional Hilbert space is built by the combined electron-nuclear states of a single antimony donor in silicon. We demonstrate the ability to navigate this large Hilbert space using both electric and magnetic fields, with gate fidelity exceeding 99.8% on the nuclear spin, and unveil fine details of the system Hamiltonian and its susceptibility to control and noise fields. These results establish high-spin donors as a rich platform for practical quantum information and to explore quantum foundations. Qudits, higher-dimensional analogues of qubits, expand quantum state space for information processing using fewer physical units. Here the authors demonstrate control over a 16-dimensional Hilbert space, equivalent to four qubits, using combined electron-nuclear states of a single Sb donor atom in Si.

Silicon nanoelectronic devices can host single-qubit quantum logic operations with fidelity better than 99.9%. For the spins of an electron bound to a single-donor atom, introduced in the silicon by ion implantation, the quantum information can be stored for nearly 1 second. However, manufacturing a scalable quantum processor with this method is considered challenging, because of the exponential sensitivity of the exchange interaction that mediates the coupling between the qubits. Here we demonstrate the conditional, coherent control of an electron spin qubit in an exchange-coupled pair of 31 P donors implanted in silicon. The coupling strength, J  = 32.06 ± 0.06 MHz, is measured spectroscopically with high precision. Since the coupling is weaker than the electron-nuclear hyperfine coupling A  ≈ 90 MHz which detunes the two electrons, a native two-qubit controlled-rotation gate can be obtained via a simple electron spin resonance pulse. This scheme is insensitive to the precise value of J , which makes it suitable for the scale-up of donor-based quantum computers in silicon that exploit the metal-oxide-semiconductor fabrication protocols commonly used in the classical electronics industry. Operating donor-based quantum computers in silicon is hindered by the dependence of inter-qubit coupling on the precise donor position. Here, the authors show controlled rotation operation on exchange-coupled electron spins in the weak-exchange regime, loosening the requirements on positioning precision.

Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal one- and two-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity 91.3 ± 3.0%, and concurrence 0.87 ± 0.05. These results form the necessary basis for scaling up donor-based quantum computers. Donors spins in silicon are coherent, high-performance qubits, but scale-up has been challenging. Here the authors present the first experimental demonstration of exchange-based, entangling two qubit gates between electrons bound to 31 P donors in Si.

Fault-tolerant quantum computing requires initializing the quantum register in a well-defined fiducial state. In solid-state systems, this is typically achieved through thermalization to a cold reservoir, such that the initialization fidelity is fundamentally limited by temperature. Here, we present a method of preparing a fiducial quantum state with a confidence beyond the thermal limit. It is based on real-time monitoring of the qubit through a negative-result measurement—the equivalent of a “Maxwell’s demon” that triggers the experiment only upon the appearance of a qubit in the lowest-energy state. We experimentally apply it to initialize an electron spin qubit in silicon, achieving a ground-state initialization fidelity of 98.9(4)%, corresponding to a20×reduction in initialization error compared to the unmonitored system. A fidelity approaching 99.9% could be achieved with realistic improvements in the bandwidth of the amplifier chain or by slowing down the rate of electron tunneling from the reservoir. We use a nuclear spin ancilla, measured in quantum nondemolition mode, to prove the value of the electron initialization fidelity far beyond the intrinsic fidelity of the electron readout. However, the method itself does not require an ancilla for its execution, saving the need for additional resources. The quantitative analysis of the initialization fidelity reveals that a simple picture of spin-dependent electron tunneling does not correctly describe the data. Our digital Maxwell’s demon can be applied to a wide range of quantum systems, with minimal demands on control and detection hardware.

Nuclear spins were among the first physical platforms to be considered for quantum information processing 1 , 2 , because of their exceptional quantum coherence 3 and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, owing to the lack of methods with which to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted 31 P donor nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled- Z gate is obtained by imparting a geometric phase to a shared electron spin 4 , and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterized using gate set tomography (GST) 5 , yielding one-qubit average gate fidelities up to 99.95(2)%, two-qubit average gate fidelity of 99.37(11)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors 6 . We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger–Horne–Zeilinger three-qubit state with 92.5(1.0)% fidelity. Because electron spin qubits in semiconductors can be further coupled to other electrons 7 – 9 or physically shuttled across different locations 10 , 11 , these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins. Universal quantum logic operations with fidelity exceeding 99%, approaching the threshold of fault tolerance, are realized in a scalable silicon device comprising an electron and two phosphorus nuclei, and a fidelity of 92.5% is obtained for a three-qubit entangled state.

Ferromagnetic shape memory alloys are characterized by strong magneto-mechanical coupling occurring at the atomic scale causing large magnetically inducible strains at the macroscopic level. Employing combined atomic and magnetic force microscopy studies at variable temperature, we systematically explore the relation between the magnetic domain pattern and the underlying structure for as-deposited and freestanding single-crystalline Fe 7 Pd 3 thin films across the martensite-austenite transition. We find experimental evidence that magnetic domain appearance is strongly affected by the presence and absence of nanotwinning. While the martensite-austenite transition upon temperature variation of as-deposited films is clearly reflected in topography by the presence and absence of a characteristic surface corrugation pattern, the magnetic domain pattern is hardly affected. These findings are discussed considering the impact of significant thermal stresses arising in the austenite phase. Freestanding martensitic films reveal a hierarchical structure of micro- and nanotwinning. The associated domain organization appears more complex, since the dominance of magnetic energy contributors alters within this length scale regime.

Ferromagnetic shape memory alloys are characterized by strong magneto-mechanical coupling occurring at the atomic scale causing large magnetically inducible strains at the macroscopic level. Employing combined atomic and magnetic force microscopy studies at variable temperature, we systematically explore the relation between the magnetic domain pattern and the underlying structure for as-deposited and freestanding single-crystalline Fe Pd thin films across the martensite-austenite transition. We find experimental evidence that magnetic domain appearance is strongly affected by the presence and absence of nanotwinning. While the martensite-austenite transition upon temperature variation of as-deposited films is clearly reflected in topography by the presence and absence of a characteristic surface corrugation pattern, the magnetic domain pattern is hardly affected. These findings are discussed considering the impact of significant thermal stresses arising in the austenite phase. Freestanding martensitic films reveal a hierarchical structure of micro- and nanotwinning. The associated domain organization appears more complex, since the dominance of magnetic energy contributors alters within this length scale regime.

Ferromagnetic shape memory alloys are characterized by strong magneto-mechanical coupling occurring at the atomic scale causing large magnetically inducible strains at the macroscopic level. Employing combined atomic and magnetic force microscopy studies at variable temperature, we systematically explore the relation between the magnetic domain pattem and the underlying structure for as-deposited and freestanding single-crystalline Fe sub(7)Pd sub(3) thin films across the martensite-austenite transition. We find experimental evidence that magnetic domain appearance is strongly affected by the presence and absence of nanotwinning. While the martensite-austenite transition upon temperature variation of as-deposited films is clearly reflected in topography by the presence and absence of a characteristic surface corrugation pattern, the magnetic domain pattern is hardly affected. These findings are discussed considering the impact of significant thermal stresses arising in the austenite phase. Freestanding martensitic films reveal a hierarchical structure of micro- and nanotwinning. The associated domain organization appears more complex, since the dominance of magnetic energy contributors alters within this length scale regime.