@article {3444, title = {Free Quantum Codes from Twisted Unitary $t$-groups}, year = {2024}, month = {2/2/2024}, abstract = {

We introduce twisted unitary t-groups, a generalization of unitary t-groups under a twisting by an irreducible representation. We then apply representation theoretic methods to the Knill-Laflamme error correction conditions to show that twisted unitary t-groups automatically correspond to quantum codes with distance d=t+1. By construction these codes have many transversal gates, which are naturally fault tolerant.

}, url = {https://arxiv.org/abs/2402.01638}, author = {Eric Kubischta and Ian Teixeira} } @article {3493, title = {Topology and entanglement of molecular phase space}, year = {2024}, month = {3/7/2024}, abstract = {

We formulate a quantum phase space for molecular rotational and nuclear-spin states. Taking in molecular geometry and nuclear-spin data, our framework yields admissible position and momentum states, inter-convertible via a generalized Fourier transform. We classify molecules into three types -- asymmetric, rotationally symmetric, and perrotationally symmetric -- with the last type having no macroscopic analogue due to nuclear-spin statistics constraints. We identify two features in perrotationally symmetric state spaces that are Hamiltonian-independent and induced solely by symmetry and spin statistics. First, many molecular species are intrinsically rotation-spin entangled in a way that cannot be broken without transitioning to another species or breaking symmetry. Second, each molecular position state houses an internal pseudo-spin or \"fiber\" degree of freedom, and the fiber\&$\#$39;s Berry phase or matrix after adiabatic changes in position yields naturally robust operations, akin to braiding anyonic quasiparticles or realizing fault-tolerant quantum gates. We outline scenarios where these features can be experimentally probed.

}, url = {https://arxiv.org/abs/2403.04572}, author = {Victor V. Albert and Eric Kubischta and Mikhail Lemeshko and Lee R. Liu} } @article {3296, title = {A Family of Quantum Codes with Exotic Transversal Gates}, year = {2023}, month = {5/11/2023}, abstract = {

Recently it has been shown that the binary icosahedral group 2I together with a certain involution forms the most efficient single-qubit universal gate set. In order for this to be viable, one must construct a quantum code with transversal gate group 2I, however, no such code has ever been demonstrated explicitly. We fill this void by constructing a novel family of quantum codes that all have transversal gate group 2I.

}, url = {https://arxiv.org/abs/2305.07023}, author = {Eric Kubischta and Ian Teixeira} }