Pushing the Limits of Quantum Error Correction with High-Performance Quantum Simulation

Quantum systems are tremendously fragile with even the slightest disturbance affecting the quantum state. This fundamental obstacle has made achieving reliable, large-scale quantum information processing extremely challenging.

That’s why quantum error correction is so crucial to the advancement of this technology. It enables quantum computers to detect and fix errors, ensuring stable and fault-tolerant operations. To effectively scale quantum systems, quantum error correction is therefore essential.

Yet, conventional quantum error correction approaches come with a massive cost: the requirement of thousands of physical qubits to encode individual logical qubits. What does this really mean? A quantum computer with 1,000 logical qubits would require upwards of a million total qubits in its system, making a useful quantum computer an incredibly resource intensive endeavour requiring large-scale systems to operate.

A Radically Different Approach

At Nord Quantique, we take a different approach to this challenge. We focus on bosonic codes which leverage the large Hilbert space of quantum oscillators to achieve quantum error correction at the physical level. This means we are correcting errors at each physical qubit, dramatically reducing the hardware overhead. Our qubits maintain a 1:1 ratio of logical qubit per physical cavity.

This radically different approach to fault tolerant quantum computing relies on three main pillars:

1. Logical Qubits with No Physical Overhead
   Each Nord Quantique’s error-corrected physical qubit acts as a single logical qubit, drastically reducing hardware requirements by maintaining a one-to-one ratio of logical qubit per physical cavity.
2. Low Logical Error Rates
   Our approach enables autonomously error-corrected qubits that are within reach of practical, utility-scale applications.
   
   
3. Scalable with Fast Clock Rates
   Our superconducting architecture allows for a fully scalable system, operating logical qubits at speeds in the MHz regime, providing faster computations.

Unlike conventional qubits, bosonic qubits leverage their large Hilbert space to enable robust quantum error correction. Understanding these intricate mechanisms requires powerful numerical simulations.

Advantage of Multimode Bosonic Codes

Standard quantum error correction approaches require increasing the number of physical qubits per logical qubit. At Nord Quantique, we are pioneering the development of multimode bosonic codes. 
Multimode bosonic codes provide a unique scaling axis: the ability to add modes to a single physical cavity without increasing hardware size. This feature makes multimode bosonic codes a hardware-efficient and scalable approach to fault-tolerant quantum computing. 

Multimode bosonic codes allow:

❖    Design of qubits that are resilient to additional sources of noise, such as control-induced errors, by increasing the number of modes per qubit.

❖    Improved quantum error correction capabilities compared to single-mode GKP qubits which already have the potential to outperform standard qubit-based architectures.

Another key advantage of bosonic codes is enhanced real-time confidence information about the logical qubit. While performing autonomous quantum error correction, we can extract valuable information about the reliability of the computation. This information can be efficiently used in error mitigation strategies, further improving the stability of quantum operations. Multimode bosonic codes offer even richer confidence information compared to single-mode implementations, enhancing our ability to detect errors.

Engineering Multimode Bosonic Codes with Numerical Simulations

Nord Quantique’s vision is simple: engineer larger multimode bosonic codes to enhance quantum error correction capabilities while maintaining a one-to-one ratio of logical qubit per physical cavity. This approach aims to significantly improve error resilience and logical qubit performance while drastically cutting down the resources required for scaling. 

Numerical simulations demonstrate that by simply extending the single-mode grid state qubit (GKP qubit) to a two-mode implementation (Tesseract code) we can significantly improve correction of the dominant source of error. These simulated results are consistent with recent theoretical work from Liang Jiang's group at University of Chicago [arXiv:2412.06715]. Liang Jiang’s insights highlight the advantages of multimode encodings in enhancing quantum error correction performance. This result reinforces our approach of scaling multimode encodings as the key to unlocking utility-scale quantum computing. 

The Tesseract code, a particular multimode code using two modes, demonstrates how leveraging multimode superconducting cavities enhances error resilience. This further validates our strategy of designing increasingly robust multimode QEC architectures to push quantum computing beyond its current limitations.

The Need for Powerful Simulation

Today, at GTC 25, we highlighted how the latest advancements in high-performance quantum simulation support the Nord Quantique approach. NIVIDIA’s CUDA-Q platform presents the opportunity to push the boundaries of bosonic code-based quantum error correction even further.

Numerical simulations show that the Tesseract code significantly outperforms single-mode GKP qubits in correcting photon loss errors. For physical error rates and mean photon numbers per mode achievable in the lab, the Tesseract code can reduce logical error rates far below 10e-10 and beyond what is possible with single-mode implementations. 

However, quantum hardware experiences more than just photon loss—additional sources of noise must be addressed to achieve such low logical error rates experimentally, hence the importance of extending beyond two modes to develop even more powerful multimode QEC codes capable of handling all error sources present in the lab. Accurately modeling these effects to engineer such multimode codes requires detailed quantum dynamics simulations—an area where CUDA-Q Dynamics function plays a crucial role in accelerating development and optimization

With its ability to leverage GPU acceleration, CUDA-Q presents a powerful platform for simulating quantum systems, outperforming standard solutions currently available in the field. Tools like CUDA-Q can significantly accelerate the development of scalable fault-tolerant architectures. 

We believe the CUDA-Q platform, refined for bosonic code simulation, will help unlock greater performance gains, surpassing all existing classical simulation platforms. Its ability to accurately simulate bosonic codes is key to designing, optimizing, and scaling our quantum processors.

The Future of Scalable, Fault-Tolerant Quantum Computing

At Nord Quantique, our mission is to build scalable, hardware-efficient quantum processors that operate with fast clock rates. We are demonstrating a path toward error rates that unlock utility-scale quantum computing — without the massive overhead of traditional approaches.

As quantum hardware and simulation technologies evolve in tandem, close collaboration between quantum computing pioneers and high-performance computing leaders like NVIDIA will drive future breakthroughs. By refining and expanding quantum simulation capabilities, we move closer to unlocking the full potential of quantum computing.