⚛️ quantum physics

Demonstration of low-overhead quantum error correction codes

Using a 32-qubit superconducting processor with long-range couplers, the authors demonstrate the feasibility of low-overhead quantum error correction by successfully implementing and measuring the performance of two distinct quantum low-density parity-check (qLDPC) codes.

Original authors: Ke Wang, Zhide Lu, Chuanyu Zhang, Gongyu Liu, Jiachen Chen, Yanzhe Wang, Yaozu Wu, Shibo Xu, Xuhao Zhu, Feitong Jin, Yu Gao, Ziqi Tan, Zhengyi Cui, Ning Wang, Yiren Zou, Aosai Zhang, Tingting Li, Fanh

Published 2026-01-27

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Ke Wang, Zhide Lu, Chuanyu Zhang, Gongyu Liu, Jiachen Chen, Yanzhe Wang, Yaozu Wu, Shibo Xu, Xuhao Zhu, Feitong Jin, Yu Gao, Ziqi Tan, Zhengyi Cui, Ning Wang, Yiren Zou, Aosai Zhang, Tingting Li, Fanhao Shen, Jiarun Zhong, Zehang Bao, Zitian Zhu, Yihang Han, Yiyang He, Jiayuan Shen, Han Wang, Jia-Nan Yang, Zixuan Song, Jinfeng Deng, Hang Dong, Zheng-Zhi Sun, Weikang Li, Qi Ye, Si Jiang, Yixuan Ma, Pei-Xin Shen, Pengfei Zhang, Hekang Li, Qiujiang Guo, Zhen Wang, Chao Song, H. Wang, Dong-Ling Deng

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to send a delicate message across a stormy ocean. The message is made of glass (quantum information), and the waves (errors) are constantly trying to shatter it. In the world of quantum computing, keeping this glass intact is the biggest hurdle.

For a long time, scientists have tried to protect this glass by building a massive, redundant fortress around it. This is called Quantum Error Correction. The most popular fortress design, known as the "surface code," works like a giant grid. To protect just one piece of glass (a "logical qubit"), you need a huge square of physical glass pieces (physical qubits). It's like using 100 bricks to build a single, strong wall. While it works, it's incredibly expensive and wasteful; you need thousands of bricks just to build a small house.

The Breakthrough: A Smarter Blueprint
This paper, from a team at Zhejiang University and Tsinghua University, introduces a new, much more efficient blueprint. They didn't just build a bigger wall; they redesigned the architecture entirely using something called qLDPC codes (specifically "bivariate bicycle" codes).

Think of the old method as building a wall where every brick only talks to its four immediate neighbors. The new method is like a high-tech city where every building has secret, long-distance tunnels connecting it to buildings far away. This allows them to use fewer bricks to build a stronger wall.

The Experiment: The "Kunlun" Processor
To test this, the team built a new superconducting quantum processor named Kunlun.

The Hardware: Imagine a chessboard, but instead of pieces only moving to adjacent squares, the pieces have special "long-range couplers" (like invisible bridges) that let them talk to pieces on the other side of the board. They managed to connect 32 qubits (the basic units of information) in a complex, 3D-like web on a flat chip.
The Test: They used this chip to run two different error-correction codes:
1. A Distance-4 code that protected 4 logical qubits using only 18 physical qubits.
2. A Distance-3 code that protected 6 logical qubits using 18 physical qubits.

The Results: Less Waste, Better Protection
The team found that their new "bicycle" codes were incredibly efficient.

The Efficiency Gain: To get the same level of protection with the old "surface code," they would have needed nearly four times as many physical qubits. Their new method achieved the same goal with a fraction of the resources.
The Performance: They ran the system through many cycles (like running a marathon to see if the runner stays steady). They measured how often the "logical" information got corrupted.
- For the 4-qubit code, the error rate was about 8.9% per cycle.
- For the 6-qubit code, it was about 7.8% per cycle.

The Catch: The "Break-Even" Point
Here is the honest part of the story: While the new codes are more efficient, they haven't yet become perfect.
Currently, the "logical" qubits (the protected information) are still making mistakes slightly more often than the "physical" qubits (the raw hardware) do on their own. In the world of error correction, this is called not having reached the "break-even" point yet.

Think of it like a new type of life jacket. This new life jacket is much lighter and takes up less space than the old bulky ones (high efficiency), but it still doesn't keep you perfectly dry in a storm yet (the error rate is still slightly higher than the raw hardware). However, the paper proves that the design works and that if we just make the hardware slightly better (stronger bridges, clearer signals), this new design will eventually outperform the old bulky ones significantly.

Why This Matters
This paper is a crucial step because it proves that we don't need millions of qubits to build a powerful quantum computer. By using these "long-range" connections and smarter codes, we can build a much smaller, more manageable machine that still protects its information effectively. It's the difference between trying to build a skyscraper with a mountain of bricks versus using a few, incredibly strong, pre-fabricated steel beams.

