KetQat Decision Report -- Layered H/CX/T circuit, 12 qubits

Executive summary

• Workload: Layered H/CX/T circuit, 12 qubits. 12 logical qubits, 12 T gates and 0 Toffoli gates, depth 8. Counts are DERIVED.
• Classical baseline: 0.0144 s on Apple M2 Pro, classified MEASURED, measured 2026-08-14.
• Conservative: TECHNICALLY_FEASIBLE. 10,530 physical qubits total, 1.200e-4 s runtime, distance 9. Binding constraint: MAGIC_STATE_THROUGHPUT.
• Base: TECHNICALLY_FEASIBLE. 3,250 physical qubits total, 1.200e-4 s runtime, distance 5. Binding constraint: MAGIC_STATE_THROUGHPUT.
• Optimistic: TECHNICALLY_FEASIBLE. 900 physical qubits total, 2.400e-5 s runtime, distance 3. Binding constraint: MAGIC_STATE_THROUGHPUT.

The decision, per assumption set

One row per assumption set. There is no aggregate row: the sets differ in what they assume, so a figure combining them would describe no machine anybody could build.

What would change this answer

• State the physical qubit capacity of the target device, with a source and a date.
• State a quantum machine-cost assumption, even a hypothetical one, so the economic thresholds become computable.
• Characterize magic-state factory throughput on the target architecture: it, not logical-qubit count, sets the runtime here.
• Measure the two-qubit physical error rate on the target device. It is the parameter this result depends on most, and it is measurable.

Workload definition

• The exact circuit whose classical simulation was measured: two layers of Hadamards, a CX chain, and T gates on alternating qubits.
• Source: OPENQASM3 (ketqat-benchmarks reference measurement).
• Gate set: cx, h, t.
• Logical qubits 12, depth 8, 58 gates, 46 Clifford, 12 T, 0 Toffoli, 0 needing synthesis.
• The classical baseline for this workload is a measurement taken on 2026-08-14, not an estimate.
• Reference case. Not evidence about any organisation's production workload.

Classical baseline

• Evidence class: MEASURED.
• Runtime: 0.0144 s.
• Cost: not recorded.
• Environment: Single core, CPython 3.14.4, pure-Python statevector simulation..
• Hardware: Apple M2 Pro.
• Workload size: 12 qubits, 2 layers, 58 gates.
• Solution quality: exact output distribution = 1.
• Measured on: 2026-08-14.
• Single-core pure Python understates classical capability; an optimised simulator would be faster still, which widens rather than narrows the gap against quantum.
• One machine, one date. A runtime transfers to other hardware only as an order of magnitude.

Scenarios and assumptions

• Conservative (CONSERVATIVE, revision 1): Device parameters at the pessimistic end of what good superconducting hardware has demonstrated. Chosen so that a favourable answer here is not an artefact of favourable assumptions.
• Hardware: Generic reference device, conservative parameters, USER_ASSUMPTION, physical error rate 0.003, cycle 1000 ns, capacity unstated. A conventional pessimistic reading of demonstrated two-qubit error rates on superconducting devices, with the 1 microsecond surface-code cycle used throughout the fault-tolerance literature.
• QEC: SURFACE_CODE_ROTATED, threshold 0.01, prefactor 0.03 (Fowler conventional). Layout: LATTICE_SURGERY_2D.
• Factory: FIFTEEN_TO_ONE, raw state error 0.003, target 1e-10, 1 in parallel.
• Error budget 0.01. Runtime target 0.0144. Economic model: none supplied.
• Base (BASE, revision 1): The parameters most fault-tolerance resource analyses use: a 1e-3 physical error rate and a 1 microsecond surface-code cycle. Comparable with published estimates that state the same assumptions.
• Hardware: Generic reference device, standard literature parameters, USER_ASSUMPTION, physical error rate 0.001, cycle 1000 ns, capacity unstated. The physical error rate and cycle time used as the standard case in surface-code resource analyses, for example Gidney and Ekera (2019), arXiv:1905.09749.
• QEC: SURFACE_CODE_ROTATED, threshold 0.01, prefactor 0.03 (Fowler conventional). Layout: LATTICE_SURGERY_2D.
• Factory: FIFTEEN_TO_ONE, raw state error 0.001, target 1e-10, 1 in parallel.
• Error budget 0.01. Runtime target 0.0144. Economic model: none supplied.
• Optimistic (OPTIMISTIC, revision 1): Device parameters an order of magnitude better than the standard case, and a five-times faster cycle. This is a target, not an observation: it states what hardware would have to reach, which is the question the threshold engine answers rather than a prediction that it will.
• Hardware: Generic reference device, improvement-target parameters, USER_ASSUMPTION, physical error rate 0.0001, cycle 200 ns, capacity unstated. An improvement target stated for comparison, not a measurement or a vendor roadmap. No device is claimed to achieve these parameters.
• QEC: SURFACE_CODE_ROTATED, threshold 0.01, prefactor 0.03 (Fowler conventional). Layout: LATTICE_SURGERY_2D.
• Factory: FIFTEEN_TO_ONE, raw state error 0.0001, target 1e-10, 1 in parallel.
• Error budget 0.01. Runtime target 0.0144. Economic model: none supplied.

