Screening the low-activation alloys that make up a fusion reactor's plasma-facing and structural components by density-functional theory (DFT) runs into a wall: on the correlated 3d transition metals that constitute the family, the computed energetics depend on the exchange–correlation functional at the level of hundreds of millihartree, which is comparable to or larger than the composition differences the screen must resolve. A screen whose verdict changes with the functional is not a screen. We close that gap with an adaptive variational quantum eigensolver. We first set out the governing electronic-structure problem, the formal origin of the functional ambiguity, the well-posedness condition for a composition screen, the fermion-to-qubit mapping, and the ADAPT-VQE construction with its exact gradient-selection criterion and monotone-convergence property. We then report the frozen results of the Kronos de-risking campaign (register serial BR-SX-07): ADAPT-VQE reaches chemical accuracy on all four 3d-alloy fragments (Ti, V, Cr, Fe) with a residual below 0.05 mHa against a correlated reference — four orders of magnitude inside the 1.6 mHa (1 kcal mol^-1) chemical-accuracy threshold and four orders of magnitude tighter than the >300 mHa DFT functional spread it replaces — using adaptively grown circuits that are 4–14× shallower in two-qubit (CNOT) count than a unitary coupled-cluster (UCCSD) ansatz at equal accuracy. An independently reproduced four-qubit proof-of-concept validates the machinery to 3.9×10^-6 Ha against exact diagonalization. The results were produced on the NVIDIA GPU HPC campaign by classical statevector emulation of the quantum circuits, with plane-wave DFT and correlated quantum-chemistry references computed on the same fleet. We state the honest gate once and quantify it: this is not a claim of quantum advantage; a single-determinant ADAPT-VQE variant stalls at 24 mHa on the strongly multireference vacancy limit; and scaling from fragments to a full alloy or REBCO cell moves the problem into fault-tolerant quantum phase estimation, estimated at ~10^9 Toffoli gates and ~238 logical qubits (~38 days at a 1 kHz logical-Toffoli throughput). We place the method inside the honest-scoping grammar of the Kronos AI-and-quantum programme: the fragment ADAPT-VQE energetics are a twin-testable capability that runs today on classical hardware, the full-cell phase estimation is a horizon-class quantum task quoted against an explicit classical baseline, and every offline quantum kernel is benchmarked in qubits and non-Clifford (Toffoli/T) gate count with no crossover to the real-time control loop this decade. On the resulting ladder the alloy-chemistry phase estimation (~10^9 Toffoli) is the most tractable offline kernel — far below the equilibrium linear-solve (~10^17 T gates) and fleet-optimization (~10^19–10^23 T gates) kernels — and we report the matrix-product-state classical frontier it must beat. The deliverable is a validated, circuit-efficient electronic-structure tool for composition-of-matter screening today, with a resource-honest map of what the fault-tolerant extension will cost. Key results (frozen anchors): Q = 3.076; delta = -0.30; kappa = 2.0; p = 1; q = 1; s = 1. Methods & codes: OpenMC, VQE, ADAPT-VQE. Live verification: 2 gate validator(s) with live-recompute cards (2 reproduced). See the Verification section and data/verification.csv. Related: Paper page · De-risking register · 3D model · Learn more about Kronos Part of the 2026 Kronos publication series; independently re-run and stamped in the Kronos de-risking register (DOI 10.5281/zenodo.22645689). All numerical values are frozen design-point anchors; see the register. Public research artifact. No proprietary, financial, or supply-chain information is included.
