QGPU: Parallel logic in quantum LDPC codes
We introduce
#clusteredcycliccodes and show how to pursue highly parallelized surface-code style quantum logic with quantum low density parity check codes featuring simple logicals.
lnkd.in/dgnkNTXm
In detail,
#quantumerrorcorrection is critical in the design and manufacture of scalable quantum computing systems. In recent years, there has been growing interest in quantum low-density parity-check codes as a resource-efficient alternative to the traditional
#surfacecode approach. However, their widespread adoption has been limited by the difficulty of compiling
#faulttolerant logical operations. A key challenge is that logical qubits in quantum low-density parity-check codes do not necessarily correspond to distinct groups of physical qubits, which limits the number of logical operations that can be performed in parallel compared with the surface code.
In this work, we introduce clustered-cyclic codes, a family of quantum low-density parity-check codes with finite-size instances such as [[136,8,14]] and [[198,18,10]] that are competitive with current state-of-the-art constructions. These codes are designed to support a directly addressable
#logicalbasis and therefore enable highly parallel logical measurement layers.
To exploit this structure, we introduce parallel product surgery for quantum product codes. The protocol uses an additional copy of the data code patch as an auxiliary patch together with an engineered product connection structure to implement many logical Pauli-product measurements within a single surgery round at small and fixed overhead, enabling surface-code-style maximal parallelism for clustered-cyclic codes: up to k/2 disjoint Pauli-product measurements can be scheduled in a single round under explicit algebraic conditions.
To establish fault tolerance, we prove that parallel product surgery preserves the code distance when applied to
#hypergraph product codes and numerically verify that it preserves the distance for all listed clustered-cyclic code instances with logical dimension k = 8. Finally, we give an explicit example using the [[24,8,3]] clustered-cyclic code: by treating half of the logical qubits as auxiliaries, parallel product surgery enables arbitrary logical CNOT gates on disjoint pairs of qubits to be executed in parallel, and together with symmetry-derived operations, we show that these gates generate the full Clifford group fault-tolerantly.
Warm thanks to Boren Gu - for which this is the first arXiv paper - Andy Liu,
@armanda_oq, Qian Xu, and Joschka Roffe for this wonderful collaboration.