Resource estimates

• Conservative: feasible.
• Algorithm patches: 1,944 physical qubits (not the machine size).
• With routing space: 5,670 physical qubits.
• Magic-state factory: 4,860 physical qubits.
• Total machine: 10,530 physical qubits.
• Code distance 9, 12 magic states, 2 distillation level(s), 2,700 raw states.
• Runtime 1.200e-4 s, limited by MAGIC_STATE_THROUGHPUT. Cycle-limited 7.200e-5 s, factory-limited 1.200e-4 s.
• Achieved logical error 0.007 probability against a budget of 0.01 probability.
• Arithmetic: Magic states: 12 T + 4 x 0 Toffoli = 12.
• Arithmetic: Logical cycles: max(depth 8, 1) = 8.
• Arithmetic: Occupied logical patches under LATTICE_SURGERY_2D: 35 (algorithm register 12).
• Arithmetic: Per-patch footprint: 2 x 9^2 = 162 physical qubits.
• Arithmetic: Cycle-limited runtime: 8 cycles x 9 rounds x 1000 ns = 7.200e-5 s.
• Arithmetic: Distillation: 2 level(s) of 15-to-1, 225 raw states per output, 2700 raw states total.
• Base: feasible.
• Algorithm patches: 600 physical qubits (not the machine size).
• With routing space: 1,750 physical qubits.
• Magic-state factory: 1,500 physical qubits.
• Total machine: 3,250 physical qubits.
• Code distance 5, 12 magic states, 2 distillation level(s), 2,700 raw states.
• Runtime 1.200e-4 s, limited by MAGIC_STATE_THROUGHPUT. Cycle-limited 4.000e-5 s, factory-limited 1.200e-4 s.
• Achieved logical error 0.0029 probability against a budget of 0.01 probability.
• Arithmetic: Magic states: 12 T + 4 x 0 Toffoli = 12.
• Arithmetic: Logical cycles: max(depth 8, 1) = 8.
• Arithmetic: Occupied logical patches under LATTICE_SURGERY_2D: 35 (algorithm register 12).
• Arithmetic: Per-patch footprint: 2 x 5^2 = 50 physical qubits.
• Arithmetic: Cycle-limited runtime: 8 cycles x 5 rounds x 1000 ns = 4.000e-5 s.
• Arithmetic: Distillation: 2 level(s) of 15-to-1, 225 raw states per output, 2700 raw states total.
• Optimistic: feasible.
• Algorithm patches: 216 physical qubits (not the machine size).
• With routing space: 630 physical qubits.
• Magic-state factory: 270 physical qubits.
• Total machine: 900 physical qubits.
• Code distance 3, 12 magic states, 1 distillation level(s), 180 raw states.
• Runtime 2.400e-5 s, limited by MAGIC_STATE_THROUGHPUT. Cycle-limited 4.800e-6 s, factory-limited 2.400e-5 s.
• Achieved logical error 2.880e-4 probability against a budget of 0.01 probability.
• Arithmetic: Magic states: 12 T + 4 x 0 Toffoli = 12.
• Arithmetic: Logical cycles: max(depth 8, 1) = 8.
• Arithmetic: Occupied logical patches under LATTICE_SURGERY_2D: 35 (algorithm register 12).
• Arithmetic: Per-patch footprint: 2 x 3^2 = 18 physical qubits.
• Arithmetic: Cycle-limited runtime: 8 cycles x 3 rounds x 200 ns = 4.800e-6 s.
• Arithmetic: Distillation: 1 level(s) of 15-to-1, 15 raw states per output, 180 raw states total.