Screening the low-activation alloys that make up a fusion reactor's plasma-facing and structural components by density-functional theory (DFT) runs into a wall: on the correlated 3d transition metals that constitute the family, the computed energetics depend on the exchange–correlation functional at the level of hundreds of millihartree, which is comparable to or larger than the composition differences the screen must resolve. A screen whose verdict changes with the functional is not a screen. We close that gap with an adaptive variational quantum eigensolver. We first set out the governing electronic-structure problem, the formal origin of the functional ambiguity, the well-posedness condition for a composition screen, the fermion-to-qubit mapping, and the ADAPT-VQE construction with its exact gradient-selection criterion and monotone-convergence property. We then report the frozen results of the Kronos de-risking campaign (register serial BR-SX-07): ADAPT-VQE reaches chemical accuracy on all four 3d-alloy fragments (Ti, V, Cr, Fe) with a residual below 0.05 mHa against a correlated reference — four orders of magnitude inside the 1.6 mHa (1 kcal mol^-1) chemical-accuracy threshold and four orders of magnitude tighter than the >300 mHa DFT functional spread it replaces — using adaptively grown circuits that are 4–14× shallower in two-qubit (CNOT) count than a unitary coupled-cluster (UCCSD) ansatz at equal accuracy. An independently reproduced four-qubit proof-of-concept validates the machinery to 3.9×10^-6 Ha against exact diagonalization. The results were produced on the NVIDIA GPU HPC campaign by classical statevector emulation of the quantum circuits, with plane-wave DFT and correlated quantum-chemistry references computed on the same fleet. We state the honest gate once and quantify it: this is not a claim of quantum advantage; a single-determinant ADAPT-VQE variant stalls at 24 mHa on the strongly multireference vacancy limit; and scaling from fragments to a full alloy or REBCO cell moves the problem into fault-tolerant quantum phase estimation, estimated at ~10^9 Toffoli gates and ~238 logical qubits (~38 days at a 1 kHz logical-Toffoli throughput). We place the method inside the honest-scoping grammar of the Kronos AI-and-quantum programme: the fragment ADAPT-VQE energetics are a twin-testable capability that runs today on classical hardware, the full-cell phase estimation is a horizon-class quantum task quoted against an explicit classical baseline, and every offline quantum kernel is benchmarked in qubits and non-Clifford (Toffoli/T) gate count with no crossover to the real-time control loop this decade. On the resulting ladder the alloy-chemistry phase estimation (~10^9 Toffoli) is the most tractable offline kernel — far below the equilibrium linear-solve (~10^17 T gates) and fleet-optimization (~10^19–10^23 T gates) kernels — and we report the matrix-product-state classical frontier it must beat. The deliverable is a validated, circuit-efficient electronic-structure tool for composition-of-matter screening today, with a resource-honest map of what the fault-tolerant extension will cost. Key results (frozen anchors): Q = 3.076; delta = -0.30; kappa = 2.0; p = 1; q = 1; s = 1. Methods & codes: OpenMC, VQE, ADAPT-VQE. Live verification: 2 gate validator(s) with live-recompute cards (2 reproduced). See the Verification section and data/verification.csv. Related: Paper page · De-risking register · 3D model · Learn more about Kronos Part of the 2026 Kronos publication series; independently re-run and stamped in the Kronos de-risking register (DOI 10.5281/zenodo.22645689). All numerical values are frozen design-point anchors; see the register. Public research artifact. No proprietary, financial, or supply-chain information is included.
