Researchers Steered a Quantum Map on IBM Hardware With Up to 100 Qubits

Researchers used adaptive, monitored quantum circuits and conditional feedback to steer a quantum version of the classically chaotic Bernoulli map on IBM superconducting hardware, with systems of up to 100 qubits. Published in Nature Physics on October 9, 2026, the study reports a transition between quantum and classical dynamics.

How feedback steered the Bernoulli map

A Bernoulli map is a mathematical rule for updating a system; the classical version studied here is chaotic. In the quantum experiment, the map scrambled quantum information, while researchers used local measurements and resets during the circuit to steer the dynamics toward a fixed point.

The circuits were adaptive: measurement results informed conditional feedback during the computation. The study reports up to nearly 5,000 entangling gates and 5,000 non-unitary mid-circuit operations. Entangling gates connect qubits, while the measurements and resets were interspersed with the circuit’s other operations.

The reported transition between quantum and classical dynamics

The study reports a dynamical phase transition between quantum and classical behavior and estimates of universal critical properties. The researchers analyzed the result using noisy simulations, matrix product states, and mappings to statistical-mechanics models.

The Quantum Insider reported that the shift was sharp near an approximate 50-50 balance between scrambling and measurement-and-reset activity. In that account, scrambling dominated above half the task frequency, while checking and resetting dominated below the approximate balance.

What the result says about fault tolerance

The experiment controlled dynamics in a deliberately designed map. That is a specific feedback-control task, distinct from a general-purpose quantum computer correcting arbitrary errors during calculations.

Publication and access to the study materials

Nature Physics published the study on October 9, 2026. The experimental dataset and numerical simulations are available from the corresponding author on reasonable request; the study code is available from the corresponding author on request.