Long-range-enhanced surface codes

Abstract

The surface code is a quantum error-correcting code for one logical qubit, protected by spatially localized parity checks in two dimensions. Due to fundamental constraints from spatial locality, storing more logical qubits requires either sacrificing the robustness of the surface code against errors or increasing the number of physical qubits. We bound the minimal number of spatially nonlocal parity checks necessary to add logical qubits to a surface code while maintaining, or improving, robustness to errors. We saturate the lower limit of this bound, when the number of added logical qubits is a constant, using a family of hypergraph product codes, interpolating between the surface code and constant-rate low-density parity-check codes. Fault-tolerant protocols for logical gates in the quantum code can be inherited from its classical parent codes. We provide near-term practical implementations of this code for hardware based on trapped ions or neutral atoms in mobile optical tweezers. Long-range-enhanced surface codes outperform conventional surface codes using hundreds of physical qubits, and represent a practical strategy to enhance the robustness of logical qubits to errors in near-term devices.

23 pages, 15 figures, 1 table; v2 changes: fixed typos and added citations; v3 changes: updated numerics and new logical gadgets; v4 changes: reworded abstract and incorporated referee suggestions

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Cited by in corpus (11)

• A universal neutral-atom quantum computer with individual optical addressing and non-destructive readout
• Entangling four logical qubits beyond break-even in a nonlocal code
• High-rate quantum LDPC codes for long-range-connected neutral atom registers
• Quantum Error Correction resilient against Atom Loss
• Quantum memory at nonzero temperature in a thermodynamically trivial system
• Low-density parity-check codes as stable phases of quantum matter
• Quantum Routing with Teleportation
• Adaptive Syndrome Extraction
• Single-shot preparation of hypergraph product codes via dimension jump
• Enhanced Lieb-Robinson bounds for commuting long-range interactions
• Hierarchical Quantum Error Correction with Hypergraph Product Code and Rotated Surface Code