Non-local resources for error correction in quantum LDPC codes

• URL: http://arxiv.org/abs/2409.05818v1
• Date: Mon, 9 Sep 2024 17:28:41 GMT
• Title: Non-local resources for error correction in quantum LDPC codes
• Authors: Omprakash Chandra, Gopikrishnan Muraleedharan, Gavin K. Brennen,
• Abstract summary: Surface code suffers from a low encoding rate, requiring a vast number of physical qubits for large-scale quantum computation. hypergraph product codes present a promising alternative, as both their encoding rate and distance scale with block size. Recent advancements have shown how to deterministically perform high-fidelity cavity enabled non-local many-body gates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Scaling fault-tolerant quantum computing is essential to realize the potential of quantum computation. Surface code has been the best choice over the last decade because of its effective error suppression capability. However, it suffers from a low encoding rate, requiring a vast number of physical qubits for large-scale quantum computation. In contrast, hypergraph product codes present a promising alternative, as both their encoding rate and distance scale with block size. Despite this, their non-local stabilizers necessitate long-range connectivity for stabilizer measurements, posing significant experimental challenges. Recent advancements have shown how to deterministically perform high-fidelity cavity enabled non-local many-body gates, enabling the creation of non-local cat states. We integrate the non-local resource into the DiVincenzo-Aliferis method for fault-tolerant stabilizer measurement. We apply the scheme to long-range quantum hypergraph product codes, performing circuit-level noise simulations including the the cavity error model, achieving a promising threshold. Additionally, we propose a tri-layer architectural layout for scheduling stabilizer measurements, enhancing circuit parallelizability.

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