Experimental qudit-assisted quantum operations by dimension expansion and partial measurement

Many quantum algorithms require ancilla qubits and deep circuits, yet adding and interacting with them are difficult and resource-intensive. Moreover, the high-dimensional properties of quantum systems have been demonstrated to simplify quantum circuits while enhancing efficiency. We propose a novel “Dimension Expansion and Partial Measurement” scheme for quantum information processing based on qudits’ multi-level nature. Given a d-dimensional qudit (expandable to d × r dimensions) and local single-qudit operations in d and r dimensions, we can introduce r-dimensional equivalent ancilla qudits (logically introduced via dimension expansion) and enable quantum operations in deep circuits across d and r dimensions. With successfully generated photons, our scheme efficiently cascades two-qubit/qudit gates with unity theoretical success probability; existing schemes are either probabilistic or need additional particles. In particular, this scheme can be extended to multiple ancilla qudits with measurement feedforward by the “Partially Measure-Reexpand” procedure. This leads to a resource-efficient universal high-dimensional measurement-based quantum computation scheme. On a silicon-photonic chip, starting from 2 qubits (each expandable to a four-dimensional qudit), we implemented a measurement-based quantum computation system equivalent to 5 qubits and experimentally validated our scheme. The proposed scheme applies to simplifying and scaling up various quantum systems.