Classes of topological qubits from low-dimensional quantum spin systems

RANJAN CHAUDHURY, SAMIR K. PAUL

An effective theory for a quantum spin system in low dimensions is constructed in the finite-q regime. It is shown that there are field configurations for which Wess–Zumino terms contribute to the partition functions as topological terms for ferromagnets as well as antiferromagnets in both one- and two-dimensional lattices. This is in sharp contrast to the absence of topological excitations in two-dimensional quantum antiferromagnets in the long wavelength limit.

Abhinav Saket

Abhinav Saket

Austin G. Fowler

Topological quantum error-correction codes are extremely practical, typically requiring only a two-dimensional lattice of qubits with tunable nearest-neighbor interactions yet tolerating high physical error rates $p$. It is computationally expensive to simulate the performance of such codes at low $p$, yet this is a regime we wish to study as low physical error rates lead to low qubit overhead. We present a very general method of analytically estimating the low-$p$ performance of the most promising class of topological codes. Our method can handle arbitrary periodic quantum circuits implementing the error detection associated with this class of codes, and arbitrary Pauli error models for each type of quantum gate. Our analytic expressions take only seconds to obtain, versus hundreds of hours to perform equivalent low-$p$ simulations.

S. Das Sarma

Raoul Dillenschneider, Jung‐Hoon Kim, Jung Hoon Han

A class of exact spin ground states with nonzero averages of vector spin chirality, $$, is presented. It is obtained by applying non-uniform O(2) rotations of spin operators in the XY plane on the SU(2)-invariant Affleck-Kennedy-Lieb-Tasaki (AKLT) states and their parent Hamiltonians. Excitation energies of the new ground states are studied with the use of single-mode approximation in one dimension for S=1. The excitation gap remains robust. Construction of chiral AKLT states is shown to be possible in higher dimensions. We also present a general idea to produce vector chirality-condensed ground states as non-uniform O(2) rotations of the non-chiral parent states. Dzyaloshinskii-Moriya interaction is shown to imply non-zero spin chirality.