Part 1: Logic gates on High-rate Quantum LDPC codes using ion trap devices

Part 1 will focus on the theory of computing with high rate quantum LDPC codes.  Specifically, we demonstrate the [[30, 8, 3]] Bring’s hyperbolic surface code as fault-tolerant quantum memory, and logical circuits of sufficient depth for arbitrary Clifford gate synthesis. This hyperbolic surface code hosts several symmetries, allowing for automorphism and fold-transversal gates. When augemented with an entangling gate from either a pieceably fault-tolerant gate or LDPC surgery, the complete Clifford group can be implemented.

Flexible connectivity paves the way for higher-rate non-planar LDPC codes which compactly encode more logical qubits within a single codeblock, leading to a lower overhead for quantum computation. Eight logical qubits in Bring's code require only 52 physical qubits, in comparison to 153 physical qubits for fully parallel execution on eight patches of rotated surface code of equivalent distance.

Magic states prepared in other codes can be injected into this hyperbolic surface code using LDPC surgery and universal adapters.

Part 2 of this talk will focus on the implementation of the decoding process.