Quantum computing is routinely invoked for fusion without a disciplined account of what is reachable now and what is a fault-tolerant-horizon problem. We supply that account for a specific machine — the Kronos Hyperion compact spherical-tokamak breeder (design point I_p=9.66, Q=3.076, P_ fus=85.04, negative triangularity δ=-0.30, B_0=8, elongation κ=2.0, major radius R_0=1.20, aspect ratio A=2.5, centrepost peak field 16.84) and its distinct tandem-mirror burner — through two grounded demonstrations, a resource frontier, and a pre-registered honest negative. First, a genuinely kinetic collisionless phenomenon, Landau damping, is reproduced on a 5-qubit circuit: casting the linearized Vlasov–Poisson system in an asymmetrically-weighted Fourier–Hermite basis and folding in the Poisson closure yields a Hermitian generator whose unitary evolution is a legitimate Hamiltonian-simulation target, and the circuit reproduces the analytic Landau rate to 1–7% across three wavenumbers, landing the complex dispersion at /=1.4157-0.1534 i against the textbook 1.4156-0.1533 i. Second, an adaptive variational quantum eigensolver (ADAPT-VQE) reaches chemical accuracy (better than 1.6 mHa) on the transition-metal fragments of the candidate low-activation refractory alloys, four orders of magnitude below the ~300mHa spread of density-functional exchange–correlation choices, with a fixed-ansatz depth 4–14× shallower than unitary coupled cluster. A third strand is a genuinely measured quantum capability: an in-winding nitrogen-vacancy (NV) diamond magnetometer resolves a ~100 superconducting-quench step at a per-shot signal-to-noise ratio of ~1.5×10^9 (sensitivity 0.189/Hz, bandwidth 125), giving single-shot quench-precursor detection — but its headline femto/pico-tesla sensitivity is forfeited in the reactor vessel, a second pre-registered negative we keep rather than hide. The honest boundaries are explicit: under a representative noise model the field-energy observable decoheres to the maximally-mixed floor 1/32 and the damping signature is lost, so present-day noisy hardware shows no advantage; and while the linear collisionless kinetic operator is an early-fault-tolerant target (11–19 logical qubits, 10^5–10^6 non-Clifford gates), the nonlinear five-dimensional gyrokinetic problem that actually sets confinement remains a fault-tolerant-horizon target (~10^2 logical qubits, 10^9–10^13 non-Clifford gates), and the Harrow–Hassidim–Lloyd equilibrium linear solve — the single most-invoked ``quantum inner kernel'' — costs ~1.8×10^17 T-gates once read-in and read-out are counted, a boundary and not a route this decade. Against the classical frontier — nonlinear CGYRO gyrokinetics and a quantum-inspired matrix-product-state solver that runs 21.2× faster at bond dimension 7, is the only feasible method past bond dimension 10, and drives its error to 2.2×10^-10 at bond dimension 16 — the classical tool is cheaper at every scale demonstrated here. The contribution is a set of validated encodings, a rigorous numerical formulation, and an honest, dated resource map, not a claim of quantum advantage.Key results (frozen anchors): k = 0.30 0.50; mathrmSNR = 1.5 ×10^9.Methods & codes: CGYRO, QAOA, VQE, ADAPT-VQE.Live verification: 8 gate validator(s) with live-recompute cards (5 reproduced, 3 estimated). See the Verification section and data/verification.csv.Related: Paper page · De-risking register · 3D model · Learn more about KronosPart of the 2026 Kronos publication series; independently re-run and stamped in the Kronos de-risking register (DOI 10.5281/zenodo.22645689).All numerical values are frozen design-point anchors; see the register.Public research artifact. No proprietary, financial, or supply-chain information is included.Note (REPLACE): This record replaces and supersedes DOI 10.5281/zenodo.22132180; please cite this version.
