Alladi Ramakrishnan Hall

Spacetime dual-unitary quantum circuits : From quantum many-body systems to quantum combinatorial designs

S. Aravinda

IIT-Tirupati

Maximally entangled bipartite unitary operators or gates find various applications from quantum information to many-body physics wherein they are building blocks of minimal models of quantum chaos. In the latter case, they are referred to as “dual unitaries.” Dual unitary operators that can create the maximum average entanglement when acting on product states have to satisfy additional constraints. These have been called “2-unitaries” and are examples of perfect tensors that can be used to construct absolutely maximally entangled states of four parties. Hitherto, no systematic method exists in any local dimension, which results in the formation of such special classes of unitary operators. Our main results can be grouped as follows : (1) We outline an iterative protocol, a nonlinear map on the space of unitary operators, that creates ensembles whose members are arbitrarily close to being dual unitaries. --- Ref: Suhail Ahmad Rather, S. Aravinda, and Arul Lakshminarayan, Phys. Rev. Lett. 125, 070501, (2020) <journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.070501> (2) Constructing a quantum ergodic hierarchy and deriving a condition based on the entangling power of the basic two-particle unitary bilding block of the circuit that guarantees mixing, and when maximized, corresponds to Bernoulli circuits. Ref: S. Aravinda, Suhail Ahmad Rather, and Arul Lakshminarayan, Phys. Rev. Research 3, 043034 (2021) <journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.043034> (3) Studying the construction and local equivalence of dual-unitary operators from combinatorial designs. Ref: Suhail Ahmad Rather, S. Aravinda, and Arul Lakshminarayan, arXiv: <arxiv.org/abs/2205.08842>2205.08842 <arxiv.org/abs/2205.08842> <arxiv.org/abs/2205.08842>(2022)