Planar Fault-Tolerant Quantum Computation with Low Overhead

TL;DR

This paper introduces a novel framework called code craft for implementing fault-tolerant logical operations on planar bivariate bicycle codes, enabling resource-efficient universal quantum computation within a two-dimensional qubit lattice.

Contribution

It presents a systematic method to deform and manipulate planar qLDPC codes for fault-tolerant logical operations, bridging high encoding rates with physical implementability.

Findings

Logical operations like CNOT, state transfer, and measurements are efficiently implemented.

Fault tolerance is established through numerical optimization of code distances.

Universal quantum computation is achieved by coupling a BB-code qubit to a surface-code block.

Abstract

Fault-tolerant quantum computation critically depends on architectures uniting high encoding rates with physical implementability. Quantum low-density parity-check (qLDPC) codes, including bivariate bicycle (BB) codes, achieve dramatic reductions in qubit overhead, yet their logical operations remain a key challenge under planar hardware constraints. Here, we introduce code craft, a framework for designing fault-tolerant logical operations on planar BB codes within a translationally invariant, two-dimensional qubit lattice. By systematically deforming codes through local modifications-stretching, cutting, and painting-we enable the manipulation of logical qubits using strictly planar operations. We establish fault tolerance through numerical optimization of code distances and show that logical operations, including controlled-NOT gates, state transfers, and Pauli measurements, can be efficiently implemented within this framework to assemble an individually addressable logical qubit network. Universal quantum computation can then be realized by coupling just one BB-code logical qubit to a surface-code block. By combining the high encoding efficiency of qLDPC codes with geometric locality, our approach offers a practical and resource-efficient path to fault-tolerant quantum computation.