Sensitivity

• Conservative:
• PHYSICAL_ERROR_RATE = 7.50e-4: distance 5, 3,250 physical qubits (0.309x the estimate)
• PHYSICAL_ERROR_RATE = 1.50e-3: distance 5, 3,250 physical qubits (0.309x the estimate)
• PHYSICAL_ERROR_RATE = 3.00e-3: distance 9, 10,530 physical qubits (1.00x the estimate)
• PHYSICAL_ERROR_RATE = 6.00e-3: distance 23, 68,770 physical qubits (6.53x the estimate)
• PHYSICAL_ERROR_RATE = 1.20e-2: infeasible
• LOGICAL_ERROR_PREFACTOR = Fowler conventional: distance 9, 10,530 physical qubits (1.00x the estimate)
• LOGICAL_ERROR_PREFACTOR = Gidney-Fowler (Qualtran): distance 11, 15,730 physical qubits (1.49x the estimate)
• LAYOUT_MODEL = BARE_REGISTER: distance 9, 6,804 physical qubits (0.646x the estimate)
• LAYOUT_MODEL = LATTICE_SURGERY_2D: distance 9, 10,530 physical qubits (1.00x the estimate)
• CYCLE_TIME = 250 ns: distance 9, 10,530 physical qubits (1.00x the estimate)
• CYCLE_TIME = 500 ns: distance 9, 10,530 physical qubits (1.00x the estimate)
• CYCLE_TIME = 1000 ns: distance 9, 10,530 physical qubits (1.00x the estimate)
• CYCLE_TIME = 2000 ns: distance 9, 10,530 physical qubits (1.00x the estimate)
• CYCLE_TIME = 4000 ns: distance 9, 10,530 physical qubits (1.00x the estimate)
• ERROR_BUDGET = 1.00e-3: distance 13, 21,970 physical qubits (2.09x the estimate)
• ERROR_BUDGET = 1.00e-2: distance 9, 10,530 physical qubits (1.00x the estimate)
• ERROR_BUDGET = 1.00e-1: distance 5, 3,250 physical qubits (0.309x the estimate)
• RAW_MAGIC_STATE_ERROR = 3.00e-4: distance 9, 10,530 physical qubits (1.00x the estimate)
• RAW_MAGIC_STATE_ERROR = 3.00e-3: distance 9, 10,530 physical qubits (1.00x the estimate)
• RAW_MAGIC_STATE_ERROR = 3.00e-2: distance 9, 12,960 physical qubits (1.23x the estimate)
• Base:
• PHYSICAL_ERROR_RATE = 2.50e-4: distance 3, 1,170 physical qubits (0.360x the estimate)
• PHYSICAL_ERROR_RATE = 5.00e-4: distance 3, 1,170 physical qubits (0.360x the estimate)
• PHYSICAL_ERROR_RATE = 1.00e-3: distance 5, 3,250 physical qubits (1.00x the estimate)
• PHYSICAL_ERROR_RATE = 2.00e-3: distance 7, 6,370 physical qubits (1.96x the estimate)
• PHYSICAL_ERROR_RATE = 4.00e-3: distance 13, 21,970 physical qubits (6.76x the estimate)
• LOGICAL_ERROR_PREFACTOR = Fowler conventional: distance 5, 3,250 physical qubits (1.00x the estimate)
• LOGICAL_ERROR_PREFACTOR = Gidney-Fowler (Qualtran): distance 5, 3,250 physical qubits (1.00x the estimate)
• LAYOUT_MODEL = BARE_REGISTER: distance 5, 2,100 physical qubits (0.646x the estimate)
• LAYOUT_MODEL = LATTICE_SURGERY_2D: distance 5, 3,250 physical qubits (1.00x the estimate)
