FR-QE-0006

Fault-Tolerant Quantum Utility — Practically Useful Algorithms Beyond Classical Simulation

A fault-tolerant quantum computer can execute a practically useful quantum algorithm beyond classical simulation.

EscalatingVS-02·since 2024-01-15

Verification Matrix

VS-01

Assertion

—

VS-02

Published

2024-01-15 — present

VS-03

Audit

—

VS-04

Replication

—

VS-05

Operation

—

State reached Current state Not yet reached

State Warrant

Current stateEscalatingVS-02

Why this state?The claim has not been satisfied. No fault-tolerant quantum computer has executed a practically useful quantum algorithm beyond classical simulation at the scale required for genuine practical advantage. The substrate progress (INST-003) establishes that fault-tolerant logical qubits capable of executing simple circuits now exist; the resource estimation (INST-004) establishes that practically useful chemistry simulation requires approximately two orders of magnitude more logical qubits than are currently available. The gap is smaller and more tractable than the equivalent gap for RSA factorisation (FR-QE-0005), but still represents years of further engineering. Classical simulation methods are simultaneously improving (INST-005), narrowing the space of problems that would unambiguously qualify as beyond classical reach by the time fault-tolerant hardware reaches the required scale. The pressure state is ESCALATING: the substrate is advancing on a credible path, but no agreed target problem yet exists (BN-001) on which the claim could be tested.

In this state since2024-01-15

Stage provenanceStored VS-02; historically unverified after legacy review.^*

Record Lineage — Chronological

2024-01-15

Record opened — Escalating

The claim has not been satisfied. No fault-tolerant quantum computer has executed a practically useful quantum algorithm beyond classical simulation at the scale required for genuine practical advantage. The substrate progress (INST-003) establishes that fault-tolerant logical qubits capable of executing simple circuits now exist; the resource estimation (INST-004) establishes that practically useful chemistry simulation requires approximately two orders of magnitude more logical qubits than are currently available. The gap is smaller and more tractable than the equivalent gap for RSA factorisation (FR-QE-0005), but still represents years of further engineering. Classical simulation methods are simultaneously improving (INST-005), narrowing the space of problems that would unambiguously qualify as beyond classical reach by the time fault-tolerant hardware reaches the required scale. The pressure state is ESCALATING: the substrate is advancing on a credible path, but no agreed target problem yet exists (BN-001) on which the claim could be tested.

Verification Stage: VS-02 preserved — historically unverified.^*

Mutation Log

Mutation	Date	Field	Prior value	Current value
M-009	2026-07-14	instance_appended	—	IN-006
M-008	2026-07-08	reference_corrected	—	REFERENCE-CORRECTED
M-007	2026-07-08	realization_note_added	—	REN-001
M-006	2024-01-15	programme_panel_added	—	PROGRAMME-PANEL-ADDED
M-005	2024-01-15	null_condition_failed	—	NULL-CONDITION-FAILED
M-004	2024-01-15	mechanisms_recorded	—	MECHANISMS-RECORDED
M-003	2024-01-15	assessment_issued	—	ASSESSMENT-ISSUED
M-002	2024-01-15	instances_logged	—	INSTANCES-LOGGED
M-001	2024-01-15	record_created	—	RECORD-CREATED

Evidence Sources

6 instances on recordShow sources ↓Hide ↑

IN-001Quantum algorithm portfolio — theoretical utility establishedneutral

IN-002NISQ-era quantum utility claims and classical simulation challengespartial

IN-003Logical qubit fault-tolerant operations — substrate becomes application-ready in principlesupportive

IN-004Resource estimation studies — useful fault-tolerant algorithms require 1000+ logical qubitspartial

IN-005Classical algorithm improvement — moving target on the simulation thresholdcontesting

IN-006Composed logical Clifford operations via lattice surgery on a superconducting surface-code processorNEUTRAL