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The Government Will Pay $100 Million for 100 Logical Qubits. Today's Best Is 143x Short.

Sept 17: Microsoft and Qolab defined "logical qubit" while DOE offered $215M for 100. Our math: 1-in-700 to 1-in-10-billion needs 12x/year gains for ~7 years.

By Muse · Quantum · · ☕ 8 min read

Google's best published logical qubit fails about once every 700 rounds of error correction. That is the state of the art, measured on a 105-qubit chip and published in Nature. An arXiv paper posted last Wednesday puts the entry price for useful quantum computing at roughly one failure in ten billion. On the same afternoon, the U.S. Department of Energy offered $100 million for 100 logical qubits running 100,000 hard operations by fall 2028: machines roughly 140 times better than the best ever built, on a two-year deadline, under a definition of "logical qubit" the paper's authors call too loose to mean anything. We ran the numbers.

Two announcements, one afternoon

At 15:15 UTC on September 17, Matthias Troyer and Chetan Nayak of Microsoft Quantum and John Martinis of Qolab posted "Scalable logical qubits" (arXiv:2609.20549). Eleven pages, zero experiments: vocabulary is the whole argument. As they write, today's "logical qubit" demonstrations are "often confusing or not clearly aligned with what is ultimately needed to run long, valuable algorithms." Their fix is a four-part definition of a scalable logical qubit:

  1. It is sustained during computation by repeated quantum error correction.
  2. It supports a fault-tolerant universal set of logical operations with measurement-conditioned control flow and low-latency real-time error correction.
  3. Its code family shows the logical error rate decreasing predictably as more physical qubits are devoted.
  4. Replication is credible: building N logical qubits at error rate e must cost no more than order N log(1/e) physical qubits.

Hours earlier, DOE had announced the Quantum Genesis Q Competition: up to $215 million planned, a $100 million pool for a first-generation machine with at least 100 logical qubits, and two $50 million bonuses for 150 and 200. DOE's request for applications defines the unit being bought in a single sentence: "an effective qubit spread across multiple subsystems that can be operated under a quantum error correction regime to suppress errors or environmental noise." No error rate, no scaling clause, no replication bound. Metric methodology, per the RFA, will be negotiated with the winners.

The bars, in one table

Every number comes from the primary sources cited below.

Reliability bars: the best published result, DOE's implied requirement, and the paper's utility targets.
BarRequired logical error rateSource
Best published result (Google Willow, distance-7 surface code)1.43 × 10-3 per cycle, about 1 failure in 700arXiv:2408.13687 (Nature 638, 2025)
DOE first-generation benchmark (100 logical qubits, 105 hard ops)≲ 10-5 per hard operationDOE Quantum Genesis Q RFA
Microsoft/Qolab entry price for useful computing∼ 10-10arXiv:2609.20549
Deep targets (e.g., factoring-class algorithms)10-12 to 10-15arXiv:2609.20549

Running the numbers nobody ran

Start with DOE's benchmark: for a machine to run 105 hard operations fault-tolerantly, expected logical failures across the run must stay near one or fewer. Since expected failures equal operations times error rate, the per-hard-operation logical error rate must be at most about 10-5. Google's measured 1.43 × 10-3 per error-correction cycle leaves the state of the art roughly 143 times short, so with fall 2028 two years out the industry needs about 12x per year of sustained improvement, the square root of 143.

Now aim at the paper's own bar. Between 1.43 × 10-3 and 10-10 lies a factor of 1.43 × 107, seven orders of magnitude. At the 12x-per-year pace that winning DOE's money already demands, ln(1.43 × 107)/ln(12) = 16.48/2.48 gives 6.6 years, so the paper's entry price for usefulness arrives around 2033 even if the industry sustains that aggressive pace. For the 10-15 regime named for deep algorithms, add another four and a half years.

One more calculation, using the paper's fourth clause directly: N logical qubits at error rate e must cost no more than order N log(1/e) physical qubits. Plug in DOE's target, N = 100, e = 10-10: with the natural log, 100 × ln(1010) = 100 × 23.0, about 2,300 physical qubits, and other log bases give one to three thousand. Google's Willow chip, behind the 1-in-700 record, holds 105 physical qubits total, so the paper's definition prices a scalable version of DOE's machine at 10 to 30 times the physical qubit count of today's largest research chips. DOE's one-sentence definition mentions none of this, which is precisely the paper's complaint.

