Controlling and programming quantum devices to process quantum information by the unit of quantum dit, i.e., qudit, provides the possibilities for noise-resilient quantum communications, delicate quantum molecular simulations, and efficient quantum computations, showing great potential to enhance the capabilities of qubit-based quantum technologies. Here, we report a programmable qudit-based quantum processor in silicon-photonic integrated circuits and demonstrate its enhancement of quantum computational parallelism. The processor monolithically integrates all the key functionalities and capabilities of initialisation, manipulation, and measurement of the two quantum quart (ququart) states and multi-value quantum-controlled logic gates with high-level fidelities. By reprogramming the configuration of the processor, we implemented the most basic quantum Fourier transform algorithms, all in quaternary, to benchmark the enhancement of quantum parallelism using qudits, which include generalised Deutsch-Jozsa and Bernstein-Vazirani algorithms, quaternary phase estimation and fast factorization algorithms. The monolithic integration and high programmability have allowed the implementations of more than one million high-fidelity preparations, operations and projections of qudit states in the processor. Our work shows an integrated photonic quantum technology for qudit-based quantum computing with enhanced capacity, accuracy, and efficiency, which could lead to the acceleration of building a large-scale quantum computer.

We have measured the spin-dependent nanometer-sized displacements of the spin Hall effect of the reflected light from a planar air–glass interface. In the case of the vertical polarization, the displacement is found to increase with the incident angle and subsequently decrease after $\sim 48\mathrm{deg}$, while in the case of the horizontal polarization, it changes rapidly near the Brewster angle. For a fixed incident angle of $30\mathrm{deg}$, the displacement decreases to zero as the polarization angle approaches $\sim 39\mathrm{deg}$ from $0\mathrm{deg}$ (the horizontal polarization) and then increases in the opposite direction until $90\mathrm{deg}$ (the vertical polarization).

By moving silica glass in a preprogrammed structure, we directly produced three-dimensional holes with femtosecond laser pulses in single step. When distilled water was introduced into a hole drilled from the rear surface of the glass, the effects of blocking and redeposition of ablated material were greatly reduced and the aspect ratio of the depth of the hole was increased. Straight holes of $4‐\mu \mathrm{m}$ diameter were more than $200 \mu \mathrm{m}$ deep. Three-dimensional channels can be micromachined inside transparent materials by use of this method, as we have demonstrated by drilling a square-wave-shaped hole inside silica glass.

Fabricated by femtosecond laser pulses at wavelength $\lambda$ of $780\mathrm{nm}$ , the feature size of two-photon polymerization using SCR500 was reduced to $\lambda ∕50$ . Lines with sub-$25\text{-}\mathrm{nm}$ width were produced by controlling the incident laser power and the laser focus scan speed up to $700\mu \mathrm{m}∕\mathrm{s}$ . Based on repolymerization between two structures close to each other, the feature size was further reduced to $\sim 15\mathrm{nm}$ , which demonstrated the potential for three-dimensional nanofabrication with high spatial resolution.