Power-Law Entanglement and Hilbert Space Fragmentation in Nonreciprocal Quantum Circuits.

Area of Science:

• Quantum information science
• Condensed matter physics
• Complex systems

Background:

• Quantum circuits with measurement offer unique entanglement dynamics.
• Engineering unconventional entanglement requires novel approaches.

Purpose of the Study:

• Introduce a hybrid, nonreciprocal quantum circuit controlled by a classical agent.
• Investigate the impact of classical control on entanglement growth dynamics.

Main Methods:

• Utilized a Majorana quantum chain coupled to a classical N-state Potts chain.
• Implemented measurement updates conditioned on classical spin states.
• Analyzed entanglement growth using transfer matrix of an N-colored loop model.

Main Results:

• For N=2, observed diffusive entanglement growth (S(L)∼L^{1/2}).
• For N≥3, found subdiffusive growth (S(L)∼L^{0.57}) due to Hilbert space fragmentation.
• Established equivalence to SU(N)-symmetric Temperley-Lieb Hamiltonian and surface growth models.

Conclusions:

• Classical dynamical agents can enrich entanglement dynamics in quantum circuits.
• This hybrid approach enables novel entanglement engineering in nonreciprocal architectures.