Computing efficiently in QLDPC codes

Area of Science:

• Quantum Information Science
• Quantum Computing
• Error Correction Codes

Background:

• Quantum error correction is crucial for fault-tolerant quantum computing.
• Current methods, like surface codes, require significant physical qubit overhead.
• Quantum low-density parity check (QLDPC) codes offer a path to reduce this overhead.

Purpose of the Study:

• To develop QLDPC codes capable of efficient logical Clifford operations.
• To address the limitation of existing QLDPC codes primarily supporting quantum memories.
• To enable low-circuit-depth implementation of arbitrary Clifford gates.

Main Methods:

• Introduction of a novel family of QLDPC codes.
• Utilizing transversal operations for implementing the full Clifford group.
• Conducting circuit-level simulations of logical circuits up to depth 126.

Main Results:

• The new QLDPC codes allow any m-qubit Clifford operation in O(m) syndrome extraction rounds.
• Simulations demonstrate near-memory logical performance for these operations.
• Efficient implementation of the full Clifford group is achieved.

Conclusions:

• QLDPC codes are a viable route for resource-efficient universal quantum computation.
• The developed codes significantly reduce qubit overhead compared to leading approaches.
• This work advances the practical realization of large-scale quantum computers.