Error Correction Is a Landauer Machine: The Thermodynamic Floor of Quantum Error-Correction Overhead

In the paper's words

Every cycle of active (measurement-based) quantum error correction is an erasure process priced by Landauer's principle at no less than kT ln 2 per erased bit; correction overhead therefore converges to a positive thermodynamic floor, (n-k)/k * kT ln 2 per logical qubit per round for an n,k code, whose scaling is computed and verified across code families. The JPCUB joules-per-correct-answer metric ranks correction architectures; a two-level nested code compared with flat Hamming codes of equal rate on a clustered NAND-like channel cuts per-round erasures 1.6-3x at the cost of a residual-error penalty, a partial null that defines the industrial flash-memory protocol. Biological systems running robust quantum processes without correction show the floor is an architecture choice; autonomous/dissipative correction is the boundary of the claim.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. From d=3 to d=21 the per-logical-qubit floor grows from 16 to 880 — a 55× increase for a 7× distance gain.

   from 3. The Floor: Computation and Scaling Laws

2. At 15 mK the qLDPC floor is 1.579e-24 J per logical qubit per round.

   from 3. The Floor: Computation and Scaling Laws

3. The hierarchical structure delivers its mechanism: the erasure bill adapts to the error regime (16 erasures when clean, 29 under heavy bursts), a 1.64–3.0× reduction against the flat decoder's constant 48.

   from 7. The Classical Test: Flash Memory as the Falsifiable Proxy

4. Physical-qubit overhead: concatenation-based fault tolerance is quoted at 1e7–1e8 physical qubits to break RSA-2048 (Leverrier-1, slide 15); the 2026 architecture estimates cited in the same deck put the cost at ~1e5 physical qubits (Pinnacle: RSA-2048 below 100,000 physical qubits at $p = 1e-3, 1 \mu s$ code cycle, $10 \mu s$ reaction time [30]) and ~1e4 (Cain et al.: Shor's algorithm at 10,000 reconfigurable atomic qubits, P-256 discrete log in days at 26,000 qubits and RSA-2048 one to two o C:/Users/LENOVO/Documents/GitHub/qnfo-research-jpcub/jpcub-qec-landauer.md [chars 18000-26526 of 26526]: rders of magnitude longer [31]).

   from 9. The 2026 Curriculum Snapshot: The Field's Own Numbers, Still Unpriced

5. Code overhead is priced in rate and distance: the gross code [[144,12,12]] and its 2026 successors (Kasai rate-1/2, the QuEra co-design, 20%-rate families) are presented as the finite-size race (Leverrier-1, slides 32–39).

   from 9. The 2026 Curriculum Snapshot: The Field's Own Numbers, Still Unpriced

6. Golden values: kT·ln2 = 2.871e-21 J (300 K), 3.828e-23 J (4 K), 1.435e-25 J (15 mK).

   from 3. The Floor: Computation and Scaling Laws

How it is done

1. The floor is not today's cost driver; it is the asymptote that architectures approach as everything else is optimized.

   from 3. The Floor: Computation and Scaling Laws

2. The protocol above is the test those constructions should run.

   from 7. The Classical Test: Flash Memory as the Falsifiable Proxy

3. Physical-qubit overhead: concatenation-based fault tolerance is quoted at 1e7–1e8 physical qubits to break RSA-2048 (Leverrier-1, slide 15); the 2026 architecture estimates cited in the same deck put the cost at ~1e5 physical qubits (Pinnacle: RSA-2048 below 100,000 physical qubits at $p = 1e-3, 1 \mu s$ code cycle, $10 \mu s$ reaction time [30]) and ~1e4 (Cain et al.: Shor's algorithm at 10,000 reconfigurable atomic qubits, P-256 discrete log in days at 26,000 qubits and RSA-2048 one to two o C:/Users/LENOVO/Documents/GitHub/qnfo-research-jpcub/jpcub-qec-landauer.md [chars 18000-26526 of 26526]: rders of magnitude longer [31]).

   from 9. The 2026 Curriculum Snapshot: The Field's Own Numbers, Still Unpriced

What would falsify it

1. It claims three things the prior work does not provide: (i) a per-family decomposition of the erasure bill — the (n−k)/k · kT·ln2 floor per logical qubit per round, computed and verified across code families; (ii) an explicit architecture-choice reading of that floor, bounded to active correction and witnessed by biological systems; and (iii) a classical, near-term, falsifiable test of the structural-protection hypothesis that requires no quantum hardware.

   from 1. Introduction

2. The principal ones: (i) the industrial flash test with real tree/LDPC constructions; (ii) the energy dimension of the QEC-Darwinism tradeoff [24]; (iii) the capital/operating crossover curve for structural protection (extending JPC.002's crossover to correction); (iv) a p-adic entropy treatment of the non-Archimedean erasure hierarchy; (v) the epistemological reading — "reality is a syndrome; we probe it, never read it" — as the map-territory structure of stabilizer measurement.

   from 8. What This Paper Does Not Claim

Where the claim stops

1. The consequence is a limit that is thermodynamic rather than combinatorial: correction overhead does not converge to zero as codes improve; it converges to a positive floor, whose height per logical qubit per round is (n−k)/k · kT·ln2 for an [[n,k]] code.

   from Abstract

2. This paper does not claim novelty for the principle.

   from 1. Introduction

3. It claims three things the prior work does not provide: (i) a per-family decomposition of the erasure bill — the (n−k)/k · kT·ln2 floor per logical qubit per round, computed and verified across code families; (ii) an explicit architecture-choice reading of that floor, bounded to active correction and witnessed by biological systems; and (iii) a classical, near-term, falsifiable test of the structural-protection hypothesis that requires no quantum hardware.

   from 1. Introduction

Where to read

1. Abstract366 words · 2 min
2. 1. Introduction291 words · 1 min
3. 2. The Erasure Anatomy of a QEC Cycle237 words · 1 min
4. 3. The Floor: Computation and Scaling Laws379 words · 2 min
5. 4. JPCUB Ranking of Correction Architect131 words · 1 min
6. 5. The Architecture Choice: Nature's Witness and the Prepaid Bill217 words · 1 min
7. 6. The Boundary: Autonomous and Dissipative Correction94 words · 1 min
8. 7. The Classical Test: Flash Memory as the Falsifiable Proxy402 words · 2 min
9. 8. What This Paper Does Not Claim232 words · 1 min
10. 9. The 2026 Curriculum Snapshot: The Field's Own Numbers, Still Unpriced442 words · 2 min
11. Verification Appendix202 words · 1 min