Quantum computing is routinely invoked for fusion without a disciplined account of what is reachable now and what is a fault-tolerant-horizon problem. We supply that account for a specific machine — the Kronos Hyperion compact spherical-tokamak breeder (design point I_p=9.66 MA, Q=3.076, P_fus=85.04 MW, negative triangularity δ=-0.30, B_0=8 T, elongation κ=2.0, major radius R_0=1.20 m, aspect ratio A=2.5, centrepost peak field 16.84 T) and its distinct tandem-mirror burner — through two grounded demonstrations, a resource frontier, and a pre-registered honest negative. First, a genuinely kinetic collisionless phenomenon, Landau damping, is reproduced on a 5-qubit circuit: casting the linearized Vlasov–Poisson system in an asymmetrically-weighted Fourier–Hermite basis and folding in the Poisson closure yields a Hermitian generator whose unitary evolution is a legitimate Hamiltonian-simulation target, and the circuit reproduces the analytic Landau rate to 1–7% across three wavenumbers, landing the complex dispersion at /=1.4157-0.1534 i against the textbook 1.4156-0.1533 i. Second, an adaptive variational quantum eigensolver (ADAPT-VQE) reaches chemical accuracy (better than 1.6 mHa) on the transition-metal fragments of the candidate low-activation refractory alloys, four orders of magnitude below the ~300mHa spread of density-functional exchange–correlation choices, with a fixed-ansatz depth 4–14× shallower than unitary coupled cluster. A third strand is a genuinely measured quantum capability: an in-winding nitrogen-vacancy (NV) diamond magnetometer resolves a ~100 superconducting-quench step at a per-shot signal-to-noise ratio of ~1.5×10^9 (sensitivity 0.189/Hz, bandwidth 125), giving single-shot quench-precursor detection — but its headline femto/pico-tesla sensitivity is forfeited in the reactor vessel, a second pre-registered negative we keep rather than hide. The honest boundaries are explicit: under a representative noise model the field-energy observable decoheres to the maximally-mixed floor 1/32 and the damping signature is lost, so present-day noisy hardware shows no advantage; and while the linear collisionless kinetic operator is an early-fault-tolerant target (11–19 logical qubits, 10^5–10^6 non-Clifford gates), the nonlinear five-dimensional gyrokinetic problem that actually sets confinement remains a fault-tolerant-horizon target (~10^2 logical qubits, 10^9–10^13 non-Clifford gates), and the Harrow–Hassidim–Lloyd equilibrium linear solve — the single most-invoked ``quantum inner kernel'' — costs ~1.8×10^17 T-gates once read-in and read-out are counted, a boundary and not a route this decade. Against the classical frontier — nonlinear CGYRO gyrokinetics and a quantum-inspired matrix-product-state solver that runs 21.2× faster at bond dimension 7, is the only feasible method past bond dimension 10, and drives its error to 2.2×10^-10 at bond dimension 16 — the classical tool is cheaper at every scale demonstrated here. The contribution is a set of validated encodings, a rigorous numerical formulation, and an honest, dated resource map, not a claim of quantum advantage. Key results (frozen anchors): k = 0.30 0.50. Methods & codes: CGYRO, QAOA, VQE, ADAPT-VQE. Live verification: 8 gate validator(s) with live-recompute cards (5 reproduced, 3 estimated). See the Verification section and data/verification.csv. Related: Paper page · De-risking register · 3D model · Learn more about Kronos Part of the 2026 Kronos publication series; independently re-run and stamped in the Kronos de-risking register (DOI 10.5281/zenodo.22645689). All numerical values are frozen design-point anchors; see the register. Public research artifact. No proprietary, financial, or supply-chain information is included. Previous version: DOI 10.5281/zenodo.22132180. Please cite this version.
This record has been superseded. The current, updated version is Resource-Honest Quantum Computing for Fusion: Variational Landau-Damping Emulation and ADAPT-VQE Low-Activation Alloy Chemistry Against the Classical Frontier (DOI 10.5281/zenodo.22645718). Please read and cite the current version. This page stays online so existing citations keep resolving. Quantum computing for fusion, with honest resource estimates. Landau damping reproduced on a five-qubit Hamiltonian-simulation circuit; ADAPT-VQE at chemical accuracy on the candidate fusion-alloy fragments; and a resource frontier separating the tractable linear kinetic operator (early fault-tolerant) from the nonlinear gyrokinetic problem (fault-tolerant horizon). Noisy hardware shows no advantage today; classical gyrokinetics remains cheaper at every demonstrated scale.