• CYCLE_TIME = 250 ns: distance 5, 3,250 physical qubits (1.00x the estimate)
• CYCLE_TIME = 500 ns: distance 5, 3,250 physical qubits (1.00x the estimate)
• CYCLE_TIME = 1000 ns: distance 5, 3,250 physical qubits (1.00x the estimate)
• CYCLE_TIME = 2000 ns: distance 5, 3,250 physical qubits (1.00x the estimate)
• CYCLE_TIME = 4000 ns: distance 5, 3,250 physical qubits (1.00x the estimate)
• ERROR_BUDGET = 1.00e-3: distance 7, 6,370 physical qubits (1.96x the estimate)
• ERROR_BUDGET = 1.00e-2: distance 5, 3,250 physical qubits (1.00x the estimate)
• ERROR_BUDGET = 1.00e-1: distance 3, 1,170 physical qubits (0.360x the estimate)
• RAW_MAGIC_STATE_ERROR = 1.00e-4: distance 5, 2,500 physical qubits (0.769x the estimate)
• RAW_MAGIC_STATE_ERROR = 1.00e-3: distance 5, 3,250 physical qubits (1.00x the estimate)
• RAW_MAGIC_STATE_ERROR = 1.00e-2: distance 5, 3,250 physical qubits (1.00x the estimate)
• Optimistic:
• PHYSICAL_ERROR_RATE = 2.50e-5: distance 3, 900 physical qubits (1.00x the estimate)
• PHYSICAL_ERROR_RATE = 5.00e-5: distance 3, 900 physical qubits (1.00x the estimate)
• PHYSICAL_ERROR_RATE = 1.00e-4: distance 3, 900 physical qubits (1.00x the estimate)
• PHYSICAL_ERROR_RATE = 2.00e-4: distance 3, 900 physical qubits (1.00x the estimate)
• PHYSICAL_ERROR_RATE = 4.00e-4: distance 3, 900 physical qubits (1.00x the estimate)
• LOGICAL_ERROR_PREFACTOR = Fowler conventional: distance 3, 900 physical qubits (1.00x the estimate)
• LOGICAL_ERROR_PREFACTOR = Gidney-Fowler (Qualtran): distance 3, 900 physical qubits (1.00x the estimate)
• LAYOUT_MODEL = BARE_REGISTER: distance 3, 486 physical qubits (0.540x the estimate)
• LAYOUT_MODEL = LATTICE_SURGERY_2D: distance 3, 900 physical qubits (1.00x the estimate)
• CYCLE_TIME = 50 ns: distance 3, 900 physical qubits (1.00x the estimate)
• CYCLE_TIME = 100 ns: distance 3, 900 physical qubits (1.00x the estimate)
• CYCLE_TIME = 200 ns: distance 3, 900 physical qubits (1.00x the estimate)
• CYCLE_TIME = 400 ns: distance 3, 900 physical qubits (1.00x the estimate)
• CYCLE_TIME = 800 ns: distance 3, 900 physical qubits (1.00x the estimate)
• ERROR_BUDGET = 1.00e-3: distance 3, 900 physical qubits (1.00x the estimate)
• ERROR_BUDGET = 1.00e-2: distance 3, 900 physical qubits (1.00x the estimate)
• ERROR_BUDGET = 1.00e-1: distance 3, 900 physical qubits (1.00x the estimate)
• RAW_MAGIC_STATE_ERROR = 1.00e-5: distance 3, 900 physical qubits (1.00x the estimate)
• RAW_MAGIC_STATE_ERROR = 1.00e-4: distance 3, 900 physical qubits (1.00x the estimate)
• RAW_MAGIC_STATE_ERROR = 1.00e-3: distance 3, 1,170 physical qubits (1.30x the estimate)

