Matthias Troyer and Chetan Nayak of Microsoft Quantum and John Martinis of Qolab proposed a stricter standard for logical qubits in a preprint, not yet peer reviewed, that they posted to arXiv on September 17, 2026. A logical qubit is one unit of quantum information spread across many physical qubits so that a machine can find and correct errors in individual qubits.
The authors wrote that “the term logical qubit is used today for a wide range of demonstrations.” They proposed a narrower name, the scalable logical qubit, for an encoded qubit that meets four conditions at once. On September 22, Microsoft published a blog post adapted from the preprint.
Troyer, Nayak, and Martinis posted the preprint on the day the U.S. Department of Energy (DOE) opened a competition in which it will pay companies for logical qubits. DOE plans to divide $100 million among companies that demonstrate at least 100 logical qubits at a final evaluation planned for September 2028, judged by methods it will negotiate with each company.
Martinis, who co-founded the superconducting-hardware company Qolab and is its chief technology officer, shared the 2025 Nobel Prize in Physics.
The four conditions
Under the first condition, a machine must sustain the logical qubit with repeated rounds of quantum error correction throughout a computation. Under the second, the qubit must support a universal set of fault-tolerant logical operations, enough to run any quantum algorithm. The set must include control flow, in which later steps depend on earlier measurement results.
Error-correcting codes such as the surface code natively support only a restricted set of operations, called Clifford gates, that a classical computer can simulate efficiently. A universal machine also needs at least one non-Clifford gate.
The authors attached a timing requirement to the second condition. A decoder, the classical software or hardware that turns the results of error checks into corrections, must work fast enough for a program to branch on a measurement result in real time.
Under the third condition, the qubit must come from a code family, with a supporting machine design, in which the logical error rate falls predictably as more physical qubits are devoted to each logical qubit.
A code family is a series of related codes that can be built in increasing sizes. Raising the code distance, a measure of how many physical errors a code can correct, is one way to add physical qubits to each logical qubit.
Under the fourth condition, a design must have a credible path to hundreds or thousands of logical qubits that perform as well as the first. The authors capped the hardware cost of that growth. They wrote that a machine with N logical qubits at a logical error rate ε should need no more than on the order of N log(1/ε) physical qubits.
Under that bound, the physical-qubit count should grow no faster than the number of logical qubits times the number of decimal places in the target error rate, up to a constant factor.
Error detection and utility targets
In post-selection, experimenters keep only the runs in which no error was detected. The authors wrote that “error detection and post-selection can also be powerful,” for example in producing higher-quality resource states, which a computer consumes to perform some operations. They added that “post-selection at the application level by itself does not scale to long computations,” because the chance of an error-free run typically falls rapidly as circuits get longer.
Troyer, Nayak, and Martinis placed the low end of useful computation at around 100 or more logical qubits with error rates on the order of 1 in 10 billion. They wrote that high-end applications “such as large-scale chemistry and cryptanalysis” would need more than 1,000 logical qubits at error rates of 1 in a quadrillion or better. They cited published estimates of the qubits and time such applications need, including Craig Gidney’s 2025 analysis of factoring a 2048-bit RSA key.
The authors listed five questions for early demonstrations. They asked about the number of error-correction cycles run, the capabilities shown, and the logical error rates, including whether those beat physical rates and how added physical qubits would lower them. They also asked how many logical qubits have been realized and what control system would support a machine large enough for useful applications.
The DOE competition
DOE opened the Quantum Genesis Q Competition on September 17 with up to $215 million in planned funding. DOE said $2.5 million of that is fiscal 2026 money and that funding for later years depends on congressional appropriations.
In its request for applications, DOE defined a logical qubit as “an effective qubit spread across multiple subsystems that can be operated under a quantum error correction regime” to suppress errors or environmental noise.
DOE wrote that proposals for machines capable only of error mitigation or detection, and not correction, are not of interest. In error mitigation, researchers use extra runs and classical post-processing to reduce the effect of noise on a result, without correcting the errors themselves.
DOE also plans two $50 million bonus pools for companies that reach 150 and 200 logical qubits. In the request, it set an illustrative first-generation target of 100 logical qubits and 100,000 hard operations. DOE defined a hard operation as one that is difficult in a company’s error-correction scheme but necessary for universal computation, such as a non-Clifford gate.
DOE wrote that it and each selected applicant “will, during negotiation, specify, to the extent possible, the methodology used” to define and evaluate these metrics. DOE expects to announce its first selections no earlier than November 13, after applications close on October 19.