Quantum computing and quantum sensing are routinely proposed as accelerants for fusion; a serious design program should test those proposals quantitatively rather than assume them. We deliver a resource-honest map of where the quantum toolbox helps a compact spherical-tokamak breeder and its tandem-mirror burner, and where it does not, formalised as three coupled estimation problems and computed on a single GPU-HPC campaign. On the machine-learning front we build a quantum-kernel transport surrogate and measure its classifier area-under-curve (AUC) falling with encoding width — 0.817 at four qubits to 0.691 at eight — the signature of exponential kernel concentration, for which we give the variance bound and the induced shot-cost scaling; at a realistic 37-logical-qubit problem the quantum Gram evaluation is 9–11 orders of magnitude slower than its classical counterpart. On the sensing front we derive the entanglement-advantage condition from the quantum Fisher information and specify the in-cryostat magnetometry chain for the breeder centrepost (peak field 16.84 T, kept formally distinct from the burner plug at 26.49 T): an NMR/EPR probe as the absolute monitor to ≤1 ppm, a SQUID and an NV-diamond ensemble (1 pT Hz^-1/2) for the 1 mT quench precursor, with the entanglement knee located at a normalised signal ≈0.14. Every Kronos in-bore diagnostic sits below the knee, where entanglement buys only +0.00077 AUC; above it (deep error-field mapping) a Heisenberg-limited protocol carries the standard-quantum-limit sensitivity from 5.7×10^-7 to 5.7×10^-8 T at 100 probes. On the fault-tolerant front we recompute the resource ledger from first formulas — the Grover iteration count 1.62^n and the surface-code footprint 2d^2 physical qubits per logical qubit — across 50 rows with zero discrepancy, and date the single fusion-relevant near-term niche: linear Vlasov kinetics at 11–19 logical qubits around 2029±2, with nonlinear five-dimensional gyrokinetics beyond 2035 and fleet-scale Grover search never practical (1.8×10^18 iterations). Three further workloads keep the verdict resource-honest: full six-dimensional kinetic Hamiltonian simulation at ~44 logical qubits and ~19 days, fault-tolerant phase estimation of the exact REBCO/alloy ground state at ~238 logical qubits and ~10^9 Toffoli gates, and a Harrow–Hassidim–Lloyd equilibrium linear solve at ~10^17 T-gates — all calibration-only. Two of the six quantum-track items are already twin-testable classically: a materials variational eigensolver reproduces a model ground state to 3.9×10^-6 Ha and reaches chemical accuracy on 3d alloy fragments with 4–14× shallower circuits than unitary coupled cluster (no advantage claimed), and a tensor-network kinetic solver compresses the distribution function with exponential rank convergence (2.2×10^-10 at bond rank 16, 0.19× storage). The honest bottom line is that nothing on the design critical path waits on quantum hardware — and establishing that, with the numbers behind it, is the result. Key results (frozen anchors): iter = 1.8 ×10^18; iter = 1.6 2^n. Methods & codes: CGYRO, GENE, QAOA, VQE, ADAPT-VQE. Live verification: 11 gate validator(s) with live-recompute cards (5 reproduced, 5 estimated, 1 revised). See the Verification section and data/verification.csv. Related: Paper page · De-risking register · 3D model · Learn more about Kronos Part of the 2026 Kronos publication series; independently re-run and stamped in the Kronos de-risking register (DOI 10.5281/zenodo.22645689). All numerical values are frozen design-point anchors; see the register. Public research artifact. No proprietary, financial, or supply-chain information is included.