Advantage threshold conditions

• Conservative:
• The physical two-qubit error rate must stay below 9.45e-3 for any code distance to meet this error budget.
• A surface-code cycle at or below 1.20e+5 ns would be required to finish within the 0.0144 s target.
• The magic-state factory must deliver at least 833 states per second to finish within the 0.0144 s target.
• A surface-code cycle below 1.20e+5 ns would be required to beat the supplied classical runtime.
• Maximum physical error rate: at most 0.0095 probability.
• Required total capacity: at least 10,530 physical qubits.
• Maximum cycle time to beat classical: at most 120,000 ns.
• Maximum machine-second cost: unknown (Insufficient evidence for economic comparison: the classical baseline records no monetary cost.).
• Break-even runtime: unknown (Insufficient evidence for economic comparison: the classical baseline records no monetary cost.).
• Refused (NO_HARDWARE_CAPACITY): max_physical_error_rate_within_capacity -- No physical qubit capacity was stated for this hardware model, so there is nothing to fit within. A capacity was not assumed.
• Refused (NO_HARDWARE_CAPACITY): capacity_headroom -- No physical qubit capacity was stated for this hardware model.
• Refused (NO_CLASSICAL_COST): max_machine_cost_per_second -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Refused (NO_CLASSICAL_COST): max_physical_qubit_second_cost -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Refused (NO_CLASSICAL_COST): break_even_runtime -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Refused (NO_CLASSICAL_COST): break_even_machine_cost_per_second -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Refused (NO_ECONOMIC_MODEL): projected_quantum_cost -- Insufficient evidence for economic comparison: this scenario states no quantum cost model. No price for quantum machine time was assumed, because none exists to look up.
• Refused (NO_CLASSICAL_COST): cost_ratio_to_classical -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Base:
• The physical two-qubit error rate must stay below 9.45e-3 for any code distance to meet this error budget.
• A surface-code cycle at or below 1.20e+5 ns would be required to finish within the 0.0144 s target.
• The magic-state factory must deliver at least 833 states per second to finish within the 0.0144 s target.
• A surface-code cycle below 1.20e+5 ns would be required to beat the supplied classical runtime.
• Maximum physical error rate: at most 0.0095 probability.
• Required total capacity: at least 3,250 physical qubits.
• Maximum cycle time to beat classical: at most 120,000 ns.
• Maximum machine-second cost: unknown (Insufficient evidence for economic comparison: the classical baseline records no monetary cost.).
• Break-even runtime: unknown (Insufficient evidence for economic comparison: the classical baseline records no monetary cost.).
• Refused (NO_HARDWARE_CAPACITY): max_physical_error_rate_within_capacity -- No physical qubit capacity was stated for this hardware model, so there is nothing to fit within. A capacity was not assumed.
• Refused (NO_HARDWARE_CAPACITY): capacity_headroom -- No physical qubit capacity was stated for this hardware model.
• Refused (NO_CLASSICAL_COST): max_machine_cost_per_second -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Refused (NO_CLASSICAL_COST): max_physical_qubit_second_cost -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Refused (NO_CLASSICAL_COST): break_even_runtime -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Refused (NO_CLASSICAL_COST): break_even_machine_cost_per_second -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Refused (NO_ECONOMIC_MODEL): projected_quantum_cost -- Insufficient evidence for economic comparison: this scenario states no quantum cost model. No price for quantum machine time was assumed, because none exists to look up.
• Refused (NO_CLASSICAL_COST): cost_ratio_to_classical -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Optimistic:
• The physical two-qubit error rate must stay below 9.45e-3 for any code distance to meet this error budget.
• A surface-code cycle at or below 1.20e+5 ns would be required to finish within the 0.0144 s target.
• The magic-state factory must deliver at least 833 states per second to finish within the 0.0144 s target.
• A surface-code cycle below 1.20e+5 ns would be required to beat the supplied classical runtime.
• Maximum physical error rate: at most 0.0095 probability.
• Required total capacity: at least 900 physical qubits.
• Maximum cycle time to beat classical: at most 120,000 ns.
• Maximum machine-second cost: unknown (Insufficient evidence for economic comparison: the classical baseline records no monetary cost.).
• Break-even runtime: unknown (Insufficient evidence for economic comparison: the classical baseline records no monetary cost.).
• Refused (NO_HARDWARE_CAPACITY): max_physical_error_rate_within_capacity -- No physical qubit capacity was stated for this hardware model, so there is nothing to fit within. A capacity was not assumed.
• Refused (NO_HARDWARE_CAPACITY): capacity_headroom -- No physical qubit capacity was stated for this hardware model.
• Refused (NO_CLASSICAL_COST): max_machine_cost_per_second -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Refused (NO_CLASSICAL_COST): max_physical_qubit_second_cost -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Refused (NO_CLASSICAL_COST): break_even_runtime -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Refused (NO_CLASSICAL_COST): break_even_machine_cost_per_second -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.
• Refused (NO_ECONOMIC_MODEL): projected_quantum_cost -- Insufficient evidence for economic comparison: this scenario states no quantum cost model. No price for quantum machine time was assumed, because none exists to look up.
• Refused (NO_CLASSICAL_COST): cost_ratio_to_classical -- Insufficient evidence for economic comparison: the classical baseline records no monetary cost.

