There have been a lot of announcements made recently about developments in quantum error code (QEC) research, so it might be worthwhile to review what are the desirable features of a good code:
- Low ratio of physical qubits to logical qubits for efficiency
- Significant improvement in error rates and ability to scale the level of improvement as the code size increases
- Fast logical cycle time including error decoding and correction to maximize processing speed
- Single shot decoding of the errors to minimize the logical cycle time
- Straight forward implementation for a given hardware architecture
- Enablement of efficient methods for implementing a universal gate set for processing any quantum algorithm
Microsoft has been working on a 4-dimensional geometric error correction code aimed for initial implementation on Atom Computer’s forthcoming neutral atom processor as well as other processor architectures. Details of a specific implementation of this code they have described is a [[96,6,8]] code, meaning 96 physical qubits for data, 6 logical qubits, and code distance of 8. This code would also require 128 additional ancilla qubits for error measurement. This physical to logical ratio is much more efficient than the surface code and competitive with the SHYPS code used by Photonic Inc. and the Bivariate Bicycle code used by IBM. Assuming the physical qubits have a physical error rate of 10-3, the resulting logical qubits in Microsoft’s [[96,6,8]] code would have a logical error rate of 10-6.
The code is designed for flexibility so that it can be used with any qubit modality that supports all-to-all connectivity including all-to-all connectivity neutral atoms, ion traps, and photonic qubits. However, it would probably not work with quantum computers using the superconducting modality since those modalities are typically not able to achieve the qubit-to-qubit connectivity required.
In a related paper Atom Computing has also released a paper on arXiv titled Repeated ancilla reuse for logical computation on a neutral atom quantum computer. This paper describes how Atom Computing is able to measure ancilla qubits using mid-circuit measurement, reset them for reuse, and replace any of the atoms that are lost in the process while maintaining coherence of existing atoms during the execution of a quantum circuit.
For additional information about Microsoft’s QEC research, you can access a blog post on the Microsoft Quantum webpage here. And for more technical information you can access a paper posted on arXiv last month titled Geometrically Enhanced Topological Quantum Codes available here and a follow-on new paper titled A Topologically Fault-Tolerant Quantum Computer with Four Dimensional Geometric Codes that has just been posted on arXiv here.
GQI has created a 22-page presentation titled Quantum Hardware QEC State of Play that covers many aspects of quantum error correction along with comparisons of several different codes. To learn how you can obtain this presentation, contact info@global-qi.com.
June 19, 2025
