Quantum Computation Latency-Energy Tradeoff and the JPCUB Metric

In the paper's words

Fault-tolerant quantum computation trades latency against energy through the code distance: a larger distance d costs more syndrome rounds and more physical gates per logical operation, lengthening every operation and raising its energy. This paper computes that tradeoff for the rotated surface code with a single explicit round-time convention. The model states its conventions up front: one logical operation takes t = d t_round (d syndrome rounds at round time t_round) and dissipates E = E_g 8 d^3 (the gate-energy convention of the companion energy model), so the latency-energy product scales as d^4.

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 with $t_{\mathrm{round}} = 1$ microsecond: the latency table from $d = 3$ (3.00 microseconds) to $d = 31$ (31.0 microseconds), the energy table from 2.160e-10 J to 2.383e-07 J, and the product table from 6.480e-16 J s to 7.388e-12 J s, spanning four orders of magnitude.

   from Abstract

2. The computed tables place the tradeoff on a quantitative footing: from $d = 3$ to $d = 31$ the latency grows from 3.00 to 31.0 microseconds, the energy from 2.160e-10 to 2.383e-07 J, and the product from 6.480e-16 to 7.388e-12 J s, spanning four orders of magnitude with the quartic law verified.

   from 8. Conclusion

3. Latency, energy, and product by distance. d t (s) E (J) tE (J s) 3 3.00e-06 2.160e-10 6.480e-16 5 5.00e-06 1.000e-09 5.000e-15 9 9.00e-06 5.832e-09 5.249e-14 15 1.50e-05 2.700e-08 4.050e-13 21 2.10e-05 7.409e-08 1.556e-12 31 3.10e-05 2.383e-07 7.388e-12 The product spans four orders of magnitude across the table, matching the quartic law: the ratio of the $d = 31$ product to the $d = 3$ product is 1.14e4, close to $(31/3)^{4} = 1.14e4$.

   from 5. Results

4. The script verifies the quartic law directly: $(31/3)^{4} = 1.140e4$, and the table's product ratio reproduces it.

   from 5. Results

5. v2.0 (2026-09-03): the product law tE ~ $d^{4}$ is derived and verified (product ratio 1.14e4 matches $(31/3)^{4}$); the full latency, energy, and product tables are computed; prior-work positioning added (Sections 2 and 6); HTML and PDF renderings added to the deposit; abstract rewritten with computed values, no deferred claims. v1.0 (2026-09-03): initial short-form record.

   from Changelog

6. The script computes the three tables and verifies the quartic law by comparing the product ratio across the table with $(31/3)^{4}$.

   from Verification

How it is done

1. One logical operation of a distance-d patch requires d syndrome rounds.

   from 3. Model and conventions

2. The two scaling laws combine into one product law.

   from 4. Analysis

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. Third, the parallel-execution caveat is the main scope boundary.

   from 6. Discussion

2. Where the premises end: the round time is a stated convention (1 microsecond, an order-of-magnitude surface-code round time); the gate count inherits the $8 d^{3}$ convention; and the linear model neglects the parallel execution of independent logical operations, which trades wall-clock latency against energy in a way the single-operation analysis does not capture.

   from Abstract

3. Where the premises end: $t_{\mathrm{round}}$ and $E_{g}$ are stated conventions, and the model prices a single logical operation in isolation; a real machine runs many logical operations in parallel, and wall-clock latency can be traded against energy by the degree of parallelism, which the single-operation analysis does not capture.

   from 3. Model and conventions

Where to read

1. Abstract283 words · 1 min
2. 1. Introduction155 words · 1 min
3. 2. Prior work98 words · 1 min
4. 3. Model and conventions131 words · 1 min
5. 4. Analysis141 words · 1 min
6. 5. Results130 words · 1 min
7. 6. Discussion171 words · 1 min
8. 7. What a practitioner can do with this result161 words · 1 min
9. 8. Conclusion114 words · 1 min
10. Changelog54 words · 1 min
11. Verification56 words · 1 min