Revising the Joules-per-Compute (JPCUB) Benchmark: Normalizing Energy Efficiency by Logical-Qubit Operations

In the paper's words

Energy benchmarks for quantum processors are usually quoted per physical gate or per physical qubit, figures that hide the dominant cost of a fault-tolerant machine: the error-correction overhead that multiplies physical work by a distance-dependent factor before any logical operation is delivered. This paper revises the joules-per-compute benchmark to normalize by logical-qubit operations, the unit that carries the overhead. The model states its conventions up front: a distance-d rotated surface-code patch requires N_c = 2 d^2 - 1 physical qubits and N_g = 8 d^3 physical gates per logical operation, so joules per logical-qubit operation (JPCUB) exceeds joules per physical gate by exactly the overhead factor N_g = 8 d^3.

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

Numbers it reports

1. For the rotated surface code, joules per logical operation exceeds joules per physical gate by the overhead factor $8 d^{3}$, which reaches 74088 (4.87 orders of magnitude) at distance 21.

   from 8. Conclusion

2. v2.0 (2026-09-03): the normalization argument is stated with computed overhead factors at five distances; the logarithmic-gap analysis (reaching 4.87 orders of magnitude at $d = 21$) is added; 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

3. At $d = 21$ the understatement is 4.87 orders of magnitude.

   from 5. Results

4. All quantitative claims are computed by a deposited verification script: the overhead factor table across five distances (216 at $d = 3, 1000$ at $d = 5, 5832$ at $d = 9, 27000$ at $d = 15, 74088$ at $d = 21$), and the physical-qubit count that accompanies each.

   from Abstract

5. The ratio is $N_{g} = 8 d^{3}$: at $d = 3$, the logical figure is 216 times the gate figure; at $d = 9, 5832$ times; at $d = 21, 74088$ times.

   from 4. Analysis

6. Overhead factor by distance. d $N_{c}$ (physical qubits) $N_{g}$ per logical operation $\log10(N_{g})$ 3 17 216 2.33 5 49 1000 3.00 9 161 5832 3.77 15 449 27000 4.43 21 881 74088 4.87 The last column is the number of orders of magnitude by which a per-gate benchmark understates the per-logical-operation figure.

   from 5. Results

How it is done

1. Convention 1 (physical qubits).

   from 3. Model and conventions

2. The analysis is the algebra of overhead.

   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. Second, the benchmark revision does not add physics; it changes the unit of reporting.

   from 6. Discussion

2. A per-gate benchmark understates the energy of a fault-tolerant machine by the overhead of its error correction, and any energy comparison that does not carry the overhead compares regimes rather than efficiency.

   from 8. Conclusion

3. The central consequence is that a per-physical-gate benchmark understates the energy of a logical machine by between two and four orders of magnitude depending on the code distance, and any cross-architecture comparison that does not normalize by logical operations compares overhead regimes rather than computational efficiency.

   from Abstract

Where to read

1. Abstract301 words · 1 min
2. 1. Introduction169 words · 1 min
3. 2. Prior work145 words · 1 min
4. 3. Model and conventions121 words · 1 min
5. 4. Analysis124 words · 1 min
6. 5. Results84 words · 1 min
7. 6. Discussion184 words · 1 min
8. 7. What a practitioner can do with this result124 words · 1 min
9. 8. Conclusion90 words · 1 min
10. Changelog56 words · 1 min
11. Verification46 words · 1 min