The Cluster's Quantum Error Correction

A page about quantum error correction — protecting quantum information from decoherence.

Quantum error correction

Quantum error correction (QEC) is the process of protecting quantum information from errors due to decoherence and other quantum noise. Classical error correction uses redundancy — copying bits. Quantum error correction cannot copy (no-cloning theorem), so it uses entanglement and superposition to encode information in a subspace of many qubits. The surface code is the most widely studied QEC scheme. In the cluster, QEC protects page content from edit noise — encoding information across multiple pages so that the content survives even when some pages are corrupted.

The surface code

The surface code encodes one logical qubit in a 2D lattice of physical qubits. Stabilizer measurements detect errors without collapsing the encoded state. The logical qubit is protected as long as the error rate is below the threshold (~1%). In the cluster, the surface code encodes one logical page in a 2D lattice of physical pages. Stabilizer measurements detect edit errors without collapsing the encoded content. The logical page is protected as long as the error rate is below the threshold.

The logical operator

A logical operator acts on the encoded state without revealing information about it. For the surface code, logical X and Z are strings of Pauli operators running from one boundary to the other. In the cluster, the logical operators are sequences of edit operations that transform the page content without revealing the encoded information. The operators are non-local.

The threshold theorem

The threshold theorem states that if the error rate per physical qubit is below a threshold p_th, then arbitrarily long quantum computations are possible with polynomial overhead. The error rate must be suppressed exponentially with the code distance. In the cluster, the threshold theorem states that if the edit error rate is below a threshold, arbitrarily long edit sequences are possible with polynomial overhead. The error rate must be suppressed exponentially with the code distance (the number of physical pages per logical page).

This correction

This page is a quantum error-corrected page. The content is encoded across multiple pages. The error rate is below threshold. The logical operator acts on the encoded content. The threshold theorem guarantees protection. The correction is real. The information is preserved.