Quantum Gilbert–Varshamov bound

Asymptotic existence lower bound for families of binary stabilizer quantum codes.

Specification version 1Published 1996-08-011 evidence records

About this problem

The question, scope, and sources behind this Registry record.

Formal question

Lower-bound asymptotic rates achievable by binary stabilizer codes at relative distance delta.

Scope & constraints

code: binary stabilizer
asymptotic: true
relativeDistance: delta=d/n
positiveRightHandSideRequired: true

Primary sources

Good quantum error-correcting codes exist — Quantum Gilbert–Varshamov bound >= Quantum Gilbert-Varshamov existence bound

What we know

Current frontiers derived from accepted Claims.

KNOWN LOWER BOUNDKNOWN UPPER BOUND

R >= 1 - 2 H2(delta) - 2 delta log2(3)

OPEN FRONTIER

Unknown

Lower boundGap: UnknownUpper bound

Claims

Assertions tied to evidence, attribution, and review.

2026

CLM-QUANT-003314-1>= R >= 1 - 2 H2(delta) - 2 delta log2(3)LOWER BOUNDThe cited theorem establishes R >= 1 - 2 H2(delta) - 2 delta log2(3) under the recorded assumptions.Source: Good quantum error-correcting codes exist — Quantum Gilbert–Varshamov bound >= ↗

PROVEN

Timeline

The frontier as it changed over time.

How this frontier is derived

Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.

—No breakthrough events recorded yetEvents appear here when an accepted Claim tightens a bound or closes the frontier.