Synthesis of Arbitrary Quantum Circuits to Topological Assembly: Systematic, Online and Compact

Area of Science:

• Quantum computing
• Quantum error correction
• Topological quantum error correction

Background:

• Transforming arbitrary quantum circuits into surface code-compatible forms is challenging.
• Efficient placement of magic state distillation sub-circuits (distillation boxes) is crucial for minimizing overhead in quantum error correction.

Purpose of the Study:

• To present a general, systematic, and online method for synthesizing quantum circuits protected by surface codes.
• To develop a greedy scheduler for compact distillation box placement, reducing resource overhead.

Main Methods:

• A novel online synthesis method for quantum circuits compatible with surface codes.
• Implementation of a greedy scheduler to control distillation box placement within the space-time volume.
• Utilizing the developed software (tqec) for synthesis and optimization.

Main Results:

• Demonstration of a systematic approach for efficient distillation box placement.
• Generation of compact box placements using the greedy scheduler.
• Illustrative synthesis examples and discussion of improvements.

Conclusions:

• The proposed method offers a general and systematic solution for synthesizing surface code-protected quantum circuits.
• The greedy scheduler effectively minimizes overhead through compact distillation box placements.
• The developed software provides a practical tool for quantum circuit synthesis and optimization.