Abhishodh Prakash

Computational Power of Symmetry-Protected Topological Phases

We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order as resources for measurement-based quantum computation (MBQC). We show that, for a wide range of SPT phases, the computational power of ground states is uniform throughout each phase. This computational power, defined as the Lie group of executable gates in MBQC, is determined by the same algebraic information that labels the SPT phase itself. We prove that these Lie groups always contain a full set of single-qubit gates, thereby affirming the long-standing conjecture that general SPT phases can serve as computationally useful phases of matter.

Eigenstate phases with finite on-site non-Abelian symmetry

We study the eigenstate phases of disordered spin chains with on-site finite non-Abelian symmetry. We develop a general formalism based on standard group theory to construct local spin Hamiltonians invariant under any on-site symmetry. We then specialize to the case of the simplest non-Abelian group,

Symmetry-protected topological phases with uniform computational power in one dimension

S_3

Ground states of one-dimensional symmetry-protected topological phases and their utility as resource states for quantum computation

, and numerically study a particular two parameter spin-1 Hamiltonian. We observe a thermal phase and a many-body localized phase with a spontaneous symmetry breaking (SSB) from

Unwinding short-range entanglement

S_3

Detection of gapped phases of a one-dimensional spin chain with on-site and spatial symmetries

to

Title: Classification of Floquet drives of one-dimensional fermions.

\mathbb{Z}_3

Ergodicity and symmetry breaking in disordered spin chains with on-site non-Abelian symmetry

in our model Hamiltonian. We diagnose these phases using full entanglement distributions and level statistics. We also use a spin-glass diagnostic specialized to detect spontaneous breaking of the

Ergodicity and symmetry breaking in disordered spin chains with non-Abelian on-site symmetry.

S_3

Determining the computational power of symmetry protected topological phases

symmetry down to