Guanyu Zhu [IBM]

Abstract: 

Quantum low-density parity-check (qLDPC) codes are promising candidates for quantum information storage with high encoding rate, which greatly reduce the space overhead. In this talk, I explore their potential as computational resources, showing how qLDPC codes can be used to produce a large number of logical magic states in parallel—an architecture we term a magic state fountain. Remarkably, the high encoding rate of qLDPC codes is directly converted into a high magic-state production rate.

This construction is enabled by a new topological theory of transversal non-Clifford gates on three-dimensional homological product codes via generalized symmetries. The framework maps a broad class of qLDPC codes to CW complexes via a generalized Freedman–Hastings code-to-manifold correspondence, followed by a deformation retraction to a CW complex that supports cohomological operations such as cup products. Physically, these operations correspond to higher symmetries in the underlying topological quantum field theory (TQFT).

Applying this theory to 3D homological product codes built from a pair of asymptotically good quantum and classical LDPC codes, we obtain a transversal logical CCZ gate on codes with constant stabilizer weight w=O(1), constant rate K=Θ(N), and polynomial distance D=Ω(N1/2), surpassing the N1/3 distance barrier implied by the Bravyi-König bound for conventional topological codes. This structure enables a magic state fountain that fault-tolerantly prepares Θ(N1/2) magic states in parallel in a single shot. When combined with single-shot code switching between 3D and 2D product codes—which provides individually addressable logical Clifford gates—this approach yields a universal logical gate set. Finally, I will also present an alternative scheme for realizing logical non-Clifford gates and a magic state fountain on 2D product codes using a spacetime path-integral formulation.

Research Interests:

Quantum information theory as well as its connection to quantum many-body physics, including quantum error correction and fault-tolerance, quantum LDPC codes, generalized symmetries in topological quantum field theories, topological order, entanglement and complexity of quantum matter, and quantum computing architecture such as superconducting qubits and AMO platforms.