Long-range-enhanced surface codes

Understand

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.