Quantum computing and quantum sensing are routinely proposed as accelerants for fusion; a serious design program should test those proposals quantitatively rather than assume them. We deliver a resource-honest map of where the quantum toolbox helps a compact spherical-tokamak breeder and its tandem-mirror burner, and where it does not, formalised as three coupled estimation problems and computed on a single GPU-HPC campaign. On the machine-learning front we build a quantum-kernel transport surrogate and measure its classifier area-under-curve (AUC) falling with encoding width — 0.817 at four qubits to 0.691 at eight — the signature of exponential kernel concentration, for which we give the variance bound and the induced shot-cost scaling; at a realistic 37-logical-qubit problem the quantum Gram evaluation is 9–11 orders of magnitude slower than its classical counterpart. On the sensing front we derive the entanglement-advantage condition from the quantum Fisher information and specify the in-cryostat magnetometry chain for the breeder centrepost (peak field 16.84 T, kept formally distinct from the burner plug at 26.49 T): an NMR/EPR probe as the absolute monitor to ≤1 ppm, a SQUID and an NV-diamond ensemble (1 pT Hz^-1/2) for the 1 mT quench precursor, with the entanglement knee located at a normalised signal ≈0.14. Every Kronos in-bore diagnostic sits below the knee, where entanglement buys only +0.00077 AUC; above it (deep error-field mapping) a Heisenberg-limited protocol carries the standard-quantum-limit sensitivity from 5.7×10^-7 to 5.7×10^-8 T at 100 probes. On the fault-tolerant front we recompute the resource ledger from first formulas — the Grover iteration count 1.62^n and the surface-code footprint 2d^2 physical qubits per logical qubit — across 50 rows with zero discrepancy, and date the single fusion-relevant near-term niche: linear Vlasov kinetics at 11–19 logical qubits around 2029±2, with nonlinear five-dimensional gyrokinetics beyond 2035 and fleet-scale Grover search never practical (1.8×10^18 iterations). Three further workloads keep the verdict resource-honest: full six-dimensional kinetic Hamiltonian simulation at ~44 logical qubits and ~19 days, fault-tolerant phase estimation of the exact REBCO/alloy ground state at ~238 logical qubits and ~10^9 Toffoli gates, and a Harrow–Hassidim–Lloyd equilibrium linear solve at ~10^17 T-gates — all calibration-only. Two of the six quantum-track items are already twin-testable classically: a materials variational eigensolver reproduces a model ground state to 3.9×10^-6 Ha and reaches chemical accuracy on 3d alloy fragments with 4–14× shallower circuits than unitary coupled cluster (no advantage claimed), and a tensor-network kinetic solver compresses the distribution function with exponential rank convergence (2.2×10^-10 at bond rank 16, 0.19× storage). The honest bottom line is that nothing on the design critical path waits on quantum hardware — and establishing that, with the numbers behind it, is the result.Key results (frozen anchors): y_i = 0 eq; hbar = 2 ×28.03; iter = 1.8 ×10^18; iter = 1.6 2^n.Methods & codes: CGYRO, GENE, QAOA, VQE, ADAPT-VQE.Live verification: 11 gate validator(s) with live-recompute cards (5 reproduced, 5 estimated, 1 revised). See the Verification section and data/verification.csv.Related: Paper page · De-risking register · 3D model · Learn more about KronosPart of the 2026 Kronos publication series; independently re-run and stamped in the Kronos de-risking register (DOI 10.5281/zenodo.22645689).All numerical values are frozen design-point anchors; see the register.Public research artifact. No proprietary, financial, or supply-chain information is included.
Fixed-ansatz Variational Quantum Eigensolvers (VQE), such as the Unitary Coupled Cluster with Singles and Doubles (UCCSD) framework, frequently suffer from severe initialization paralyzation and zero-gradient traps when evaluated using the non-local Bravyi-Kitaev (BK) fermion-to-qubit mapping. In this work, we systematically demonstrate how the Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT-VQE) framework shatters these structural limitations across three distinct electronic and geometric molecular pillars: Lithium Hydride (LiH), Hydrogen Fluoride (HF), and Water (H2O), under heavily stretched or asymmetric multi-reference configurations. While conventional UCCSD-VQE flatlines completely at a zero energy shift (0.000000~Ha) due to global phase cancellations inherent to the BK tree structures, our dynamic ADAPT-VQE loop successfully isolates the dominant symmetry-breaking operators using analytical commutator gradients. To bypass the severe O(N3) computational bottlenecks of dense matrix exponentiation and Singular Value Decomposition on larger registers, we implement a highly optimized, vector-based Taylor series expansion state-evolution engine. Our numerical results show that the accelerated ADAPT-VQE framework achieves instant, exact Full Configuration Interaction (FCI) convergence within the very first macro-cycle across all three molecular systems, maintaining absolute numerical stability up to a 12-qubit register space. This study establishes a robust, hardware-efficient path for simulating strongly correlated, highly polarized triatomic chemical environments on near-term local architectures.