The US Energy Department Named Eight Science Problems for Its First Fault-Tolerant Quantum Computers Without Setting Problem Sizes or Classical Baselines

October 8, 2026 – The U.S. Department of Energy (DOE) released eight Quantum Genesis Priority Applications, a set of scientific problems the department will use to judge whether its first fault-tolerant quantum computers are scientifically relevant and to direct hardware, software and application research under its Quantum Genesis initiative.

In its priority applications document, DOE grouped the eight applications into chemistry, materials, subatomic physics and applied mathematics, four domains it said offer scientific relevance within five years. DOE said the order of the domains implies no priority and that other fields remain of interest to the department.

The eight applications are:

• Chemistry. Reaction mechanisms and dynamics in complex chemical systems.
• Materials. Equilibrium and ground states of quantum materials as well as the dynamics of materials driven out of equilibrium or placed in extreme environments.
• Subatomic physics. Dynamics and thermalization of strongly interacting matter; physics at high density; nuclear structure and interactions.
• Applied mathematics. Linear systems and partial differential equations.

Each application lists two to five example targets. They include computing the ground-state energy of the doped Fermi-Hubbard model and its energy gap on lattices larger than classical computers can handle, calculating nuclear matrix elements for neutrinoless double-beta decay with parameters matching current or planned experiments, and simulating a turbulent classical fluid flow. The Fermi-Hubbard model describes interacting electrons on a lattice and is a standard model for high-temperature superconductors.

DOE wrote that it did not set target problem sizes. The department instead selected problems for which small demonstrations would be feasible on the first generation of what it calls scientifically relevant quantum computers, or SRQCs, and favored applications for which algorithms, resource estimates and early implementations already exist.

DOE defines an SRQC as a fault-tolerant quantum computer that solves problems of interest to the department’s science mission, and judges its relevance by “the result itself, not the machine that produced it.” DOE listed biological modeling, fusion and plasma science, data analysis and optimization separately, as emerging areas where it said the research is not yet mature enough to name as priorities.

Under Secretary for Science Darío Gil called the applications “a bold declaration of how quantum computing capabilities will open up new scientific frontiers.” DOE said the program will bring domain scientists into partnership with quantum researchers and benchmark quantum results against the most advanced supercomputing methods.

DOE said the applications will guide all three parts of Quantum Genesis: a competition to build fault-tolerant machines, a national quantum computing user facility and research on applications of fault-tolerant quantum computers. The department also said it is working with the Department of War, the Laboratory for Physical Sciences and NASA on quantum applications more broadly.

DOE announced Quantum Genesis on June 23, 2026, one day after President Trump signed Executive Order 14413, Ushering in the Next Frontier of Quantum Innovation. The order established a national effort to deliver at least one quantum computer for scientific discovery to a DOE facility.

The Q Competition, announced on September 17, offers private companies up to $215 million, of which fiscal year 2026 money accounts for $2.5 million and the remainder depends on congressional appropriations. Its second phase pays from a $100 million pool for a first-generation SRQC with at least 100 logical qubits, and from two $50 million bonus pools for systems with 150 and 200 logical qubits, each pool split evenly among the awardees that qualify. Applications close on October 19, and DOE expects to announce selections no earlier than November 13.

In the competition’s request for applications, DOE listed illustrative targets for three generations of machine. A prototype has 10 logical qubits and performs 10³ hard fault-tolerant operations; a first-generation SRQC has 100 logical qubits and 10⁵ hard operations; a next-generation SRQC has 1,000 logical qubits and 10⁷ hard operations. DOE defines a hard operation as one that is difficult in a competitor’s error-correction scheme, and wrote that an actual machine may differ from these figures. In slides for an applicant webinar, DOE said it will consider applicants that propose to reach the first generation no later than 2030.

DOE has also asked its national laboratories to propose a Quantum High Performance Computing Validation and Verification Testbed for checking the performance of fault-tolerant quantum computers, with $45 million planned, of which fiscal year 2026 money accounts for $14 million. Proposals are due on November 10.

DOE said the priority applications draw on the Blueprint for DOE Quantum Supercomputing, which DOE laboratory researchers published in April 2026, and on roadmaps from the leaders of DOE’s National Quantum Information Science Research Centers. In September, the Office of Science Advisory Committee published a roadmap that recommended milestone-driven competitions toward a scientifically relevant, error-corrected quantum computing capability by 2028.

