3D topological quantum memory with a power-law energy barrier

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Computer Science

Background:

• Quantum memories are crucial for quantum computation but susceptible to errors.
• Existing quantum error correction codes face challenges in achieving high energy barriers for effective self-correction.
• Kitaev's surface code provides a foundational framework for quantum error correction.

Purpose of the Study:

• To investigate energy barriers in the context of self-correcting quantum memories.
• To introduce and analyze a novel 3D quantum error correction code.
• To explore methods for enhancing the performance of quantum error correction codes.

Main Methods:

• Introduction of the 'solid code,' a three-dimensional analog of Kitaev's surface code.
• Application of 'welding' techniques to combine multiple solid codes.
• Analysis of the resulting stabilizer code's properties, including its energy barrier and logical/physical qubit ratio.
• Modification of the code to break microscopic translation invariance.

Main Results:

• The proposed welded solid code achieves a [[O(L³),1,O(L(4/3))]] stabilizer code structure.
• An energy barrier of O(L(2/3)) was achieved, representing an exponential improvement over previous 3D codes.
• The energy barrier scales favorably with the code size (L).
• Breaking microscopic translation invariance was key to overcoming theoretical limitations ('no-go' results).

Conclusions:

• The developed 3D solid code offers a significant enhancement in energy barriers for quantum memories.
• This approach provides a pathway towards more robust and scalable self-correcting quantum memories.
• The strategy of breaking translation invariance is effective in circumventing no-go theorems in quantum error correction.