A new study has shown that the complexity of random unitary quantum circuits grows almost linearly with time, at a rate of Ω(T/log T). This finding is significant for understanding how information is processed and becomes incompressible in complex quantum systems. Circuit complexity refers to the minimum number of quantum gates required to implement it, and its linear growth suggests that these circuits intrinsically become harder to simulate or describe as they evolve.

This result improves previous lower bounds for complexity growth, which were derived from properties such as spectral gaps and unitary designs. Prior estimates showed a polynomial dependence on n (the system size), whereas the new bound is independent of n, making it more general and robust. The bound is valid for a wide range of times, from T=2 up to T=4ⁿ, covering most of the relevant evolution of these systems.

The methodology employed in this research draws on a combination of stochastic calculus, geometric functional analysis, and randomized linear algebra. Instead of relying on convergence to high-order unitary designs, the approach exploits the circuit's response to variations of individual gates. This technique allows for a more precise characterization of how complexity accumulates gate by gate, providing a new perspective on information dynamics in random quantum circuits.