My Analysis

DOE picked the problems the published evidence supports. In seven of the eight applications, DOE asks a quantum computer to simulate quantum mechanics in molecules, materials, nuclei and quantum fields. Finance, logistics and generic machine learning, the areas where I found the weakest evidence when I built my Quantum Utility Map, are not on the list, and optimization appears only among the emerging areas.

DOE presents the list as a basis for judging whether a fault-tolerant machine is scientifically relevant. DOE published no problem size, accuracy target or named classical baseline for any of the eight applications. Of the related problems at classically challenging sizes for which I found published resource estimates, all but one need more operations than DOE’s illustrative figure for the 2028 machine, most of them by a factor of ten or more.

In the Q Competition, DOE requires each awardee to specify a problem and its operation counts and to agree a validation plan with the department. The public list has none of these. DOE can add them before the first machines are evaluated in 2028, mostly with numbers that its own researchers and Google’s team have already published.

Seven of the Eight Applications Are Quantum Simulation

DOE defined a scientifically relevant quantum computer by what it computes. A machine qualifies only when its output answers a question in DOE’s science mission, which rules out sampling benchmarks such as Google’s 2019 random-circuit experiment.

Seven of the applications are quantum simulation, the class of problem where my Quantum Utility Ladder found the strongest published evidence and where Google Quantum AI’s 2025 applications perspective collects most of its end-to-end resource estimates. The eighth, linear systems and partial differential equations, is the one I would move.

The authors moved optimization, data analysis and biological modeling into the emerging category and explained the choice. They favored better-studied problems with existing algorithms, resource estimates and early implementations. That is a stricter test than DOE’s advisory committee applied three weeks earlier, when the committee listed large optimization speedups for finance and supply-chain data among the payoffs it expects. Most quantum optimization proposals with proven speedups rely on quadratic ones. Babbush and colleagues argued in 2021 that quadratic speedups will not overcome error-correction overhead on the first generations of error-corrected hardware without a significant improvement in error correction, and I reached the same conclusion for finance. DOE held the emerging list to a looser standard. Under optimization, it names superintelligence training as an application, with no reference or estimate attached.

DOE also weighted the list toward dynamics. Three applications concern how systems evolve in time, and two more include time-evolution targets, neutrino flavor oscillations under high-density physics and neutrino-nucleon scattering under nuclear structure. Google’s team argues that classical methods struggle with non-equilibrium dynamics, and quenches of spin and Hubbard models are among the nearest-term entries in its compendium of resource estimates. In a quench, researchers switch a model’s parameters suddenly and follow how the system evolves.

DOE framed both chemistry applications as embedding problems, with a strongly correlated active site computed on the quantum machine inside a classically modeled environment. That matches the conclusion of my assessment of quantum chemistry about how these machines will most likely be used in chemistry. DOE tied the high-density and nuclear targets to RHIC, the LHC and DUNE, and asked for parameters matching current or planned experiments in quantum materials and in neutrinoless double-beta decay. Google’s team argues that a useful quantum computation should be checkable, whether by a classical computer, another quantum device or nature itself. For targets matched to experiments, researchers can compare the computed observable with the measured one, within the experiment’s uncertainty.

No Public Problem Sizes, Accuracy Targets or Classical Baselines

In its announcement, DOE said the list provides a concrete basis for judging the scientific relevance of fault-tolerant quantum computers, and the priority applications document says progress on each application requires resource estimates and benchmarking against the best-known classical alternatives. DOE then chose not to set problem sizes.

A target that can be judged needs four things: the instance and its size, the accuracy the answer must reach, the classical method and computing budget it must beat or the experiment it must match, and the method of verification. The priority document gives parts of this for some targets, mostly the experiments to match, and a complete, quantitative specification for none. In the Fermi-Hubbard target, DOE asks for lattices larger than classical computers can currently handle, without naming the classical method or the computing budget for the comparison.

For its own awardees, DOE wrote part of this into the Q Competition’s request for applications. DOE will benchmark machines partly on the number of hard operations they complete reliably. Each awardee must specify a problem and solution algorithm at the start of the program and estimate the hard and easy operations and wall-clock time it needs to run its proposed applications. It is expected to deliver a verification and validation plan within six months. Its demonstrations must come with validation data, code and input and output data. The first-generation workflow may run at sizes classical computers can still handle. DOE settles these details with each awardee separately, so two of them could demonstrate different instances of the same target at different sizes and accuracies, with no public specification to compare the results against.

