# qLDPC Codes **Quantum low-density parity-check (qLDPC) codes** are [[Stabilizer Codes|stabilizer codes]] whose parity checks are *sparse* — each check involves only a few qubits, and each qubit is involved in only a few checks — but whose connectivity is **not restricted to a flat 2D grid**. This lets them protect the same information with far fewer physical qubits than the [[Surface Code|surface code]]. ## First principles "Low-density" refers to the parity-check structure (inherited from classical LDPC codes): keeping checks sparse means each [[Syndrome Extraction]] measurement stays simple and low-noise. The surface code is technically a qLDPC code, but a deliberately *local* one — its checks only ever touch neighbours on a plane. General qLDPC codes relax that constraint: a check may connect qubits that are not physically adjacent. Allowing a few **long-range connections** dramatically improves efficiency. $ \underbrace{\text{surface code}}_{\text{2D-local, high overhead}} \;\longrightarrow\; \underbrace{\text{general qLDPC}}_{\text{some long-range links, low overhead}} $ > [!intuition] Friends across town > If you may only check parity with next-door neighbours, you need a huge town to store one secure secret. Allow a handful of long-distance friendships and the same security needs far fewer people. The price is the wiring to reach across town. ## Why it matters - **Lower overhead.** qLDPC codes can encode many [[Physical vs Logical Qubits|logical qubits]] per block, slashing the physical-qubit cost of fault tolerance — a major reason several roadmaps favour them. - **Hardware demand.** They require **non-local connectivity**, which is hard on a fixed chip but natural where qubits can be moved or reach across the system — see [[Qubit Connectivity and Reconfigurability]]. > [!note] Codes are matched to machines > Which code is "cheap" depends on what connectivity the hardware offers. qLDPC codes are attractive precisely on platforms that can realize their long-range checks. ## Related - [[Stabilizer Codes]] - [[Surface Code]] - [[Qubit Connectivity and Reconfigurability]] - [[Physical vs Logical Qubits]] - [[Quantum Error Correction]]