KetQat Decision Report -- Shor factoring, 2048-bit RSA (Gidney-Ekera construction)

Executive summary

• Workload: Shor factoring, 2048-bit RSA (Gidney-Ekera construction). 6189 logical qubits, 0 T gates and 2624225018 Toffoli gates, depth 2143289344. Counts are DERIVED.
• No classical baseline was supplied, so no speedup or economic conclusion appears anywhere in this report.
• Conservative: CONDITIONALLY_FEASIBLE. 7.097e+7 physical qubits total, 113,594.3352 s runtime, distance 53. Binding constraint: TOTAL_PHYSICAL_QUBIT_CAPACITY.
• Base: CONDITIONALLY_FEASIBLE. 1.842e+7 physical qubits total, 104,969.0007 s runtime, distance 27. Binding constraint: MAGIC_STATE_THROUGHPUT.
• Optimistic: TECHNICALLY_FEASIBLE. 4.265e+6 physical qubits total, 20,993.8001 s runtime, distance 13. 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

• Measure the current classical solution on the real problem size and record the hardware and date.
• Measure the two-qubit physical error rate on the target device. It is the parameter this result depends on most, and it is measurable.
• Characterize magic-state factory throughput on the target architecture: it, not logical-qubit count, sets the runtime here.

Workload definition

• Logical resources for factoring a 2048-bit RSA integer, computed from the parametric expressions published in arXiv:1905.09749.
• Source: MANUAL_LOGICAL_COUNTS.
• Gate set: toffoli.
• Logical qubits 6189, depth 2143289344, 2624225018 gates, 0 Clifford, 0 T, 2624225018 Toffoli, 0 needing synthesis.
• Counts computed from the source's published expressions, not quoted as totals and not recalled.
• One-qubit, two-qubit and Clifford counts are recorded as zero because the source states the cost in Toffolis; a zero here means 'not stated by the source', and the Clifford-derived figures in this assessment are correspondingly incomplete.
• Reference case. Not evidence about any organisation's production workload.

Classical baseline

• None supplied.
• Resource estimation runs without one. Every economic and speedup conclusion is refused, by name, wherever it would otherwise appear.

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 20000000. 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 28800. 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 20000000. 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 28800. 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 20000000. 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 28800. Economic model: none supplied.