Decision assessment

• Conservative: TECHNICALLY_FEASIBLE
• Under this model the computation needs 10,530 physical qubits and 0.000120 s at code distance 9. The computation is technically feasible under this model, but no economic conclusion can be made because no quantum machine-cost assumption was supplied. The binding constraint is magic-state throughput, not logical-qubit capacity: the runtime is set by how fast distilled states arrive rather than by the depth of the logical circuit. A surface-code cycle below 1.20e+5 ns would be required to beat the supplied classical runtime.
• SCIENTIFIC_FEASIBILITY: SATISFIED -- A code distance of 9 meets the 0.01 error budget at a physical error rate of 0.003, under the SURFACE_CODE_ROTATED model.
• ENGINEERING_FEASIBILITY: SATISFIED -- The machine is 10,530 physical qubits: 5,670 for the algorithm including routing space, and 4,860 for the magic-state factory.
• HARDWARE_READINESS: INSUFFICIENT_EVIDENCE -- No physical qubit capacity is stated for this hardware model, so there is nothing to compare the requirement against. A capacity was not assumed. The device parameters are an assumption, not an observation of a working machine, so this reading is conditional on them being reached.
• ECONOMIC_READINESS: INSUFFICIENT_EVIDENCE -- Insufficient evidence for economic comparison: no quantum machine-cost assumption was supplied. No price for fault-tolerant quantum machine time was assumed, because none exists to look up.
• EVIDENCE_CONFIDENCE: SATISFIED -- Logical counts are DERIVED; hardware parameters are USER_ASSUMPTION at MEDIUM confidence; the classical baseline is MEASURED; the quantum cost model is absent. These are different kinds of claim and are not averaged into a score.
• SENSITIVITY_RISK: NOT_SATISFIED -- The widest spread comes from the physical error rate: a 21.2x range in total physical qubits across the swept values.
• Reason codes: BASELINE_MEASURED, HARDWARE_BASIS_USER_ASSUMPTION, HIGH_SENSITIVITY_TO_ERROR_RATE, NO_CLASSICAL_COST, NO_ECONOMIC_MODEL, NO_STATED_CAPACITY, RUNTIME_ADVANTAGE_UNDER_ASSUMPTIONS, RUNTIME_LIMITED_BY_FACTORY, RUNTIME_WITHIN_TARGET, WORKLOAD_COUNTS_DERIVED_FROM_CIRCUIT.
• Uncertainty: A factor-of-four change in the physical error rate changes the machine size by 21.2x. Quoting the point estimate without this range presents it as more precise than it is.
• Next: State the physical qubit capacity of the target device, with a source and a date.
• Next: State a quantum machine-cost assumption, even a hypothetical one, so the economic thresholds become computable.
• Next: Characterize magic-state factory throughput on the target architecture: it, not logical-qubit count, sets the runtime here.
• Next: Measure the two-qubit physical error rate on the target device. It is the parameter this result depends on most, and it is measurable.
• Base: TECHNICALLY_FEASIBLE
• Under this model the computation needs 3,250 physical qubits and 0.000120 s at code distance 5. The computation is technically feasible under this model, but no economic conclusion can be made because no quantum machine-cost assumption was supplied. The binding constraint is magic-state throughput, not logical-qubit capacity: the runtime is set by how fast distilled states arrive rather than by the depth of the logical circuit. A surface-code cycle below 1.20e+5 ns would be required to beat the supplied classical runtime.
• SCIENTIFIC_FEASIBILITY: SATISFIED -- A code distance of 5 meets the 0.01 error budget at a physical error rate of 0.001, under the SURFACE_CODE_ROTATED model.
• ENGINEERING_FEASIBILITY: SATISFIED -- The machine is 3,250 physical qubits: 1,750 for the algorithm including routing space, and 1,500 for the magic-state factory.
• HARDWARE_READINESS: INSUFFICIENT_EVIDENCE -- No physical qubit capacity is stated for this hardware model, so there is nothing to compare the requirement against. A capacity was not assumed. The device parameters are an assumption, not an observation of a working machine, so this reading is conditional on them being reached.
