High-dimensional quantum information processing on programmable integrated photonic chips

In quantum information processing, encoding and processing high-dimensional quantum information could provide unique advantages, for example, stronger violation of Bell’s non-locality, quantum communications with higher capacity and noise-resistance, and quantum computations with improved efficiency and accuracy. Despite of significant progress in two-dimensional quantum bit (qubit) systems, another major focus has expanded to high-dimensional quantum dit (qudit) technologies and devices.

Photons represents a natural carrier of high-dimensional quantum information, by encoding the qudit states in a variety of degrees of freedom (DoF) such as path, frequency, orbital angular momentum, multitude spatial mode, and time-bins. The development of integrated quantum photonics enables the realization of the quantum computing system on a photonic chip, thus providing a scalable, programmable, and stable quantum photonic platform for high-dimensional quantum information processing.

In order to realize the organization and review of past works in high-dimensional quantum information processing and accelerate the accumulation and absorption of the latest knowledge into the existing knowledge system. This article reviews the progress of high-dimensional quantum information processing in photonic systems. First, they introduce the definitions of qudit states, single-qudit and multi-qudit gates. Second, they introduce the on-chip implementations and characterizations of photonic path-encoded qudit states and quantum gates, such as the structure of linear-optical circuits for single-qudit and multi-qudit gates. Then, they introduce how to improve quantum information processing with the assistance of qudit states, including Hamiltonian learning, simplifying quantum gates using qudits, the linear combination of unitary operations (LCU), and quantum error correction assisted by qudits. Finally, they introduce the generalized quantum algorithms for qudits, such as the Deutsch-Jozsa algorithm, Bernstein-Vazirani algorithm, phase estimation and order finding algorithms. The experimental realizations of qudit-based quantum computing algorithms will be discussed.

The main focus in this review article are as follows:

（1）The research progress of high-dimensional quantum information processing in photonic systems is summarized

（2）The intrinsic correlation between high-dimensional quantum information processing based on photonics and the implementation of LCU is summarized

（3）This paper introduces qudit-based quantum algorithms and their experimental implementations generalized in traditional two-dimensional situations

The experimental results reviewed in this paper are mainly composed of three parts. First is the result of the generation, manipulation and characterization of high-dimensional quantum states, such as high-dimensional quantum state tomography and quantum process tomography. They can measure the density matrix and process matrix of high-dimensional quantum states and quantum gates. The second is to combine high-dimensional quantum states and gates into the quantum information processing process. Resulting the high-dimensional assisted quantum information processing, for example, quantum circuit simplification, LCU, high-dimensional clustered quantum computing and quantum error correction experiments. The third is the experimental results of generalizing traditional quantum algorithms to high-dimensional situations, such as high-dimensional quantum phase estimation and ordering algorithms on programmable high-dimensional quantum processors.

It has been found that a more remarkable Hilbert space can be achieved using qudit. The quantum information can be encoded more freely, with a higher photon count rate at the same computing power. By adding auxiliary qudit, quantum circuits can be improved and simplified, and LCU can be implemented, enabling quantum operations in a broader sense. At the same time, extending traditional quantum algorithms to higher dimensions can obtain a more comprehensive range of algorithms and applications. Qudit allows more input, processing, and output of information during the computation, further enabling shallower circuit depth, higher computational accuracy, better fault tolerance, and more minor cumulative errors.

See the article:

High-dimensional Quantum Information Processing on Programmable Integrated Photonic Chips

https://doi.org/10.1007/s11432-021-3432-6