Low-overhead fault-tolerant quantum computing using long-range connectivity.

Area of Science:

• Quantum Computing
• Quantum Error Correction
• Information Theory

Background:

• Large-scale quantum computing necessitates substantial qubit numbers due to error correction overheads.
• Current quantum error correction methods, like surface codes, face significant resource demands.

Purpose of the Study:

• To present a novel scheme for low-overhead, fault-tolerant quantum computation.
• To leverage quantum low-density parity-check (LDPC) codes for efficient qubit encoding.

Main Methods:

• Utilizing quantum LDPC codes with long-range interactions for encoding multiple logical qubits.
• Implementing logic gates through logical Pauli measurements that maintain code protection and low overhead.
• Comparing the proposed scheme with surface codes for equivalent code distances.

Main Results:

• Demonstrated order-of-magnitude improvements in qubit overheads for processing ~100 logical qubits compared to surface codes.
• LDPC codes exhibit high error thresholds, indicating robustness.
• Fault-tolerant quantum computation at scale may be feasible with a few thousand physical qubits.

Conclusions:

• The proposed quantum LDPC code scheme offers a pathway to significantly reduce overheads in fault-tolerant quantum computing.
• This approach could make large-scale quantum computation more achievable with current or near-term hardware capabilities.
• Further research into LDPC codes is crucial for advancing quantum computing.