In May, Q-CTRL reported a 120-qubit simulation of one-dimensional Fermi-Hubbard dynamics on IBM hardware that finished in under three minutes, against more than 100 hours for its chosen classical solver. A week later, Algorithmiq reproduced the result for a single lattice site in two and a half minutes on a laptop. Q-CTRL replied that its run had produced all 120 single-site occupations and more than 7,000 two-point spin correlations at once, and that Algorithmiq had published no error analysis. Four weeks after Q-CTRL’s announcement, Multiverse Computing researchers reported fully converged classical results across the whole simulation window, at bond dimensions up to about 62,000 on four NVIDIA H200 GPUs. At a bond dimension comparable to Q-CTRL’s best classical run, the Multiverse code finished in about 100 minutes. The three comparisons differed in the observables, the accuracy and the classical method. DOE’s targets often name the observable, but none sets an accuracy or names a classical method. Q-CTRL ran on physical qubits without error correction, and a fault-tolerant demonstration of a DOE target would face the same questions.

The missing numbers exist. Google’s team lists, for each simulation instance in its compendium, the logical qubits and Toffoli gates required and the classical method it was compared against, for example matrix product states for an Ising quench and the density matrix renormalization group (DMRG) for FeMoco. FeMoco, the iron-molybdenum cofactor of the nitrogen-fixing enzyme nitrogenase, has been the standard benchmark for quantum chemistry resource estimates since Reiher and colleagues costed it in 2017. Researchers at DOE’s National Energy Research Scientific Computing Center published an assessment in September 2025 that set resource requirements for materials, chemistry and high-energy physics against ten vendors’ roadmaps. DOE’s advisory committee proposed the staging the list needs: validate fault-tolerant runs against classical methods or experiments first, then push past classical limits, then deliver new predictive capability or efficiency gains by 2028.

DOE says the list draws heavily on the April 2026 Blueprint. Whatever resource estimates the Blueprint contains, DOE didn’t attach any to the eight applications, and it marked none of the example targets with a stage.

DOE has also described the first-generation machine’s operations in three ways. Its September 17 announcement described a machine capable of hundreds of millions of fault-tolerant operations. The request for applications defines the first generation as capable of “thousands of hard fault-tolerant operations” for a specific scientific workflow and lists 10⁵ in its table of illustrative figures. DOE counts as hard only the operations that are difficult in a machine’s error-correction scheme, so the announcement’s figure probably counts every logical operation and the other two only the expensive ones, which would explain most of the gap. DOE hasn’t said how the three figures relate.

Published Resource Estimates for Related Problems

I set each application beside the published end-to-end resource estimate I found for a related problem. None was made for one of DOE’s example targets as DOE worded it, and they count different things. Most give the cost of one circuit run, while the stopping-power figure totals every run of a campaign. Estimating an observable usually takes many runs, which costs time but doesn’t lengthen any single circuit. Resource estimates count non-Clifford gates, the operations that consume magic states in most error-correction schemes, as Toffoli or T gates. A Toffoli can be built from one CCZ magic state or from four to seven T gates, depending on the construction. Because DOE leaves the definition of a hard operation to each competitor’s error-correction scheme, I compare the reported counts with DOE’s illustrative figures by counting each Toffoli or T gate as one hard operation. That is the most generous reading for the machine, and the comparisons are approximate.

The smallest examples in the table need 131 to 162 logical qubits, which a machine at the Q Competition’s 200-qubit bonus tier would cover. Their operation counts range over two orders of magnitude. Only the Ising quench, at 4×10⁴ Toffolis, fits within the first generation’s illustrative 10⁵ hard operations. The Hubbard and Heisenberg quenches need 10 and 60 times more; the 8×8 Hubbard ground-state estimates need 14 to 23 times more. The condensed-matter problems that Google’s compendium and my Utility Ladder both rank as the earliest candidates pair a qubit count near DOE’s first-generation figure with an operation count between its first- and next-generation figures. I chose these examples from the published literature; smaller instances exist, and DOE’s rules allow a first-generation workflow at sizes classical computers can still handle.

DOE put reaction mechanisms in a domain it expects to show scientific relevance within five years. The reaction-mechanism examples in the table are single ground-state energies at 2×10⁸ to 10⁹ Toffolis, 20 to 100 times DOE’s illustrative next-generation figure. DOE wants free-energy landscapes, competing pathways and selectivity from that application, and each of those takes many such calculations plus the cost of embedding them in a classically modeled environment. The reaction-dynamics example, a singlet-fission run at 3×10⁶ Toffolis, needs far less.

