11 papers
Transversal non-Clifford gates on almost-good quantum LDPC and quantum locally testable codes
Yiming Li, Zimu Li, Zi-Wen Liu
We exhibit nontrivial transversal logical multi-controlled- gates on quantum low-density parity-check (qLDPC) codes with soundness , c…
Theory of (Co)homological Invariants on Quantum LDPC Codes
Zimu Li, Yuguo Shao, Fuchuan Wei +2
With recent breakthroughs in the construction of good qLDPC codes and nearly good qLTCs, the study of (co)homological invariants of quantum code complexes, which fundamentally unde…
Theory of low-weight quantum codes
Fuchuan Wei, Zhengyi Han, Austin Yubo He +2
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. H…
Poincaré Duality and Multiplicative Structures on Quantum Codes
Yiming Li, Zimu Li, Zi-Wen Liu +1
Quantum LDPC codes have attracted intense interest due to their advantageous properties for realizing efficient fault-tolerant quantum computing. In particular, sheaf codes represe…
Toward Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU() Symmetry
Han Zheng, Zimu Li, Sergii Strelchuk +2
We introduce a framework of the equivariant convolutional quantum algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU sym…
No-go theorems for logical gates on product quantum codes
Esther Xiaozhen Fu, Han Zheng, Zimu Li +1
Quantum error-correcting codes are essential to the implementation of fault-tolerant quantum computation. Homological products of classical codes offer a versatile framework for co…