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<jats:title>Abstract</jats:title><jats:p>High-fidelity control of quantum bits is paramount for the reliable execution of quantum algorithms and for achieving fault tolerance—the ability to correct errors faster than they occur<jats:sup>1</jats:sup>. The central requirement for fault tolerance is expressed in terms of an error threshold. Whereas the actual threshold depends on many details, a common target is the approximately 1% error threshold of the well-known surface code<jats:sup>2,3</jats:sup>. Reaching two-qubit gate fidelities above 99% has been a long-standing major goal for semiconductor spin qubits. These qubits are promising for scaling, as they can leverage advanced semiconductor technology<jats:sup>4</jats:sup>. Here we report a spin-based quantum processor in silicon with single-qubit and two-qubit gate fidelities, all of which are above 99.5%, extracted from gate-set tomography. The average single-qubit gate fidelities remain above 99% when including crosstalk and idling errors on the neighbouring qubit. Using this high-fidelity gate set, we execute the demanding task of calculating molecular ground-state energies using a variational quantum eigensolver algorithm<jats:sup>5</jats:sup>. Having surpassed the 99% barrier for the two-qubit gate fidelity, semiconductor qubits are well positioned on the path to fault tolerance and to possible applications in the era of noisy intermediate-scale quantum devices.</jats:p>

<jats:title>Abstract</jats:title><jats:p>Phase transitions connect different states of matter and are often concomitant with the spontaneous breaking of symmetries. An important category of phase transitions is mobility transitions, among which is the well known Anderson localization<jats:sup>1</jats:sup>, where increasing the randomness induces a metal–insulator transition. The introduction of topology in condensed-matter physics<jats:sup>2–4</jats:sup> lead to the discovery of topological phase transitions and materials as topological insulators<jats:sup>5</jats:sup>. Phase transitions in the symmetry of non-Hermitian systems describe the transition to on-average conserved energy<jats:sup>6</jats:sup> and new topological phases<jats:sup>7–9</jats:sup>. Bulk conductivity, topology and non-Hermitian symmetry breaking seemingly emerge from different physics and, thus, may appear as separable phenomena. However, in non-Hermitian quasicrystals, such transitions can be mutually interlinked by forming a triple phase transition<jats:sup>10</jats:sup>. Here we report the experimental observation of a triple phase transition, where changing a single parameter simultaneously gives rise to a localization (metal–insulator), a topological and parity–time symmetry-breaking (energy) phase transition. The physics is manifested in a temporally driven (Floquet) dissipative quasicrystal. We implement our ideas via photonic quantum walks in coupled optical fibre loops<jats:sup>11</jats:sup>. Our study highlights the intertwinement of topology, symmetry breaking and mobility phase transitions in non-Hermitian quasicrystalline synthetic matter. Our results may be applied in phase-change devices, in which the bulk and edge transport and the energy or particle exchange with the environment can be predicted and controlled. </jats:p>

<jats:title>Abstract</jats:title><jats:p>Inorganic–organic hybrid materials represent a large share of newly reported structures, owing to their simple synthetic routes and customizable properties<jats:sup>1</jats:sup>. This proliferation has led to a characterization bottleneck: many hybrid materials are obligate microcrystals with low symmetry and severe radiation sensitivity, interfering with the standard techniques of single-crystal X-ray diffraction<jats:sup>2,3</jats:sup> and electron microdiffraction<jats:sup>4–11</jats:sup>. Here we demonstrate small-molecule serial femtosecond X-ray crystallography (smSFX) for the determination of material crystal structures from microcrystals. We subjected microcrystalline suspensions to X-ray free-electron laser radiation<jats:sup>12,13</jats:sup> and obtained thousands of randomly oriented diffraction patterns. We determined unit cells by aggregating spot-finding results into high-resolution powder diffractograms. After indexing the sparse serial patterns by a graph theory approach<jats:sup>14</jats:sup>, the resulting datasets can be solved and refined using standard tools for single-crystal diffraction data<jats:sup>15–17</jats:sup>. We describe the ab initio structure solutions of mithrene (AgSePh)<jats:sup>18–20</jats:sup>, thiorene (AgSPh) and tethrene (AgTePh), of which the latter two were previously unknown structures. In thiorene, we identify a geometric change in the silver–silver bonding network that is linked to its divergent optoelectronic properties<jats:sup>20</jats:sup>. We demonstrate that smSFX can be applied as a general technique for structure determination of beam-sensitive microcrystalline materials at near-ambient temperature and pressure.</jats:p>