Resource estimates

• Conservative: feasible.
• Algorithm patches: 3.477e+7 physical qubits (not the machine size).
• With routing space: 7.080e+7 physical qubits.
• Magic-state factory: 168,540 physical qubits.
• Total machine: 7.097e+7 physical qubits.
• Code distance 53, 1.050e+10 magic states, 2 distillation level(s), 2.362e+12 raw states.
• Runtime 113,594.3352 s, limited by LOGICAL_CYCLES. Cycle-limited 113,594.3352 s, factory-limited 104,969.0007 s.
• Achieved logical error 0.003 probability against a budget of 0.01 probability.
• Arithmetic: Magic states: 0 T + 4 x 2624225018 Toffoli = 10496900072.
• Arithmetic: Logical cycles: max(depth 2143289344, 1) = 2143289344.
• Arithmetic: Occupied logical patches under LATTICE_SURGERY_2D: 12602 (algorithm register 6189).
• Arithmetic: Per-patch footprint: 2 x 53^2 = 5618 physical qubits.
• Arithmetic: Cycle-limited runtime: 2143289344 cycles x 53 rounds x 1000 ns = 1.136e+5 s.
• Arithmetic: Distillation: 2 level(s) of 15-to-1, 225 raw states per output, 2361802516200 raw states total.
• Base: feasible.
• Algorithm patches: 9.024e+6 physical qubits (not the machine size).
• With routing space: 1.837e+7 physical qubits.
• Magic-state factory: 43,740 physical qubits.
• Total machine: 1.842e+7 physical qubits.
• Code distance 27, 1.050e+10 magic states, 2 distillation level(s), 2.362e+12 raw states.
• Runtime 104,969.0007 s, limited by MAGIC_STATE_THROUGHPUT. Cycle-limited 57,868.8123 s, factory-limited 104,969.0007 s.
• Achieved logical error 0.004 probability against a budget of 0.01 probability.
• Arithmetic: Magic states: 0 T + 4 x 2624225018 Toffoli = 10496900072.
• Arithmetic: Logical cycles: max(depth 2143289344, 1) = 2143289344.
• Arithmetic: Occupied logical patches under LATTICE_SURGERY_2D: 12602 (algorithm register 6189).
• Arithmetic: Per-patch footprint: 2 x 27^2 = 1458 physical qubits.
• Arithmetic: Cycle-limited runtime: 2143289344 cycles x 27 rounds x 1000 ns = 5.787e+4 s.
• Arithmetic: Distillation: 2 level(s) of 15-to-1, 225 raw states per output, 2361802516200 raw states total.
• Optimistic: feasible.
• Algorithm patches: 2.092e+6 physical qubits (not the machine size).
• With routing space: 4.259e+6 physical qubits.
• Magic-state factory: 5,070 physical qubits.
• Total machine: 4.265e+6 physical qubits.
• Code distance 13, 1.050e+10 magic states, 1 distillation level(s), 1.575e+11 raw states.
• Runtime 20,993.8001 s, limited by MAGIC_STATE_THROUGHPUT. Cycle-limited 5,572.5523 s, factory-limited 20,993.8001 s.
• Achieved logical error 0.004 probability against a budget of 0.01 probability.
• Arithmetic: Magic states: 0 T + 4 x 2624225018 Toffoli = 10496900072.
• Arithmetic: Logical cycles: max(depth 2143289344, 1) = 2143289344.
• Arithmetic: Occupied logical patches under LATTICE_SURGERY_2D: 12602 (algorithm register 6189).
• Arithmetic: Per-patch footprint: 2 x 13^2 = 338 physical qubits.
• Arithmetic: Cycle-limited runtime: 2143289344 cycles x 13 rounds x 200 ns = 5.573e+3 s.
• Arithmetic: Distillation: 1 level(s) of 15-to-1, 15 raw states per output, 157453501080 raw states total.