Why the paper matters more than the prize

Nothing in the paper is new physics. Its power is as a lie detector. Clause one kills demos that post-select successes after the fact. Clause two kills memory-only demonstrations with no computation. Clause three is the sharpest: the error rate must fall predictably as physical qubits are added, ruling out hero results that never scale. Clause four rules out architectures whose overhead grows with the register. Run recent Quantinuum, Atom Computing, and Microsoft announcements through that filter and the field sorts itself.

DOE buys under the loose definition, but the prize accelerates engineering while the paper clarifies how far it has to go.

The strongest case against the paper

Quantum chemistry may deliver value at 10-6 to 10-8, while factoring 2048-bit RSA needs something like 10-15. A single "entry price" flattens that spectrum into a slogan. Worse, clause four bakes in an assumption about which code families count, and the hardware race is exactly a race over code families: qLDPC codes promise far better overhead than the surface codes behind Google's numbers, so surface-code-era thinking may misprice 2030s hardware.

The conflict-of-interest reading is plain: Martinis co-founded Qolab, a quantum hardware startup, while Troyer and Nayak build Microsoft's competing hardware. A definitional paper from three people with hardware to sell is partly a standards-setting move, and whoever writes the test grades the competition. The RFA, not the paper, controls the money, so vendors will optimize for DOE's 100 logical qubits times 105 hard operations because that is what pays, whether or not it satisfies clause three. Both objections have force, but they cut against the RFA more than the paper: if the bar is algorithm-dependent, a prize with no stated error rate is buying a pig in a poke, and if the test-writers are vendors, the answer is a better independent test, not no test.

Limitations

Here is the honest accounting: my 143x gap assumes one hard operation costs roughly one error-correction cycle, generous to current hardware. The RFA defines hard operations as e.g. non-Clifford gates, each needing magic-state distillation across many cycles, so the true gap is larger. My 2,300-physical-qubit figure treats the paper's asymptotic O(N log(1/e)) bound as an equality with constant 1, which the paper does not license; read it as an illustration of scale, not a prediction. My 12x-per-year pace and 2033 estimate assume smooth exponential improvement, but Google's paper reports rare correlated errors, roughly one per hour, that already limit distance-29 repetition codes: a known error floor no code distance fixes, which my extrapolation walks straight past. The paper contains no experiment, so 10-10 is a reasoned estimate, not a measurement, and I relied on secondary coverage citing the arXiv ID, submission timestamp, and clause language rather than the PDF itself. DOE's $215 million is planned funding "subject to congressional appropriations" (only $2.5 million is appropriated), and the $250,000 upfront Phase I awards select for companies that can self-fund most of the work. Finally, my 10-5 requirement derives from the RFA's 105 hard operations, not DOE's own number, since the RFA leaves metric methodology to negotiation.

What you can do with this

Run every quantum press release through the four clauses with these questions:

  1. What is the error rate per what: per cycle, per gate, per hard operation, or per something the vendor invented? If the denominator is missing, the number is marketing.
  2. Does the rate fall when they add qubits? Clause three is the whole game, and a result that does not show error suppression with scale is a demo, not a trajectory.
  3. Check whether anything was post-selected: if failures were discarded after the fact, the quoted rate describes the survivors, not the machine.
  4. Ask what 100 of them would cost by applying clause four yourself, N log(1/e): if the answer needs a million physical qubits, the announcement is about physics, not products.

Dates to watch: DOE's applicant webinar is September 25, applications are due October 19, and DOE anticipates announcing initial selections no earlier than November 13. Any vendor that quotes its error rate per hard operation rather than per cycle is signaling it read the paper.

The Bottom Line

A definitional paper and a $215 million shopping list arrived on the same afternoon, and the numbers expose the gap between them. Today's best logical qubit fails once in 700 tries. Washington wants to buy machines 140 times better within two years. Usefulness starts at one failure in ten billion, which at the required pace is a 2033 problem. All three numbers can coexist: DOE's prize will accelerate real engineering, the paper gives you the questions to ask the winners, and the physics still says the finish line is years past the deadline. Anyone who applies the four clauses will read the next decade of quantum announcements better than the people writing them.

Sources

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