Fig. 2: A qudit-based programmable quantum processing unit in a photonic integrated circuit chip.
a Quantum circuit, and b physical implementation of the multiqudit QPU. It bases on multiphoton multidimensional entanglement of \({\left|{{\mbox{GHZ}}}\right\rangle }_{n+1,d}\), where n + 1 is the number of photonic qudits and d is the local dimensionality of each qudit. Pi is an arbitrary single-qudit gate; Fd is a generalised d-level Fourier gate; Mi is an arbitrary single-qudit projector; Oi,j (i = 1,..., n, j = 1,..., d) is an arbitrary single-qudit logic gate that is locally performed on the i-th qudit of the y-register, and the Oi,j gates are coherently entangled with the x-register state. The process of “space expansion--local operation--coherent compression" results in the multiqudit entangling gate, with a success probability of 1/d, independent on n. c The simplified schematic of a two-ququart d-QPU: (I) generation of four-level entangled state in an array of four integrated identical SFWM sources; (II) Hilbert space expansion and arbitrary single-qudit preparation of the y-register state; (III) arbitrary single-qudit operation of the x-register state; (IV) arbitrary single-qudit operation (loading in the four layers) of the y-register state, in which the operations are coherently entangled with the x-register state, thus forming the MVCU entangling gate, where the state-gate entanglement is indicated by the four colourful links; (V) coherent compression of Hilbert space by an indistinguishable erasure of spatial information; (VI) and (VII) arbitrary single-qudit projective measurement in the x and y registers. Insets: left top, measured resistance of all thermal-optic phase shifters (TOPSs); measured interference visibility of all 2-dimensional Mach-Zehnder Interferometers (MZIs); bottom right, measured classical statistic fidelities (Fc) for the Pauli X4 gate with a mean of 0.988(13) and Fourier F4 gate with a mean of 0.967(19). d A microscopy image of the d-QPU chip. It monolithically integrates 451 optical components, including 4 SFWM sources, 116 reconfigurable TOPS, 131 multimode interferometer (MMI) beamsplitters, 4 wavelength-division multiplexing (WDM) filters, 156 waveguide crossings and 40 grating couplers (GC). The d-QPU chip is wire bounded and can be flexibly controlled by classical electronics, and can be reliably reprogrammed and reconfigured to benchmark a spectrum of different quaternary quantum algorithms.