Sensitivity

• Conservative:
• PHYSICAL_ERROR_RATE = 7.50e-4: distance 25, 15,790,000 physical qubits (0.222x the estimate)
• PHYSICAL_ERROR_RATE = 1.50e-3: distance 33, 27,512,496 physical qubits (0.388x the estimate)
• PHYSICAL_ERROR_RATE = 3.00e-3: distance 53, 70,966,576 physical qubits (1.00x the estimate)
• PHYSICAL_ERROR_RATE = 6.00e-3: distance 123, 382,219,056 physical qubits (5.39x the estimate)
• PHYSICAL_ERROR_RATE = 1.20e-2: infeasible
• LOGICAL_ERROR_PREFACTOR = Fowler conventional: distance 53, 70,966,576 physical qubits (1.00x the estimate)
• LOGICAL_ERROR_PREFACTOR = Gidney-Fowler (Qualtran): distance 55, 76,423,600 physical qubits (1.08x the estimate)
• LAYOUT_MODEL = BARE_REGISTER: distance 53, 34,938,342 physical qubits (0.492x the estimate)
• LAYOUT_MODEL = LATTICE_SURGERY_2D: distance 53, 70,966,576 physical qubits (1.00x the estimate)
• CYCLE_TIME = 250 ns: distance 53, 70,966,576 physical qubits (1.00x the estimate)
• CYCLE_TIME = 500 ns: distance 53, 70,966,576 physical qubits (1.00x the estimate)
• CYCLE_TIME = 1000 ns: distance 53, 70,966,576 physical qubits (1.00x the estimate)
• CYCLE_TIME = 2000 ns: distance 53, 70,966,576 physical qubits (1.00x the estimate)
• CYCLE_TIME = 4000 ns: distance 53, 70,966,576 physical qubits (1.00x the estimate)
• ERROR_BUDGET = 1.00e-3: distance 55, 76,423,600 physical qubits (1.08x the estimate)
• ERROR_BUDGET = 1.00e-2: distance 53, 70,966,576 physical qubits (1.00x the estimate)
• ERROR_BUDGET = 1.00e-1: distance 49, 60,658,864 physical qubits (0.855x the estimate)
• RAW_MAGIC_STATE_ERROR = 3.00e-4: distance 53, 70,966,576 physical qubits (1.00x the estimate)
• RAW_MAGIC_STATE_ERROR = 3.00e-3: distance 53, 70,966,576 physical qubits (1.00x the estimate)
• RAW_MAGIC_STATE_ERROR = 3.00e-2: distance 53, 71,050,846 physical qubits (1.00x the estimate)
• Base:
• PHYSICAL_ERROR_RATE = 2.50e-4: distance 17, 7,301,296 physical qubits (0.396x the estimate)
• PHYSICAL_ERROR_RATE = 5.00e-4: distance 21, 11,141,424 physical qubits (0.605x the estimate)
• PHYSICAL_ERROR_RATE = 1.00e-3: distance 27, 18,417,456 physical qubits (1.00x the estimate)
• PHYSICAL_ERROR_RATE = 2.00e-3: distance 39, 38,426,544 physical qubits (2.09x the estimate)
• PHYSICAL_ERROR_RATE = 4.00e-3: distance 69, 120,281,904 physical qubits (6.53x the estimate)
• LOGICAL_ERROR_PREFACTOR = Fowler conventional: distance 27, 18,417,456 physical qubits (1.00x the estimate)
• LOGICAL_ERROR_PREFACTOR = Gidney-Fowler (Qualtran): distance 29, 21,247,024 physical qubits (1.15x the estimate)
• LAYOUT_MODEL = BARE_REGISTER: distance 27, 9,067,302 physical qubits (0.492x the estimate)
• LAYOUT_MODEL = LATTICE_SURGERY_2D: distance 27, 18,417,456 physical qubits (1.00x the estimate)
• CYCLE_TIME = 250 ns: distance 27, 18,417,456 physical qubits (1.00x the estimate)
