Insider Brief
- Microsoft unveiled new geometric quantum error-correcting codes that reduce physical qubit requirements and enable more efficient, fault-tolerant quantum computing.
- Krysta Svore, Microsoft Technical Fellow, said the codes are “very efficient both in space and time,” and demonstrated performance improvements of up to 1,000× in simulation.
- Svore said the codes will support simulations in chemistry and materials science and could generate high-accuracy data to train classical AI models as quantum systems scale to 100 logical qubits.
Microsoft has unveiled a new family of quantum error-correcting codes that could dramatically reduce the number of physical qubits required to run reliable quantum computations. The approach uses high-dimensional geometry to boost code performance—offering a path toward practical, fault-tolerant quantum computing on emerging hardware platforms.
The findings, published on a pre-print server arXiv and discussed in a summary research story in The Quantum Insider story here, explore how rotating and reshaping topological codes in higher dimensions can lower the overhead typically required for fault-tolerant architectures. This method generalizes ideas from the well-known toric code to three, four, and even higher-dimensional lattices, delivering more efficient encoding and logical operations with fewer qubits.
Geometry as a Tool For Scalability
The new codes build on topological error correction, a method that protects quantum information by distributing it across a structured grid of qubits. In this study, Microsoft researchers reshaped that grid — known as a lattice — using a mathematical method called Hermite normal form. Simply put, it’s a tool for rotating and compressing the grid into a more efficient shape. This allowed the team to reduce the physical volume of the code’s layout while preserving — or even improving — its ability to detect and correct errors.
This geometric reshaping results in substantial reductions in qubit count. In one notable case, they achieved six logical qubits using just 96 physical qubits, which is a 16-to-1 ratio that would mark a significant improvement over standard two-dimensional codes.
“These are quantum error correcting codes that are very efficient both in space and time,” said Krysta Svore, Technical Fellow and lead for Microsoft’s quantum systems team, said in an interview with TQI. “They use very few physical qubits to enable a logical qubit. They have a very fast logical clock speed, and… we can extract the right information bits about the noise in the system very readily at low depth.”
Single-Shot, High-Threshold Codes
The geometric codes are also designed for “single-shot” error correction, meaning they can detect and correct errors with minimal repeated measurements. That property has long been sought in the field, and its presence here signals a step forward in reliability.
According to Svore, these codes deliver “provably single-shot” performance and can tolerate relatively high error rates in hardware—up to 1% or more—making them viable on current-generation devices like neutral atom or trapped-ion systems.
“With one of our code instances in the family we call the Hadamard code, we can achieve close to three orders of magnitude reduction in that failure rate,” she said, noting a drop from one error in 1,000 operations to one in a million in simulation.
Built for Emerging Hardware
The work was co-designed with advances in hardware in mind. As newer qubit modalities have emerged—including neutral atom, trapped ion, and photonic systems—they have enabled architectures with flexible or long-range connectivity between qubits.
“When you relax the geometry constraints, one can achieve much higher rates — meaning fewer physical qubits to enable a logical qubit — while still maintaining very good performance,” Svore said.
This flexibility makes the codes well-suited to near-term quantum computers that offer non-local qubit interactions. Microsoft is already integrating the codes into its Qubit Virtualization System, which tailors software stacks to the specific physical qubits and error models of partner devices.
“We’ve been inventing and seeking to co-design quantum error correcting codes that really take advantage of the characteristics of the quantum hardware,” Svore said.
From Slicing to Symmetries
Beyond geometric rotations, the study introduces techniques such as “slicing” higher-dimensional codes into multiple lower-dimensional ones, producing entangled logical states like Bell pairs or GHZ states. This creates direct routes to building stabilizer-based quantum computers — in other words, systems that continuously check and correct errors to protect quantum information — using fewer physical resources.
The researchers also explore how symmetries in the lattice, known as crystalline symmetries, can be harnessed to implement logical gate operations without physically moving qubits. These symmetries act like internal logic, allowing universal Clifford operations through code deformations and measurement-based interactions.
In four-dimensional codes, the team demonstrated how to reduce stabilizer weights while preserving code distance, using alternative cellulations like the 24-cell honeycomb structure. The techniques also support low-overhead methods for state injection, a crucial step in enabling non-Clifford operations and universal quantum computing.
Real-World Applications and Future Directions
Microsoft is rolling the new codes into its commercial offering, the Microsoft Quantum Suite, which combines hardware from partners such as Atom Computing with Microsoft’s software and simulation stack. The company projects that near-term implementations could support up to 50 logical qubits with error rates low enough to perform simulations beyond classical reach.
For Microsoft, the significance of reaching 50 to 100 logical qubits goes beyond raw compute — it opens up new possibilities in developing practical applications for quantum computers and could even serve as a new channel between quantum and classical systems.
“We will be able to show things you can’t do on a classical machine, but also starting to demonstrate instances in material science and chemistry and starting to explore the accuracy of the solutions one can get there,” said Svore.
She said the long-term vision is to use high-fidelity quantum outputs to, for example, improve traditional machine learning.
“Ultimately, we envision using that as data for training an AI model, a classical AI model,” she said. “So ultimately, as we go from 50 to 100 logical qubits and beyond, these systems can be used to develop highly accurate data for for problems across material science or chemistry. And then we can use that data to to augment how we train classical AI models today, bringing more predictability and efficiency to those AI models.”
You can read more about the discovery here.
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