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Paper 1
Addressable fault-tolerant universal quantum gate operations for high-rate lift-connected surface codes
Josias Old, Juval Bechar, Markus Müller, Sascha Heußen
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2511.10191
- arXiv
- 2511.10191
Quantum low-density parity check (qLDPC) codes are among the leading candidates to realize error-corrected quantum memories with low qubit overhead. Potentially high encoding rates and large distance relative to their block size make them appealing for practical suppression of noise in near-term quantum computers. In addition to increased qubit-connectivity requirements compared to more conventional topological quantum error correcting codes, qLDPC codes remain notoriously hard to compute with. In this work, we introduce a construction to implement all Clifford quantum gate operations on the recently introduced lift-connected surface (LCS) codes (Old et al. 2024). These codes can be implemented in a 3D-local architecture and achieve asymptotic scaling $[[n, \mathcal{O}(n^{1/3}), \mathcal{O}(n^{1/3})]]$. In particular, LCS codes realize favorable instances with small numbers of qubits: For the $[[15,3,3]]$ LCS code, we provide deterministic fault-tolerant (FT) circuits of the logical gate set $\{\overline{H}_i, \overline{H}_i, \overline{C_i X_j}\}_{i,j \in (0,1,2)}$ based on flag qubits. By adding a procedure for FT magic state preparation, we show quantitatively how to realize an FT universal gate set in $d=3$ LCS codes. Numerical simulations indicate that our gate constructions can attain pseudothresholds in the range $p_{\mathrm{th}} \approx 4.8\cdot 10^{-3}-1.2\cdot 10^{-2}$ for circuit-level noise. The schemes use a moderate number of qubits and are therefore feasible for near-term experiments, facilitating progress for fault-tolerant error corrected logic in high-rate qLPDC codes.
Open paperPaper 2
Chiral gapped states are universally non-topological
Xiang Li, Ting-Chun Lin, Yahya Alavirad, John McGreevy
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2510.23720
- arXiv
- 2510.23720
We propose an operator generalization of the Li-Haldane conjecture regarding the entanglement Hamiltonian of a disk in a 2+1D chiral gapped groundstate. The logic applies to regions with sharp corners, from which we derive several universal properties regarding corner entanglement. These universal properties follow from a set of locally-checkable conditions on the wavefunction. We also define a quantity $(\mathfrak{c}_{\text{tot}})_{\text{min}}$ that reflects the robustness of corner entanglement contributions, and show that it provides an obstruction to a gapped boundary. One reward from our analysis is that we can construct a local gapped Hamiltonian within the same chiral gapped phase from a given wavefunction; we conjecture that it is closer to the low-energy renormalization group fixed point than the original parent Hamiltonian. Our analysis of corner entanglement reveals the emergence of a universal conformal geometry encoded in the entanglement structure of bulk regions of chiral gapped states that is not visible in topological field theory. Our formalism also gives an explanation of the modular commutator formula for the chiral central charge.
Open paper