Coprime Bivariate Bicycle Codes and Their Layouts on Cold Atoms

Abstract

Quantum computing is deemed to require error correction at scale to mitigate physical noise by reducing it to lower noise levels while operating on encoded logical qubits. Popular quantum error correction schemes include CSS code, of which surface codes provide regular mappings onto 2D planes suitable for contemporary quantum devices together with known transversal logical gates. Recently, qLDPC codes have been proposed as a means to provide denser encoding with the class of bivariate bicycle (BB) codes promising feasible design for devices. This work contributes a novel subclass of BB codes suitable for quantum error correction. This subclass employs {\em coprimes} and the product $xy$ of the two generating variables $x$ and $y$ to construct polynomials, rather than using $x$ and $y$ separately as in vanilla BB codes. In contrast to vanilla BB codes, where parameters remain unknown prior to code discovery, the rate of the proposed code can be determined beforehand by specifying a factor polynomial as an input to the numerical search algorithm. Using this coprime-BB construction, we found a number of surprisingly short to medium-length codes that were previously unknown. We also propose a layout on cold atom arrays tailored for coprime-BB codes. The proposed layout reduces both move time for short to medium-length codes and the number of moves of atoms to perform syndrome extractions. We consider an error model with global laser noise on cold atoms, and simulations show that our proposed layout achieves significant improvements over prior work across the simulated codes.

accepted by quantum

References in corpus (16)

• Surface codes: Towards practical large-scale quantum computation
• Good Quantum Error-Correcting Codes Exist
• Logical quantum processor based on reconfigurable atom arrays
• High-threshold and low-overhead fault-tolerant quantum memory
• Stim: a fast stabilizer circuit simulator
• Sparse Graph Codes for Quantum Error-Correction
• Quantum Low-Density Parity-Check Codes
• Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
• Decoding Across the Quantum LDPC Code Landscape
• Continuous operation of a coherent 3,000-qubit system
• Steerable optical tweezers for ultracold atom studies
• Entangling four logical qubits beyond break-even in a nonlocal code
• Toward a 2D Local Implementation of Quantum LDPC Codes
• Accelerating the assembly of defect-free atomic arrays with maximum parallelisms
• Architecture for fast implementation of qLDPC codes with optimized Rydberg gates
• Lowering Connectivity Requirements For Bivariate Bicycle Codes Using Morphing Circuits

Cited by in corpus (1)

• Qudit low-density parity-check codes