• ECONOMIC_READINESS: INSUFFICIENT_EVIDENCE -- Insufficient evidence for economic comparison: no quantum machine-cost assumption was supplied. No price for fault-tolerant quantum machine time was assumed, because none exists to look up.
• EVIDENCE_CONFIDENCE: SATISFIED -- Logical counts are DERIVED; hardware parameters are USER_ASSUMPTION at MEDIUM confidence; the classical baseline is MEASURED; the quantum cost model is absent. These are different kinds of claim and are not averaged into a score.
• SENSITIVITY_RISK: NOT_SATISFIED -- The widest spread comes from the physical error rate: a 18.8x range in total physical qubits across the swept values.
• Reason codes: BASELINE_MEASURED, HARDWARE_BASIS_USER_ASSUMPTION, HIGH_SENSITIVITY_TO_ERROR_RATE, NO_CLASSICAL_COST, NO_ECONOMIC_MODEL, NO_STATED_CAPACITY, RUNTIME_ADVANTAGE_UNDER_ASSUMPTIONS, RUNTIME_LIMITED_BY_FACTORY, RUNTIME_WITHIN_TARGET, WORKLOAD_COUNTS_DERIVED_FROM_CIRCUIT.
• Uncertainty: A factor-of-four change in the physical error rate changes the machine size by 18.8x. Quoting the point estimate without this range presents it as more precise than it is.
• Next: State the physical qubit capacity of the target device, with a source and a date.
• Next: State a quantum machine-cost assumption, even a hypothetical one, so the economic thresholds become computable.
• Next: Characterize magic-state factory throughput on the target architecture: it, not logical-qubit count, sets the runtime here.
• Next: Measure the two-qubit physical error rate on the target device. It is the parameter this result depends on most, and it is measurable.
• Optimistic: TECHNICALLY_FEASIBLE
• Under this model the computation needs 900 physical qubits and 0.0000240 s at code distance 3. The computation is technically feasible under this model, but no economic conclusion can be made because no quantum machine-cost assumption was supplied. The binding constraint is magic-state throughput, not logical-qubit capacity: the runtime is set by how fast distilled states arrive rather than by the depth of the logical circuit. A surface-code cycle below 1.20e+5 ns would be required to beat the supplied classical runtime.
• SCIENTIFIC_FEASIBILITY: SATISFIED -- A code distance of 3 meets the 0.01 error budget at a physical error rate of 0.0001, under the SURFACE_CODE_ROTATED model.
• ENGINEERING_FEASIBILITY: SATISFIED -- The machine is 900 physical qubits: 630 for the algorithm including routing space, and 270 for the magic-state factory.
• HARDWARE_READINESS: INSUFFICIENT_EVIDENCE -- No physical qubit capacity is stated for this hardware model, so there is nothing to compare the requirement against. A capacity was not assumed. The device parameters are an assumption, not an observation of a working machine, so this reading is conditional on them being reached.
• ECONOMIC_READINESS: INSUFFICIENT_EVIDENCE -- Insufficient evidence for economic comparison: no quantum machine-cost assumption was supplied. No price for fault-tolerant quantum machine time was assumed, because none exists to look up.
• EVIDENCE_CONFIDENCE: SATISFIED -- Logical counts are DERIVED; hardware parameters are USER_ASSUMPTION at LOW confidence; the classical baseline is MEASURED; the quantum cost model is absent. These are different kinds of claim and are not averaged into a score.
• SENSITIVITY_RISK: SATISFIED -- The widest spread comes from the layout model: a 1.85x range in total physical qubits across the swept values.
• Reason codes: BASELINE_MEASURED, HARDWARE_BASIS_USER_ASSUMPTION, HARDWARE_CONFIDENCE_LOW, NO_CLASSICAL_COST, NO_ECONOMIC_MODEL, NO_STATED_CAPACITY, RUNTIME_ADVANTAGE_UNDER_ASSUMPTIONS, RUNTIME_LIMITED_BY_FACTORY, RUNTIME_WITHIN_TARGET, SENSITIVITY_WITHIN_ONE_ORDER, WORKLOAD_COUNTS_DERIVED_FROM_CIRCUIT.
• Next: State the physical qubit capacity of the target device, with a source and a date.
• Next: State a quantum machine-cost assumption, even a hypothetical one, so the economic thresholds become computable.
• Next: Characterize magic-state factory throughput on the target architecture: it, not logical-qubit count, sets the runtime here.