A Google and Sandia team that included Andrew Baczewski, who also contributed to DOE’s advisory committee report, estimated that classically intractable stopping-power calculations for inertial fusion need roughly as many logical qubits as the FeMoco and P450 simulations of the time and about 100 times as many Toffoli gates. Google’s compendium lists 6,200 logical qubits, six times DOE’s illustrative next-generation figure, and 10¹⁵ Toffolis across all the runs. DOE lists a related target, the stopping power of a plasma-facing material under fusion-relevant conditions, among its examples, while noting elsewhere in the same document that current estimates put some studied applications out of reach for the first generation.

For the strongly interacting matter application, the nearest estimate I found covers particle scattering in a scalar field theory, simpler than the gauge theories DOE targets, at about 500 to 1,000 logical qubits and 10¹² T gates, or about a day on 4 million physical qubits with a 100-nanosecond surface-code cycle. For DOE’s targets in SU(3) lattice gauge theory, the discretized formulation of the strong force between quarks, Balaji and colleagues have published circuits and resource scalings, but I found no end-to-end estimate for a specific target.

The Q Competition’s Bonus Pools Pay for Logical Qubits

To share the $100 million general pool, an awardee must demonstrate a first-generation SRQC, with at least 100 logical qubits performing thousands of hard operations for a specific scientific workflow. The two $50 million bonus pools go in equal shares to awardees that reach 150 and 200 total logical qubits while meeting the other first-generation goals, and DOE can negotiate equivalent metrics for architectures not naturally measured in logical qubits. DOE pays no bonus for more operations. An awardee that reaches 200 logical qubits at the illustrative 10⁵ hard operations and meets the other goals qualifies for a share of all three pools, and still can’t run the Hubbard ground-state estimates in the table.

Sandia researchers measured the same constraint on today’s hardware with their QUOPS benchmark, which I covered in September. They found today’s processors about five orders of magnitude short of the circuit sizes needed to run their challenge problems, while the fastest superconducting processors, measured on physical qubits, already exceed the operation rate a FeMoco calculation would need to finish in five days.

DOE can still change the incentive when it negotiates the awards. It already plans to benchmark hard operations and asks each applicant to estimate the operations needed to run its applications. DOE could therefore tie the bonus pools to an operation count as well as to qubits. A 200-logical-qubit machine sustaining about 3×10⁶ hard operations would run the Ising and Hubbard quenches, the 8×8 ground-state estimates and, at the margin, the singlet-fission run. At 10⁵ hard operations, it would run only the Ising quench.

The Weak Case for Linear Systems and Fluid Dynamics

Linear systems and partial differential equations are the application I would move to DOE’s emerging list. Quantum algorithms for linear systems are well developed. Google’s team wrote that, for the HHL linear-systems algorithm and its more than 4,000 citations, they are “not aware of any paper identifying a promising real-world instantiation” with a better-than-quadratic speedup.

Researchers at Los Alamos National Laboratory and University College London proved in 2024 that, for a system with at least one positive Lyapunov exponent (the mark of chaos) and solutions that grow sub-exponentially, described in natural coordinates, any quantum algorithm that outputs a state approximating the normalized solution must run for a time that grows at least exponentially with the simulated time. Turbulent flow is chaotic, though the proof covers only algorithms that output the full solution state. Jennings and colleagues published the most complete end-to-end fluid-dynamics algorithm I know of last December, and PRX Quantum accepted it in July. They bound its speedup polynomially and describe the advantage as “small, but nontrivial” for selected observables at loose error tolerances.

DOE acknowledged in its applied mathematics section that these advantages are hard to demonstrate rigorously on near-term devices. In the fusion and plasma entry on its emerging list, DOE calls nonlinear turbulence a longer-term goal, while listing the simulation of a turbulent fluid flow among its five-year targets. The other 4.A target is sampling the solution of a linear system whose matrix is supplied as a quantum oracle. In its five-stage framework, Google’s team places oracle-model results of this kind at Stage I until someone shows how to build classically hard instances.

