Noncommuting charges can increase entanglement and induce critical dynamics
The cross pollination of quantum-many body physics and quantum error correction/mitigation has benefited both fields. A recent conjecture arising from their intersection posits that the noncommutation of conserved quantities, known as “charges,” might inhibit thermalization [1]—a key factor in decoherence. Verifying this conjecture and exploring its practical applications in the field of quantum technology are ongoing areas of research. This study requires a detailed examination of the effects caused from the noncommutation of charges.
First, how can one argue that charges’ noncommutation caused a result? To isolate the effects of charges’ noncommutation, we constructed and compared analogous models that differ in whether their charges commute. This comparison revealed a notable increase in entanglement within the model featuring noncommuting charges [2]. Further, we incorporated these noncommuting charges, which exhibit an SU(2) symmetry, into monitored quantum circuits. These circuits are defined by unitary evolutions interspersed with mid-circuit projective measurements. The SU(2)-symmetric model introduced a state of critical dynamics, characterized by long-range entanglement, replacing the usual area-law phase typically observed in such circuits [3]. Time permitting, I will also briefly explain how one can use Lie Algebra theory to build the Hamiltonians necessary for experimentally testing the predictions of noncommuting charge physics [4].
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