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Dua, Arpit

Publications and source records attributed to Dua, Arpit.

4 records
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DOE OSTI2024

Nonlocal Finite-Depth Circuits for Constructing Symmetry-Protected Topological States and Quantum Cellular Automata

Whether a given target state can be prepared by starting with a simple product state and acting with a finite-depth quantum circuit is a key question in condensed matter physics and quantum information science. It underpins classifications of topological phases, as well as the understanding of topological quantum codes, and has obvious relevance for device implementations. Traditionally, this question assumes that the quantum circuit is made up of unitary gates that are . Inspired by the advent of noisy intermediate-scale quantum devices, we reconsider this question with k - gates, i.e., gates that act on no more than k degrees of freedom but are not restricted to be geometrically local. First, we construct explicit finite-depth circuits of symmetric k -local gates that create symmetry-protected topological (SPT) states from an initial product state. Our construction applies to SPT states protected by global symmetries or subsystem symmetries but not to those with higher-form symmetries, which we conjecture remain nontrivial. Next, we show how to implement arbitrary translationally invariant quantum cellular automata in any dimension using finite-depth circuits of k -local gates. These results imply that the topological classifications of SPT phases and quantum cellular automata both collapse to a single trivial phase in the presence of k -local interactions. We furthermore argue that SPT phases are fragile to k -local symmetric perturbations. We conclude by discussing the implications for other phases, such as fracton phases, and surveying future directions. Our analysis opens a new experimentally motivated conceptual direction examining the stability of phases and the feasibility of state preparation without the assumption of geometric locality. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Loops in 4+1d topological phases

2+1d topological phases are well characterized by the fusion rules and braiding/exchange statistics of fractional point excitations. In 4+1d, some topological phases contain only fractional loop excitations. What kind of loop statistics exist? We study the 4+1d gauge theory with 2-form \mathbb{Z}_2 ℤ 2 gauge field (the loop-only toric code) and find that while braiding statistics between two different types of loops can be nontrivial, the self “exchange” statistics are all trivial. In particular, we show that the electric, magnetic, and dyonic loop excitations in the 4+1d toric code are not distinguished by their self-statistics. They tunnel into each other across 3+1d invertible domain walls which in turn give explicit unitary circuits that map the loop excitations into each other. The SL(2, \mathbb{Z}_2 ℤ 2 ) symmetry that permutes the loops, however, cannot be consistently gauged and we discuss the associated obstruction in the process. Moreover, we discuss a gapless boundary condition dubbed the “fractional Maxwell theory” and show how it can be Higgsed into gapped boundary conditions. We also discuss the generalization of these results from the \mathbb{Z}_2 ℤ 2 gauge group to \mathbb{Z}_N ℤ N .

Chen, Xie↗
DOE OSTI2022

Fractionalization of subsystem symmetries in two dimensions

The fractionalization of global symmetry charges is a striking hallmark of topological quantum order. Here, we discuss the fractionalization of subsystem symmetries in two-dimensional topological phases. In line with previous no-go arguments, we show that subsystem symmetry fractionalization is not possible in many cases due to the additional rigid geometric structure of the symmetries. However, we identify a mechanism that allows fractionalization, involving global relations between macroscopically many symmetry generators. We find that anyons can fractionalize such relations, meaning that the total charge carried under all generators involved in the global relation is nontrivial, despite the fact that these generators multiply to the identity. We first discuss the general algebraic framework needed to characterize this type of fractionalization, and then explore this framework using a number of exactly solvable models with Z 2 topological order, including models having line and fractal symmetries. These models all showcase another necessary property of subsystem symmetry fractionalization: Fractionalized anyons must have restricted mobility when the symmetry is enforced, such that they are confined to a single line or point in the case of line and fractal symmetries, respectively. Looking forward, we expect that our identification of the importance of global relations in fractionalization will hold significance for the classification of phases with subsystem symmetries in all dimensions.

2-dimensional systems↗