• CYCLE_TIME = 500 ns: distance 27, 18,417,456 physical qubits (1.00x the estimate)
• CYCLE_TIME = 1000 ns: distance 27, 18,417,456 physical qubits (1.00x the estimate)
• CYCLE_TIME = 2000 ns: distance 27, 18,417,456 physical qubits (1.00x the estimate)
• CYCLE_TIME = 4000 ns: distance 27, 18,417,456 physical qubits (1.00x the estimate)
• ERROR_BUDGET = 1.00e-3: distance 29, 21,247,024 physical qubits (1.15x the estimate)
• ERROR_BUDGET = 1.00e-2: distance 27, 18,417,456 physical qubits (1.00x the estimate)
• ERROR_BUDGET = 1.00e-1: distance 25, 15,790,000 physical qubits (0.857x the estimate)
• RAW_MAGIC_STATE_ERROR = 1.00e-4: distance 27, 18,395,586 physical qubits (0.999x the estimate)
• RAW_MAGIC_STATE_ERROR = 1.00e-3: distance 27, 18,417,456 physical qubits (1.00x the estimate)
• RAW_MAGIC_STATE_ERROR = 1.00e-2: distance 27, 18,417,456 physical qubits (1.00x the estimate)
• Optimistic:
• PHYSICAL_ERROR_RATE = 2.50e-5: distance 11, 3,053,314 physical qubits (0.716x the estimate)
• PHYSICAL_ERROR_RATE = 5.00e-5: distance 11, 3,053,314 physical qubits (0.716x the estimate)
• PHYSICAL_ERROR_RATE = 1.00e-4: distance 13, 4,264,546 physical qubits (1.00x the estimate)
• PHYSICAL_ERROR_RATE = 2.00e-4: distance 17, 7,292,626 physical qubits (1.71x the estimate)
• PHYSICAL_ERROR_RATE = 4.00e-4: distance 19, 9,109,474 physical qubits (2.14x the estimate)
• LOGICAL_ERROR_PREFACTOR = Fowler conventional: distance 13, 4,264,546 physical qubits (1.00x the estimate)
• LOGICAL_ERROR_PREFACTOR = Gidney-Fowler (Qualtran): distance 15, 5,677,650 physical qubits (1.33x the estimate)
• LAYOUT_MODEL = BARE_REGISTER: distance 13, 2,096,952 physical qubits (0.492x the estimate)
• LAYOUT_MODEL = LATTICE_SURGERY_2D: distance 13, 4,264,546 physical qubits (1.00x the estimate)
• CYCLE_TIME = 50 ns: distance 13, 4,264,546 physical qubits (1.00x the estimate)
• CYCLE_TIME = 100 ns: distance 13, 4,264,546 physical qubits (1.00x the estimate)
• CYCLE_TIME = 200 ns: distance 13, 4,264,546 physical qubits (1.00x the estimate)
• CYCLE_TIME = 400 ns: distance 13, 4,264,546 physical qubits (1.00x the estimate)
• CYCLE_TIME = 800 ns: distance 13, 4,264,546 physical qubits (1.00x the estimate)
• ERROR_BUDGET = 1.00e-3: distance 15, 5,677,650 physical qubits (1.33x the estimate)
• ERROR_BUDGET = 1.00e-2: distance 13, 4,264,546 physical qubits (1.00x the estimate)
• ERROR_BUDGET = 1.00e-1: distance 13, 4,264,546 physical qubits (1.00x the estimate)
• RAW_MAGIC_STATE_ERROR = 1.00e-5: distance 13, 4,264,546 physical qubits (1.00x the estimate)
• RAW_MAGIC_STATE_ERROR = 1.00e-4: distance 13, 4,264,546 physical qubits (1.00x the estimate)
• RAW_MAGIC_STATE_ERROR = 1.00e-3: distance 13, 4,269,616 physical qubits (1.00x the estimate)

