Landauer-Limit Energy Floor and JPCUB Normalization for Cryogenic Quantum Control Electronics

In the paper's words

Cryogenic quantum control electronics dissipate energy many orders of magnitude above the thermodynamic minimum implied by Landauer's principle, and the gap matters for the joules-per-compute economics of fault-tolerant machines. This paper computes the Landauer floor for a rotated surface-code control plane and compares it with the realistic dissipation of cryo-CMOS electronics. The model states its conventions up front: erasing one bit costs at least k_B T ln 2; one logical operation of a distance-d surface-code patch requires N_g = 8 d^3 physical gates (the counting convention of a companion record); and a realistic gate energy is taken to be of order 1 pJ, which is between ten and eleven orders of magnitude above the 4 K Landauer floor.

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

Numbers it reports

1. All quantitative claims are computed by a deposited verification script: the floor $k_{B} T \ln 2$ per bit at 300 K (2.871e-21 J), 77 K (7.369e-22 J), 4 K (3.828e-23 J), and 20 mK (1.914e-25 J); the per-logical-operation floor at distance 7 (1.050e-19 J at 4 K) and distance 11 (4.076e-19 J at 4 K); and the ratio of realistic gate dissipation to the 4 K floor, 2.6 x 10^10 at every distance, because both quantities scale identically in d.

   from Abstract

2. Where the premises end: the 1 pJ gate energy is an order-of-magnitude engineering convention, not a measured value; the gate count inherits the rotated-surface-code convention; and Landauer's bound applies to erasure-limited dissipation, which real gates exceed by many orders of magnitude.

   from Abstract

3. Where the premises end: the gate count inherits the rotated-surface-code convention and is an order-of-magnitude engineering figure; the 1 pJ gate energy is a stated assumption, not a measurement; and the Landauer bound applies to erasure-limited dissipation, which real control electronics exceed by orders of magnitude - exactly the gap this paper quantifies.

   from 3. Model and conventions

4. Moving the control plane from room temperature to 4 K reduces the floor by a factor of 75; to 20 mK by another factor of 200.

   from 4. Analysis

5. Temperature $k_{B} T \ln 2 (J/\mathrm{bit})$ 300 K 2.871e-21 77 K 7.369e-22 4 K 3.828e-23 20 mK 1.914e-25 Per-logical-operation floor and the ratio at realistic gate energy. d $N_{g}$ $E_{\mathrm{\min}}$ at 4 K (J) E at $E_{g} = 1 \,\mathrm{pJ} (J)$ Ratio $E_{g}/E_{\mathrm{land}}(4 \,\mathrm{K})$ 7 2744 1.050e-19 2.744e-09 2.6e+10 11 10648 4.076e-19 1.065e-08 2.6e+10 Ratio invariance.

   from 5. Results

How it is done

1. The reader should care because roadmap cost models that cite the Landauer bound as a floor for quantum control are off by ten orders of magnitude in the wrong direction: the floor is real but irrelevant at current dissipation levels, and the useful planning number is the gap between realistic gate energy and the floor, not the floor itself.

   from Abstract

2. The model computes the thermodynamic floor of a cryogenic surface-code control plane.

   from 3. Model and conventions

3. The analysis has three steps.

   from 4. Analysis

4. First, the Landauer floor is not a useful planning bound for cryogenic control at current dissipation levels.

   from 6. Discussion

What would falsify it

The paper's text states no explicit falsification criterion; the limits below are what it says about where the claim stops.

Where the claim stops

1. Because it is independent of distance, improving the code (better fidelity, smaller d) does not close the gap to the floor; only improving the control electronics does.

   from 6. Discussion

2. This paper does not cite a specific measurement; it adopts an order-of-magnitude gate energy of 1 pJ as an explicit convention and computes the consequences, leaving the substitution of a measured value to the practitioner.

   from 2. Prior work

3. Where the premises end: the gate count inherits the rotated-surface-code convention and is an order-of-magnitude engineering figure; the 1 pJ gate energy is a stated assumption, not a measurement; and the Landauer bound applies to erasure-limited dissipation, which real control electronics exceed by orders of magnitude - exactly the gap this paper quantifies.

   from 3. Model and conventions

Where to read

1. Abstract373 words · 2 min
2. 1. Introduction215 words · 1 min
3. 2. Prior work179 words · 1 min
4. 3. Model and conventions246 words · 1 min
5. 4. Analysis189 words · 1 min
6. 5. Results193 words · 1 min
7. 6. Discussion206 words · 1 min
8. 7. What a practitioner can do with this result179 words · 1 min
9. 8. Conclusion104 words · 1 min
10. Changelog52 words · 1 min
11. Verification66 words · 1 min