175 citations · 1.7k across the 55 of their papers we have counts for
59 papers
Invertible subalgebras for chiral semion topological order
Yu-An Chen, Meng Sun, Nathanan Tantivasadakarn +2
Chiral topological order is incompatible with strictly two-dimensional local commuting-projector Hamiltonians on finite-dimensional tensor-product Hilbert spaces. Invertible subalg…
Cups and Gates II: Operads, twists, and addressable intra-code gates
Nikolas P. Breuckmann, Margarita Davydova, Jens Niklas Eberhardt +2
In Part I, we introduced a general framework for constructing logical gates in quantum CSS codes from cohomology invariants, focusing on cup products and their generalizations from…
Magic Quantum Code Surgery
Kathleen Chang, Anasuya Lyons, Yuanjie Ren +5
Non-Clifford operations required for universal quantum computation can be implemented by measuring logical Clifford operators. We present a generalized framework to fault-tolerantl…
Exact Recovery for Non-Abelian Surface Codes
Alison Warman, Nathanan Tantivasadakarn, Sakura Schafer-Nameki
We study exact recovery for non-Abelian topological surface codes based on the quantum double of any finite group . We determine an orthogonal error basis, that is compri…
Coupled-Layer Codes: Beyond Quantum Product Constructions
Shuyu Zhang, Tzu-Chieh Wei, Nathanan Tantivasadakarn
Product codes are an important class of quantum error-correcting codes constructed from multiple input codes, which can give rise to asymptotically good quantum low-density parity…
Non-Clifford quantum cellular automata from invertible topological quantum field theories
Meng Sun, Zongyuan Wang, Bowen Yang +2
Quantum cellular automata (QCAs) describe locality-preserving quantum dynamics and connect quantum information, many-body physics, and topological quantum field theory (TQFT). Cons…
Majorana-Pauli stabilizer codes and duality webs of fermionic topological phases
Meng Sun, Zongyuan Wang, Nathanan Tantivasadakarn +1
Stabilizer codes provide exact lattice realizations of bosonic topological orders. In contrast, systematic stabilizer descriptions of intrinsically fermionic topological phases rem…
Spontaneous breaking of non-invertible symmetries and duality to beyond-Landau transitions
Xie Chen, Shang Liu, Da-chuan Lu +1
Spontaneous symmetry breaking is a well-understood mechanism for generating distinct phases of matter. Recently, the notion of symmetry has been broadened to include operations wit…
Coupled-Layer Construction of Quantum Product Codes
Shuyu Zhang, Tzu-Chieh Wei, Nathanan Tantivasadakarn
Product codes are a class of quantum error correcting codes built from two or more constituent codes. They have recently gained prominence for a breakthrough yielding quantum low-d…
Quantum logic control and entanglement in hybrid atom-molecule arrays
Chi Zhang, Sara Murciano, Nathanan Tantivasadakarn +1
Polar molecules, with their rich internal structure, offer immense potential for fundamental physics, quantum technology, and controlled chemistry. However, their utilization is cu…
Generalized Kramers-Wannier Self-Duality in Hopf-Ising Models
Da-Chuan Lu, Arkya Chatterjee, Nathanan Tantivasadakarn
The Kramers-Wannier transformation of the 1+1d transverse-field Ising model exchanges the paramagnetic and ferromagnetic phases and, at criticality, manifests as a non-invertible s…
Universal Gates from Braiding and Fusing Anyons on Quantum Hardware
Chiu Fan Bowen Lo, Anasuya Lyons, Dan Gresh +8
Topological quantum computation encodes quantum information in the internal fusion space of non-Abelian anyonic quasiparticles, whose braiding implements logical gates. This goes b…
Unveiling dynamical quantum error correcting codes via non-invertible symmetries
Rajath Radhakrishnan, Adar Sharon, Nathanan Tantivasadakarn
Dynamical stabilizer codes (DSCs) have recently emerged as a powerful generalization of static stabilizer codes for quantum error correction, replacing a fixed stabilizer group wit…
Clifford quantum cellular automata from topological quantum field theories and invertible subalgebras
Meng Sun, Bowen Yang, Zongyuan Wang +2
We present a general framework for constructing quantum cellular automata (QCA) from topological quantum field theories (TQFT) and invertible subalgebras (ISA) using the cup-produc…
Sequential Circuits as Generalized Symmetry on the Lattice
Nathanan Tantivasadakarn, Xinyu Liu, Xie Chen
Generalized symmetry extends the usual notion of symmetry to ones that are of higher-form, acting on subsystems, non-invertible, etc. The concept was defined in the field theory co…
String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to -String Condensation
Pranay Gorantla, Abhinav Prem, Nathanan Tantivasadakarn +1
We present a new perspective on the -string condensation procedure for constructing 3+1D fracton phases by implementing this process via the gauging of higher-form symmetries. S…
Universal Quantum Computation with the Quantum Double: A Pedagogical Exposition
Chiu Fan Bowen Lo, Anasuya Lyons, Ruben Verresen +2
Non-Abelian topological order (TO) enables topologically protected quantum computation with its anyonic quasiparticles. Recently, TO with gauge symmetry was identified as a s…
Qutrit Toric Code and Parafermions in Trapped Ions
Mohsin Iqbal, Anasuya Lyons, Chiu Fan Bowen Lo +16
The development of programmable quantum devices can be measured by the complexity of manybody states that they are able to prepare. Among the most significant are topologically ord…
Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits
Yuanjie Ren, Nathanan Tantivasadakarn, Dominic J. Williamson
The classification of topological phases of matter is a fundamental challenge in quantum many-body physics, with applications to quantum technology. Recently, this classification h…
Protocols for Creating Anyons and Defects via Gauging
Anasuya Lyons, Chiu Fan Bowen Lo, Nathanan Tantivasadakarn +2
Creating and manipulating anyons and symmetry defects in topological phases, especially those with a non-Abelian character, constitutes a primitive for topological quantum computat…
Cups and Gates I: Cohomology invariants and logical quantum operations
Nikolas P. Breuckmann, Margarita Davydova, Jens N. Eberhardt +1
We take initial steps towards a general framework for constructing logical gates in general quantum CSS codes. Viewing CSS codes as cochain complexes, we observe that cohomology in…
Tensor networks for non-invertible symmetries in 3+1d and beyond
Pranay Gorantla, Shu-Heng Shao, Nathanan Tantivasadakarn
Tensor networks provide a natural language for non-invertible symmetries in general Hamiltonian lattice models. We use ZX-diagrams, which are tensor network presentations of quantu…
A holographic view of topological stabilizer codes
Thomas Schuster, Nathanan Tantivasadakarn, Ashvin Vishwanath +1
The bulk-boundary correspondence is a hallmark feature of topological phases of matter. Nonetheless, our understanding of the correspondence remains incomplete for phases with intr…
Non-invertible symmetry-protected topological order in a group-based cluster state
Christopher Fechisin, Nathanan Tantivasadakarn, Victor V. Albert
Despite growing interest in beyond-group symmetries in quantum condensed matter systems, there are relatively few microscopic lattice models explicitly realizing these symmetries,…