Advantage threshold conditions

• Conservative:
• The physical two-qubit error rate must stay below 7.33e-3 for any code distance to meet this error budget.
• To fit 20,000,000 physical qubits, the physical error rate must be at or below 1.07e-3.
• A surface-code cycle at or below 254 ns would be required to finish within the 28800 s target.
• The magic-state factory must deliver at least 3.64e+5 states per second to finish within the 28800 s target.
• Physical qubit capacity would have to grow by 3.55x to run this workload.
• Maximum physical error rate: at most 0.0073 probability.
• Required total capacity: at least 7.097e+7 physical qubits.
• Maximum cycle time to beat classical: unknown (Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.).
• Maximum machine-second cost: unknown (Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.).
• Break-even runtime: unknown (Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.).
• Refused (NO_CLASSICAL_BASELINE): max_cycle_time_to_beat_classical_runtime -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): runtime_speedup_over_classical -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): max_machine_cost_per_second -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): max_physical_qubit_second_cost -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): break_even_runtime -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): break_even_machine_cost_per_second -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): projected_quantum_cost -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): cost_ratio_to_classical -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Base:
• The physical two-qubit error rate must stay below 7.33e-3 for any code distance to meet this error budget.
• To fit 20,000,000 physical qubits, the physical error rate must be at or below 1.07e-3.
• A surface-code cycle at or below 274 ns would be required to finish within the 28800 s target.
• The magic-state factory must deliver at least 3.64e+5 states per second to finish within the 28800 s target.
• Maximum physical error rate: at most 0.0073 probability.
• Required total capacity: at least 1.842e+7 physical qubits.
• Maximum cycle time to beat classical: unknown (Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.).
• Maximum machine-second cost: unknown (Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.).
• Break-even runtime: unknown (Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.).
• Refused (NO_CLASSICAL_BASELINE): max_cycle_time_to_beat_classical_runtime -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): runtime_speedup_over_classical -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): max_machine_cost_per_second -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): max_physical_qubit_second_cost -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): break_even_runtime -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): break_even_machine_cost_per_second -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): projected_quantum_cost -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): cost_ratio_to_classical -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Optimistic:
• The physical two-qubit error rate must stay below 7.33e-3 for any code distance to meet this error budget.
• To fit 20,000,000 physical qubits, the physical error rate must be at or below 1.07e-3.
• A surface-code cycle at or below 274 ns would be required to finish within the 28800 s target.
• The magic-state factory must deliver at least 3.64e+5 states per second to finish within the 28800 s target.
• Maximum physical error rate: at most 0.0073 probability.
• Required total capacity: at least 4.265e+6 physical qubits.
• Maximum cycle time to beat classical: unknown (Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.).
• Maximum machine-second cost: unknown (Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.).
• Break-even runtime: unknown (Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.).
• Refused (NO_CLASSICAL_BASELINE): max_cycle_time_to_beat_classical_runtime -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): runtime_speedup_over_classical -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): max_machine_cost_per_second -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): max_physical_qubit_second_cost -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): break_even_runtime -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): break_even_machine_cost_per_second -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): projected_quantum_cost -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.
• Refused (NO_CLASSICAL_BASELINE): cost_ratio_to_classical -- Insufficient evidence for economic comparison: no classical baseline was supplied, so there is nothing to be faster or cheaper than. No baseline was assumed.

