Q-CTRL Runs 100-Qubit QFT on IBM Heron r3: Correct Answer Emerges Despite 1.8% Process Fidelity

On August 15, Sydney-based quantum control company Q-CTRL announced on the IBM Quantum platform that it had executed a 100-qubit Quantum Fourier Transform (QFT) on a 156-qubit IBM Heron r3 processor and recovered the correct answer from the output. This is the largest QFT ever run on real hardware — roughly double the 52-qubit record set by ParityQC in April 2026.

The counterintuitive part: process fidelity was only 11.4% at 50 qubits and fell to 1.8% at 80 qubits. In other words, the hardware was producing mostly noise — yet the correct answer still appeared as the most frequent bitstring among 100-qubit outputs.

Why QFT Is the Hardest Subroutine in Quantum Computing

QFT underpins most flagship quantum algorithms:

• Shor's factoring algorithm — finds hidden periods behind RSA encryption
• Quantum phase estimation (QPE) — the backbone of quantum chemistry and quantum machine learning protocols
• HHL linear-system solver — depends on QPE

Engineering QFT is brutal. A standard n-qubit QFT circuit requires controlled-phase rotations between every pair of qubits. On IBM Heron's nearest-neighbor-coupled superconducting chip, long-range rotations must be decomposed into SWAP gates, each adding depth and noise. Rule of thumb: beyond 30–40 qubits, accumulated noise buries the answer.

Convolutional QFT: One Ancilla Does the Whole Job

Q-CTRL's fix was to rewrite the compiler. Their Convolutional QFT strategy:

• Does not require all qubits to participate in pairwise phase rotations
• Uses a single ancilla qubit that walks position-by-position across the register, performing local phase rotations — like a convolution kernel sliding over an image

The result: entangling gate counts per qubit no longer grow with problem size. Q-CTRL then layered its Fire Opal automated error suppression software on top, pushing a recognizable answer to 100 qubits.

Why 1.8% Fidelity Still Yields the Correct Answer

Process fidelity measures how closely the machine's full output matches theory across all possible inputs — so at 1.8%, the processor was almost always producing noise. But the experiment's input was a single frequency, the most forgiving QFT input: nearly all output probability concentrates on one bitstring. Noise removes most of the signal, but the surviving peak still towers over the flat random-noise floor:

• At 50 qubits, the correct bitstring appeared 8.4x more often than any single incorrect bitstring
• Across all circuits up to 100 qubits, the correct answer was always the most frequent single outcome

Important caveat: single-frequency inputs are the easiest case. Real Shor-style inputs are complex superpositions whose answer is spread across carefully arranged phases — those would be dissolved by 1.8% process fidelity. The experiment therefore establishes: (1) Convolutional QFT pushed QFT's scale boundary from 30–40 to 100 qubits, and (2) for "good enough" algorithms, noise tolerance limits are looser than fidelity metrics suggest.

The Same Week: Three Parallel Anti-Noise Tracks

Around August 20, Mitsui + Mitsubishi Electric ran a comparison QFT on Quantinuum Helios:

| Team | Hardware | Approach | Key numbers | Paradigm | |---|---|---|---|---| | Q-CTRL | IBM Heron r3 (156q) | Convolutional QFT + Fire Opal | 100 qubits, 1.8% fidelity | Compilation + software error suppression | | Mitsui/Mitsubishi | Quantinuum Helios (98q) | Steane-encoded QFT | 14.3% correct rate; 12 logical qubits | Hardware-level connectivity + error correction | | IonQ | Q70/Q102 LDPC | CliNR simulation | 74x measurement speedup | LDPC + error detection |

These are three complementary answers to how compilation, algorithms, and error correction share the noise burden before fully fault-tolerant hardware exists.

Engineering Significance

1. Software-layer marginal gains remain huge: the record doubled in four months via compilers and error suppression, not new hardware. 2. The NISQ boundary extends toward practical algorithms: a 100-qubit QFT system can't break RSA (that needs millions of logical qubits) but can handle noise-tolerant subtasks like shallow variational circuits and targeted chemistry subroutines. 3. Q-CTRL was candid: their blog acknowledges single-frequency input is the easiest case and Shor's real inputs would be far harder — a restraint that boosts the result's credibility.

Six Questions to Watch

1. Can the approach handle complex superposition inputs (Shor/QPE)? 2. Will noise again dominate beyond 100 qubits (toward 5,000)? 3. Can the convolutional idea transfer to HHL, amplitude estimation, or QML feature maps? 4. Can Mitsui/Mitsubishi's shot-filtering overhead scale from 12 to 48 logical qubits? 5. Can next-gen IBM hardware push to 200 qubits under the same framework? 6. How does Convolutional QFT perform on all-to-all trapped-ion platforms (Quantinuum, IonQ)?

Takeaway for Industry Observers

1. Watch whether Fire Opal migrates across hardware platforms — if so, the software moat runs deeper than expected. 2. Track the next Convolutional QFT paper (likely 2026 Q4–2027 Q1) for harder-input results. 3. Stop evaluating quantum news by "99% fidelity or useless": the difference between single-input success rate and process fidelity is the new baseline metric for 2026–2027.

The broader lesson: with hardware fidelity approaching 99.9% (Quantinuum Helios's two-qubit gates) while compilation doubles algorithm reach and error correction accelerates, the burden of quantum usefulness is shifting from hardware to the joint design of algorithms, compilation, and error correction. As the week's five events suggest: of the "assembling era's" entrance ticket, hardware holds 30%, software holds 70%.

Sources: Q-CTRL blog "Breaking the 100-Qubit Barrier"; arXiv 2608.05435 (Aug 2026); Quantum Brief 2026-08-16/08-20; Quantum Zeitgeist (Aug 2026); HPCwire 2026-04-16 (ParityQC 52-qubit record); Phys.org (April, prior 27-qubit record).