The Unsettled Debate on Ground-State Chemistry

DOE wrote that it chose each application for a problem class with a strong scientific basis for believing classical computers face fundamental scaling barriers. For ground-state chemistry, that basis is contested. In 2023, Seunghoon Lee, Garnet Chan and 16 co-authors, including John Preskill and Google’s Ryan Babbush, found no evidence yet of an exponential quantum advantage for generic ground-state chemistry, while leaving room for polynomial speedups. In their 2025 perspective, Babbush and his Google colleagues argued that asymptotic scaling is the wrong lens for finite molecules, and that no classical method has resolved FeMoco to the accuracy chemists need.

Babbush is an author of both papers. DOE doesn’t mention the debate in the priority document. In my chemistry assessment, I concluded that the case for quantum chemistry depends on specific strongly correlated instances compared against DMRG and coupled-cluster results on the same instance, and DOE’s reaction-mechanism targets need that comparison written into them.

Example Targets Already Computed Classically or on Noisy Hardware

Several example targets have already been run at small sizes. Hayata, Hidaka and Nishimura computed the equation of state and chiral condensate of one-dimensional SU(3) quantum chromodynamics (QCD), the theory of quarks and gluons, at zero temperature and finite density with matrix product states. In 2025, Than and colleagues prepared thermal states of one-dimensional SU(2) and SU(3) gauge theories at finite density on a trapped-ion quantum computer, for a single unit cell at one temperature, in a paper DOE’s advisory committee cites; they computed the wider phase diagram classically. In its high-density target, DOE asks for the phase diagram across a range of temperatures and densities, with the chiral condensate at each point, still in one dimension.

Google researchers observed time-crystalline order in a periodically driven, disordered spin chain on a superconducting processor and reported it in Nature in November 2021. That experiment is a small instance of DOE’s target on Floquet engineering in disordered spin systems. Chernyshev, Savage and colleagues, working with IonQ, simulated a two-site lattice model in which a Majorana mass for the neutrino, built into the model, violates lepton number, the signature of neutrinoless double-beta decay. They watched the violation develop in real time on 32 trapped-ion qubits, plus four used to flag errors, in a paper published in Nature Communications in January; the authors note that the model’s parameters are not those of nature.

The shell-model target reads like a validation exercise. In the same section, DOE wrote that classical methods can calculate only small or medium-sized nuclei with high precision. DOE then asked for a shell-model calculation of a medium-mass nucleus. Whether it would be one depends on the nucleus, the model space and the interaction, and DOE specifies none of them.

Each of these makes a reasonable first run for a fault-tolerant machine. DOE hasn’t said which version of each would count as a new result.

What DOE Should Publish Before the 2028 Evaluation

Four changes would make the list usable as a test:

1. A specification sheet for each example target. It should give the instance and its size, the observable and the accuracy required, the classical method and computing budget a quantum result has to beat or the experiment it has to match, the verification route, and the best published resource estimate. Google’s team already publishes most of these fields for about twenty simulation instances.
2. Operation counts in the bonus tiers, and public workflows. The 150- and 200-qubit bonus pools should require a hard-operation count as well as qubits, and DOE should publish each awardee’s negotiated workflow, operation budget and validation results.
3. A stage for every target. DOE should assign each example target to one of the three stages its advisory committee proposed: validation against classical methods or experiment, computation beyond classical limits, or delivery of new predictive capability or efficiency gains.
4. Linear systems and partial differential equations moved to the emerging list, until someone publishes a real-world instance with an end-to-end speedup larger than the error-correction overhead.

DOE has time to make all four. Q Competition applications close on October 19, eleven days after the list appeared, and DOE expects selections no earlier than November 13. Proposals for the validation and verification testbed are due on November 10, and Executive Order 14413 gives DOE until December 19 to establish a national center for assessing the performance of quantum computers. Either would be a natural owner of these specification sheets. The first-generation evaluation follows in September 2028, and DOE’s advisory committee has warned that meeting 2028 will require “acceleration beyond current investment and development trajectories.”

For research directors in chemistry and materials, the published examples split in two. Lattice-model dynamics and the ground states of small lattices need qubit counts near DOE’s first-generation figure and operation counts up to its next-generation figure, while the molecular ground-state energies and the nuclear dynamics example need 20 to 100 times its next-generation figure. These are costs for particular algorithms and instances, often upper bounds, and later work can lower them. Anyone reading the 2028 announcements should ask for the instance size, operation count and classical comparison behind each demonstration, since DOE pays the competition’s bonuses by logical-qubit count.

DOE has named eight problems worth a fault-tolerant quantum computer’s time. It has until the 2028 evaluation to publish which answers to them would count.

From the author