Decision assessment

• Conservative: CONDITIONALLY_FEASIBLE
• Under this model the computation needs 70,966,576 physical qubits and 1.14e+5 s at code distance 53. The computation is technically feasible under this model, but no economic conclusion can be made because no classical baseline was supplied. The binding constraint is total physical qubit capacity: the machine this workload needs is larger than the device stated for it. A surface-code cycle below 254 ns would be required to finish within the 28800 s target.
• SCIENTIFIC_FEASIBILITY: SATISFIED -- A code distance of 53 meets the 0.01 error budget at a physical error rate of 0.003, under the SURFACE_CODE_ROTATED model.
• ENGINEERING_FEASIBILITY: NOT_SATISFIED -- The machine is 70,966,576 physical qubits: 70,798,036 for the algorithm including routing space, and 168,540 for the magic-state factory. The projected runtime of 1.14e+5 s exceeds the 28800 s target.
• HARDWARE_READINESS: NOT_SATISFIED -- The requirement exceeds the stated capacity of 20,000,000 physical qubits by 3.55x. 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 classical baseline was supplied, so there is nothing to be faster or cheaper than.
• EVIDENCE_CONFIDENCE: NOT_SATISFIED -- Logical counts are DERIVED; hardware parameters are USER_ASSUMPTION at MEDIUM confidence; the classical baseline is absent; 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 24.2x range in total physical qubits across the swept values.
• Reason codes: EXCEEDS_STATED_CAPACITY, HARDWARE_BASIS_USER_ASSUMPTION, HIGH_LAYOUT_SPREAD, HIGH_SENSITIVITY_TO_ERROR_RATE, NO_CLASSICAL_BASELINE, RUNTIME_EXCEEDS_TARGET, RUNTIME_LIMITED_BY_LOGICAL_CYCLES, WORKLOAD_COUNTS_DERIVED_FROM_CIRCUIT.
• Uncertainty: The two layout conventions differ by 2.03x in total physical qubits. These are not equally defensible: routing space is real hardware, so the bare-register figure is an underestimate.
• Uncertainty: A factor-of-four change in the physical error rate changes the machine size by 24.2x. Quoting the point estimate without this range presents it as more precise than it is.
• Next: Measure the current classical solution on the real problem size and record the hardware and date.
• 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: CONDITIONALLY_FEASIBLE
• Under this model the computation needs 18,417,456 physical qubits and 1.05e+5 s at code distance 27. The computation is technically feasible under this model, but no economic conclusion can be made because no classical baseline was supplied. The binding constraint is magic-state throughput, not logical-qubit capacity: the run misses its target because distilled states cannot be produced fast enough, not because the logical circuit is long. A surface-code cycle below 274 ns would be required to finish within the 28800 s target.
• SCIENTIFIC_FEASIBILITY: SATISFIED -- A code distance of 27 meets the 0.01 error budget at a physical error rate of 0.001, under the SURFACE_CODE_ROTATED model.
• ENGINEERING_FEASIBILITY: NOT_SATISFIED -- The machine is 18,417,456 physical qubits: 18,373,716 for the algorithm including routing space, and 43,740 for the magic-state factory. The projected runtime of 1.05e+5 s exceeds the 28800 s target.
• HARDWARE_READINESS: SATISFIED -- The requirement fits the stated capacity of 20,000,000 physical qubits, with 1.09x headroom. 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 classical baseline was supplied, so there is nothing to be faster or cheaper than.
• EVIDENCE_CONFIDENCE: NOT_SATISFIED -- Logical counts are DERIVED; hardware parameters are USER_ASSUMPTION at MEDIUM confidence; the classical baseline is absent; 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 16.5x range in total physical qubits across the swept values.
• Reason codes: HARDWARE_BASIS_USER_ASSUMPTION, HIGH_LAYOUT_SPREAD, HIGH_SENSITIVITY_TO_ERROR_RATE, NO_CLASSICAL_BASELINE, RUNTIME_EXCEEDS_TARGET, RUNTIME_LIMITED_BY_FACTORY, WITHIN_STATED_CAPACITY, WORKLOAD_COUNTS_DERIVED_FROM_CIRCUIT.
• Uncertainty: The two layout conventions differ by 2.03x in total physical qubits. These are not equally defensible: routing space is real hardware, so the bare-register figure is an underestimate.
• Uncertainty: A factor-of-four change in the physical error rate changes the machine size by 16.5x. Quoting the point estimate without this range presents it as more precise than it is.
• Next: Measure the current classical solution on the real problem size and record the hardware and date.
• 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 4,264,546 physical qubits and 2.10e+4 s at code distance 13. The computation is technically feasible under this model, but no economic conclusion can be made because no classical baseline 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 274 ns would be required to finish within the 28800 s target.
• SCIENTIFIC_FEASIBILITY: SATISFIED -- A code distance of 13 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 4,264,546 physical qubits: 4,259,476 for the algorithm including routing space, and 5,070 for the magic-state factory.
• HARDWARE_READINESS: SATISFIED -- The requirement fits the stated capacity of 20,000,000 physical qubits, with 4.69x headroom. 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 classical baseline was supplied, so there is nothing to be faster or cheaper than.
• EVIDENCE_CONFIDENCE: NOT_SATISFIED -- Logical counts are DERIVED; hardware parameters are USER_ASSUMPTION at LOW confidence; the classical baseline is absent; 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 physical error rate: a 2.98x range in total physical qubits across the swept values.
• Reason codes: HARDWARE_BASIS_USER_ASSUMPTION, HARDWARE_CONFIDENCE_LOW, HIGH_LAYOUT_SPREAD, NO_CLASSICAL_BASELINE, RUNTIME_LIMITED_BY_FACTORY, RUNTIME_WITHIN_TARGET, SENSITIVITY_WITHIN_ONE_ORDER, WITHIN_STATED_CAPACITY, WORKLOAD_COUNTS_DERIVED_FROM_CIRCUIT.
• Uncertainty: The two layout conventions differ by 2.03x in total physical qubits. These are not equally defensible: routing space is real hardware, so the bare-register figure is an underestimate.
• Next: Measure the current classical solution on the real problem size and record the hardware and date.
• 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: CONDITIONALLY_FEASIBLE, 70,966,576 physical qubits, 1.14e+5 s, distance 53, factory share 0%, economic INSUFFICIENT_EVIDENCE, evidence LOW.
• Base: CONDITIONALLY_FEASIBLE, 18,417,456 physical qubits, 1.05e+5 s, distance 27, factory share 0%, economic INSUFFICIENT_EVIDENCE, evidence LOW.
• Optimistic: TECHNICALLY_FEASIBLE, 4,264,546 physical qubits, 2.10e+4 s, distance 13, factory share 0%, economic INSUFFICIENT_EVIDENCE, evidence LOW.

Missing evidence

• A dated observation of a real device meeting these physical error rate and cycle time parameters.
• A classical baseline: runtime, cost, hardware, problem size, solution quality, and the date it was measured.

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.
• No classical baseline was supplied, so no economic or speedup conclusion is drawn anywhere in this bundle.

Sources

• Logical resource counts and device assumptions for 2048-bit RSA factoring: Gidney, Ekera -- How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits Published 2019-05-23. 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