Experimental observation of measurement induced phase transitions using linear cross-entropy

Quantum circuits with random unitaries and projective measurements at random points in spacetime exhibit an entanglement phase transition that depends on the rate at which the measurements occur. Previous work has observed these phase transitions experimentally by measuring the entanglement entropy between different groups of qubits [1] or a reference qubit [2]. The former computational approach is limited by the exponential scaling of the quantum state tomography required to measure the entanglement entropy and to sample the probability distribution of measurement outcomes. Recently, it was proposed [3] that the entanglement phase transition may also be observed by calculating the linear cross-entropy between pairs of random quantum circuits. This new protocol removes the underlying exponential scaling of the tomography, allowing experiments to probe larger system sizes. We implemented this protocol on IBM’s quantum hardware and have experimentally observed indications of a measurement-induced phase transition.

[1] J. M. Koh et al., https://arxiv.org/abs/2203.04338 (2022)

[2] C. Noel et al., Nat. Phys. 18, 760–764 (2022)

[3] Y. Li et al., https://arxiv.org/abs/2209.00609 (2022)