Scenario comparison

• No aggregate row is produced. Scenarios differ in their assumptions, and a mean of results computed under different assumptions is a number none of the models predicts, carrying the apparent authority of all of them. Each row is read on its own terms.
• Conservative: TECHNICALLY_FEASIBLE, 10,530 physical qubits, 0.000120 s, distance 9, factory share 46%, economic INSUFFICIENT_EVIDENCE, evidence MEDIUM.
• Base: TECHNICALLY_FEASIBLE, 3,250 physical qubits, 0.000120 s, distance 5, factory share 46%, economic INSUFFICIENT_EVIDENCE, evidence MEDIUM.
• Optimistic: TECHNICALLY_FEASIBLE, 900 physical qubits, 0.0000240 s, distance 3, factory share 30%, economic INSUFFICIENT_EVIDENCE, evidence MEDIUM.

Missing evidence

• The physical qubit capacity of the device under consideration. Without it, 'does it fit' has no answer.
• A dated observation of a real device meeting these physical error rate and cycle time parameters.
• A quantum cost model: what a machine-second, or a physical-qubit-second, is assumed to cost, and on whose authority.

Limitations

• Resource estimates are modelled, not measured. No device was run.
• The logical-error prefactor is fitted and its provenance is weak; the alternative published value is reported as model sensitivity on every estimate.
• The magic-state factory footprint and throughput are models of the standard construction, not published or measured figures.
• The error budget is allocated across the algorithm's own logical qubits; routing patches are charged for space but not against the budget.
• One QEC scheme is modelled. Other codes, other layouts, and other hardware modalities are out of scope here.
• Nothing in this bundle predicts when any device will meet any condition it states.

Sources

• Measured classical runtime: ketqat-benchmarks: measured classical baseline, exact statevector simulation Published 2026-08-14. Retrieved 2026-08-14.
  HIGH
• Surface-code threshold and logical-error model: Fowler, Mariantoni, Martinis, Cleland -- Surface codes: Towards practical large-scale quantum computation Published 2012-08-04. Retrieved 2026-08-13.
  HIGH
• Lattice-surgery layout overhead: Beverland et al. -- Assessing requirements to scale to practical quantum advantage Published 2022-11-14. Retrieved 2026-08-13.
  HIGH