Physicists have traced the phase transition of magic within a quantum system.

Stabilizer states are a class of quantum states that can be effectively simulated on classical computers. The property known as "magic" in quantum mechanics characterizes quantum states by their degree of deviation from stabilizer states.

Magic makes quantum states difficult to simulate, yet it is essential for the implementation of universal and error-resistant quantum computations. Understanding the properties responsible for this will significantly enhance the performance of quantum computers.

The authors of the new study previously published a paper demonstrating the existence of a phase transition in the entanglement of a system. They found that depending on the measurement frequency, the phase state of a quantum system can either preserve or destroy entanglement.

“Superpositions and entanglement alone are insufficient for making quantum computers more powerful than classical ones. To achieve an advantage, an additional component—magic, or deviation from the stabilizer state—is necessary. If a quantum system lacks magic, it can be simulated on a classical computer, rendering the quantum computer redundant. Only with a significant amount of magic can one surpass the capabilities of a classical computer,” explained Pradeep Niroula, the lead author of the new scientific paper.

A quantum gate, which is akin to a logical gate in classical computers, acts on qubits and aims to create entanglement between them, while measuring one of these qubits destroys it. If you introduce several gates into the quantum circuit, you can perform measurements at random locations and control the distribution of entanglement in the system.

Researchers know that with a low number of measurements, the entire quantum system becomes entangled. Conversely, with too frequent measurements, entanglement is suppressed. However, gradually increasing the measurement frequency causes entanglement to undergo a sharp phase transition from high to nearly zero.

This time, scientists investigated whether a phase transition exists in magic. They demonstrated that the code designed to protect quantum information from errors exhibits a clear phase transition from the state of "having magic" to "not having magic" without intermediate stages, in terms of magic. The study has been published in the journal Nature Physics.

Measurements also destroy magic, but to add it to the system in a controlled manner, small changes to the states of the qubits must be made. Changes in the quantum state of a qubit are referred to as rotations because they are theoretically described within a three-dimensional coordinate system.

Physicists employed a magic control scheme in a random stabilizer code through coherent errors. Such errors are predictable, constant, and are a result of the evolution of quantum states.

In the experiment, measurements sometimes destroyed magic, reverting states to stabilizer ones, while at other times they left magic unchanged. The competing forces in quantum computers turned out to be the "number of measurements" and the "rotation angle of the qubits."

The researchers found that by fixing the measurement rate, they could alter the rotation angle and transition from a phase with a high concentration of magic to a phase without it at all. The authors of the study conducted a series of numerical simulations and demonstrated that a phase transition in magic indeed occurs and then experimentally verified this hypothesis using real quantum circuits. The experiments confirmed the simulations.

“We observed signs of a phase transition even against the background noise in the system. Our work reveals a phase transition in magic. Previous studies have already identified other transitions in entanglement and charges, raising the question: Can other resources demonstrate similar transitions? Do they belong to some universal type of transitions? Can we apply this knowledge to create error-resistant quantum computers?” noted Niroula.

The existence of a transition may indicate a more general theory applicable to various quantum properties.