#### 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)*

Done