A 100-qubit Quantum Fourier Transform ran on IBM hardware: why the answer surfaced at 1.8% fidelity

Q-CTRL reported on August 10, 2026 that it executed a 100-qubit Quantum Fourier Transform (QFT) on a 156-qubit IBM Heron r3 processor and recovered the correct frequency as the mode of the measured distribution. The company describes the result as the largest experimental QFT run on any quantum hardware to date by a factor of two, a 100% increase in register width. The enabling technique is a Convolutional QFT compilation strategy built around a single ancilla qubit, which implements an n-qubit QFT on a linear nearest-neighbor topology using n²-n+2 CX gates, close to the n²-n theoretical minimum for all-to-all connectivity. Unitary process fidelity measured 11.4% at 50 qubits and 1.8% at 80 qubits, yet the correct bitstring still appeared 8.4 times and 7.5 times more often than any incorrect outcome. ASAP works from Q-CTRL's announcement and the authors' manuscript arXiv 2608.05435 to separate what this result demonstrates from what it does not.

Surfacing as the mode and running a correct circuit are two different claims

The success criterion Q-CTRL reports is selectivity of the answer, not accuracy of the whole circuit. At 50 qubits the target bitstring appeared 8.4 times more often than any incorrect output, while unitary process fidelity in the same run was 11.4%. At 80 qubits selectivity slipped to 7.5 times and fidelity fell to 1.8%. At 100 qubits, the correct target integer frequency is described as emerging as the unique mode result, standing clearly above the background noise.

The two metrics diverge so sharply because they measure different things. Process fidelity asks how faithfully the circuit reproduced the intended unitary transformation; selectivity asks how far the correct answer outran the wrong ones in the final measurement distribution. For a task like period extraction, where the answer resolves to a single integer, the second one alone is enough to read out an answer.

Read in that context, a fidelity of 1.8% means the following. Most of the quantum state that came out of the circuit is noise, but the surviving signal of under 2% concentrates on one particular bitstring, so it rises above noise that spread itself evenly across everything else. On a task whose answer is broadly distributed, the same fidelity would have yielded nothing readable.

The record came from compilation, not from more hardware

What produced this record is not a new processor but the way the circuit is mapped onto the machine. The manuscript arXiv 2608.05435 presents a method that compiles an n-qubit QFT onto a linear nearest-neighbor (LNN) topology using n²-n CX gates, with the convolutional variant adding only two CX gates in total. The device used was a 156-qubit IBM Heron r3, so 100 qubits amounts to roughly two-thirds of its register.

Structurally, the Convolutional QFT combines a single ancilla qubit with a translation-invariant kernel gadget. Per Q-CTRL's description, the circuit logic is compressed into a compact kernel that then steps sequentially along the qubit register, minimizing the number of entangling gates in each qubit's causal history. A gate count of n²-n+2 means the scheme effectively reaches the n²-n figure previously associated with all-to-all connectivity. Given that real superconducting chips connect only neighboring qubits and normally require additional swap gates, this is the technical core of the result.

Error suppression entered along four lines. Idle qubits received uninterrupted dynamical decoupling sequences while the kernel stepped along the register, and the smallest QFT rotations were truncated to balance algorithmic synthesis error against two-qubit gate noise. The schedule of algorithmic operations and error-suppression sequences was jointly optimized, and statistical readout error mitigation was applied at the end.

Deciding to throw away the small rotations is what opened the scale

The most interesting design choice is the deliberate discarding of the QFT's small rotations. A QFT circuit contains controlled phase rotations whose angles shrink exponentially with the distance between qubits. All of them are mathematically required, but implementing any one of them on a real device costs a two-qubit gate, and that gate carries noise.

A trade-off follows. Keep the tiny rotations and the algorithm stays exact while noise accumulates; truncate them and the algorithm acquires an approximation error while the circuit gets shorter. As qubit counts grow, the noise side of that ledger grows faster, so past some point truncation improves the final result. The truncation criterion Q-CTRL describes is precisely this balance.

