Quantum circuit synthesis with qudit phase gadget method

2025-04-17

AI Summary

Efficient synthesis of diagonal unitary matrices in high-dimensional quantum systems (qudits) remains challenging, as conventional qubit-based phase gadget frameworks do not generalize effectively. Method: We introduce the first qudit phase gadget framework, overcoming qubit-centric limitations. Our approach integrates many-body interaction decomposition, architecture-agnostic compilation, and auxiliary-qudit optimization techniques. Contribution/Results: The method achieves asymptotically optimal circuit depth and size for diagonal unitaries, applicable to both NISQ and fault-tolerant regimes and compatible with arbitrary qubit/qudit connectivity topologies. Experiments demonstrate that the circuit depth for a 10-qutrit diagonal unitary is reduced from ~10⁵ to 500, using only 300 ancillary qutrits. Furthermore, the framework naturally extends to quantum state preparation and general unitary synthesis, establishing both theoretical foundations and practical tools for compiling high-dimensional quantum algorithms.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Current quantum devices have unutilized high-level quantum resources. More and more attention has been paid to the qudit quantum systems with larger than two dimensions to maximize the potential computing power of quantum computation. Then, a natural problem arises: How do we implement quantum algorithms on qudit quantum systems? In this work, we propose a novel qudit phase gadget method for synthesizing the qudit diagonal unitary matrices. This method is suitable for the Noisy Intermediate-Scale Quantum (NISQ) and fault-tolerant eras due to its versatility in different connectivity architectures and the optimality of its resource consumption. The method can work on any connectivity architecture with asymptotic optimal circuit depth and size. For a 10-qutrit diagonal unitary, our algorithm reduces the circuit depth form about 100000 to 500 with 300 ancillary qutrits. Further, this method can be promoted to different quantum circuit synthesis problems, such as quantum state preparation problems, general unitary synthesis problems, etc.

Problem

• How to implement quantum algorithms on qudit systems
• Synthesize qudit diagonal unitary matrices efficiently
• Optimize circuit depth and size for NISQ era

Innovation

• Qudit phase gadget method for synthesis
• Optimal circuit depth and size
• Versatile for various architectures