Summary

Problem: Quantum computers break easily; fixing them usually requires too many resources.
Solution: A new type of code (bivariate bicycle) that uses long-range connections to protect data with far fewer qubits.
Proof: The team built a chip (Kunlun) with long-range bridges and successfully ran these codes.
Outcome: They achieved high efficiency (4x less overhead) but still need to improve hardware quality to make the protection perfect.

Technical Summary: Demonstration of Low-Overhead Quantum Error Correction Codes

Problem Statement
While quantum computers hold the potential to surpass classical machines in complex computational tasks, the fragility of quantum information and the error-prone nature of quantum operations present a significant barrier to building large-scale, fault-tolerant systems. Quantum error correction (QEC) is essential for achieving fault tolerance by encoding logical qubits redundantly into physical qubits. However, a critical limitation of many existing QEC codes, particularly the widely studied surface code, is low encoding efficiency. In surface codes, the encoding rate scales as $1/d^2$ (where $d$ is the code distance), leading to prohibitively high resource overheads for large-scale implementations. Although quantum low-density parity-check (qLDPC) codes, such as bivariate bicycle (BB) codes, offer significantly higher encoding efficiency and comparable error thresholds, their experimental realization has been hindered by stringent hardware requirements. Specifically, BB codes demand high connectivity and long-range couplings between physical qubits that exceed the capabilities of conventional two-dimensional superconducting architectures.

Methodology
The authors report the experimental demonstration of two low-overhead qLDPC codes on "Kunlun," a new 32-qubit superconducting processor featuring long-range coupled transmon qubits.

Hardware Architecture: The Kunlun processor utilizes a 32-qubit square lattice with 84 tunable couplers, including long-range connections spanning up to 6.5 mm. This design supports a torus connectivity topology with a maximum qubit degree of six, achieved via overlapping couplers and air-bridges to allow multi-coupler crossovers on a planar architecture.
Codes Implemented:
1. Distance-4 Bivariate Bicycle (BB) Code: Parameters $[[18, 4, 4]]$ , encoding 4 logical qubits into 18 data qubits with 14 check qubits.
2. Distance-3 qLDPC Code: Parameters $[[18, 6, 3]]$ , encoding 6 logical qubits into 18 data qubits with 12 check qubits.
Experimental Protocol: The team executed efficient syndrome extraction circuits to measure nonlocal weight-6 stabilizers. The circuit involves initializing data qubits, performing seven layers of CZ gates interleaved with single-qubit gates (including dynamical decoupling to mitigate dephasing), and reading out check qubits.
Error Characterization: The processor demonstrated average fidelities of 99.95% for parallel single-qubit gates and 99.22% for parallel CZ gates (both local and long-range). Readout errors were measured at 1.6% for two-state and 6.6% for three-state discrimination.
Decoding: Error syndromes were decoded using a belief propagation with ordered statistics decoder (BP-OSD) extended to the circuit-based noise model. Logical error rates were calculated by comparing the corrected logical state against the initial encoded state across multiple cycles.

Key Results

Logical Error Rates:
- For the distance-4 BB code, the logical error rate per logical qubit per cycle was measured at $(8.91 \pm 0.17)\%$ .
- For the distance-3 qLDPC code, the logical error rate per logical qubit per cycle was $(7.77 \pm 0.12)\%$ .
Stabilizer Performance: The average experimental error in measuring weight-6 stabilizers was estimated at $(8.1 \pm 2.8)\%$ . The detection probability for errors was observed to be higher than in surface codes (approx. 0.319 for Z-type and 0.318 for X-type stabilizers), attributed to the weight-6 nature of the stabilizers.
Encoding Efficiency: The implemented BB code achieved an encoding rate of 1/8. The authors note that implementing four distance-4 surface codes would require 124 physical qubits, nearly four times the number of qubits used in their distance-4 BB implementation (32 qubits total, 18 data + 14 check).
Simulation vs. Experiment: Simulations based on the current physical error rates indicate that logical error rates currently increase with code distance, suggesting the system has not yet reached the "break-even" point where logical errors are suppressed below physical errors. A transition to error suppression is predicted to occur when physical error rates are reduced by a factor of approximately 0.5 ( $s=0.5$ ).

Significance and Claims
The paper claims to establish the feasibility of implementing various qLDPC codes using long-range coupled superconducting processors. By successfully demonstrating a distance-4 BB code and a distance-3 qLDPC code, the work marks a crucial step toward large-scale, low-overhead quantum error correction. The authors emphasize that their results demonstrate a three to four-fold reduction in encoding overhead compared to surface codes for the same number of logical qubits and code distance.

The authors maintain a modest tone regarding the current state of fault tolerance, acknowledging that the logical error rates in their experiment remain higher than the physical error rates. They identify that achieving the break-even point and beyond requires further technical improvements, including higher-fidelity two-qubit gates over larger distances, faster and more accurate readout, and more efficient leakage removal methods. Furthermore, they note that the implementation of a universal, fault-tolerant logical gate set remains a significant challenge that has not yet been demonstrated for either surface codes or the qLDPC codes presented in this work. The study serves as a foundational demonstration of the hardware capabilities required for future scaling of low-overhead QEC.

Technical Summary: Demonstration of Low-Overhead Quantum Error Correction Codes

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