Seen that way, the experiment illustrates a shift in what quantum algorithm research is for. The goal is no longer to place the textbook QFT onto hardware unchanged, but to know the noise structure of the device and shave the algorithm to fit it. It is the same kind of work as rewriting a classical kernel around a hardware cache hierarchy. In a field reported through qubit counts, this result shows how much of the real progress is arriving at the compiler layer.

Naming the distance between this and breaking encryption

Because the QFT is a core component of Shor's algorithm, news like this often gets translated into a cryptographic threat, yet at least three layers separate this result from breaking RSA. The first is the rest of the circuit. In Shor's algorithm the QFT is the final period-extraction step, preceded by modular exponentiation, a far heavier computation. This experiment ran the QFT subroutine on its own, without that front half.

The second is the absence of error correction. The reported methods are error suppression techniques such as dynamical decoupling and readout error mitigation, not a layer that builds logical qubits and corrects errors. A process fidelity that falls to 1.8% at 80 qubits is itself evidence that this circuit ran on uncorrected physical qubits.

The third is the nature of the success criterion. Period extraction tolerates low fidelity because the answer only needs to be the mode, but the same tolerance does not carry over to structures that must pass an intermediate quantum state into the next computation. What the result demonstrates is that a wide circuit can run and leave a statistically readable signal, not that the resulting state can be picked up and computed on further.

One more point concerns the range of the published figures. Process fidelity is given for 50 and 80 qubits, while the headline 100-qubit run is described only as producing the correct answer as the unique mode. Verification naturally gets harder as scale grows, but citing the 100-qubit result with the same force as the other two overstates it.

What to check when reading the next qubit-count announcement

The practical lesson for companies and institutes evaluating quantum computing announcements is to reorder the checklist. The first question is not how many qubits the machine has, but whether those qubits operated together in a single circuit. A statement that 100 qubits were bound into one circuit on a 156-qubit device carries entirely different information than a statement that the device holds 156 qubits.

The second question is how success was defined. That a process fidelity of 11.4% and a selectivity of 8.4 times are two faces of the same run makes any announcement quoting only one metric hard to take at face value. When a release omits fidelity and reports only an accuracy figure, the right follow-up is which task that accuracy was measured on.

The third is separating the hardware and software contributions. This record was set on an IBM device using Q-CTRL's compilation and error suppression. For an organization weighing adoption, that means procuring hardware alone will not reproduce the result, and the control software layer deserves its own line in the evaluation. Anyone assessing a quantum investment should ask for evidence on the compilation stack alongside the chip specification sheet.

Standing conditions and what remains unverified

The first condition this result stands on is the nature of the task. The experiment extracted the period of a high-dimensional quantum state, and mode-based judgment works because the answer resolves to a single integer. Nothing here guarantees the same scale reproduces on other QFT applications.

The second is device dependence. The Convolutional QFT is designed around a linear nearest-neighbor topology and was executed on IBM Heron r3. On hardware with different connectivity, such as trapped ions, the size of the gate-count advantage changes.

The third is the scope of the comparison. The claim of double the previous maximum refers to experimentally performed QFT benchmarks and compares along a single axis, register width. Where prior records stood on other axes such as circuit depth or accuracy is not part of that statement. The manuscript was submitted on August 5, 2026 by Paul Coote, Michael J. Biercuk, and Yuval Baum, and it is a preprint rather than a peer-reviewed publication, which is worth stating alongside any citation.

Source: ASAP analysis based on Q-CTRL's announcement Breaking the 100-qubit barrier: Executing the Quantum Fourier Transform at scale on IBM hardware (2026-08-10) and the manuscript arXiv 2608.05435, Experimental demonstration of the Quantum Fourier Transform on up to 100 qubits using a convolutional compilation strategy (2026-08-05).