As an AI language model, I can provide you with some significant advancements in quantum computing in 2021, but it may not be an exhaustive list. Here are ten noteworthy advancements:

1. IonQ and Google Achieve High Quantum Volume: IonQ and Google announced advancements in quantum volume. IonQ’s trapped-ion quantum computer reached a quantum volume of 4 million, while Google’s Sycamore processor achieved a quantum volume of 1 million, marking significant milestones.

2. IBM’s Quantum Roadmap: IBM unveiled its Quantum Roadmap, outlining their plans for developing larger, more stable qubit processors with improved quantum error correction codes and cloud-based quantum services.

3. China’s Quantum Satellite Experiments: China’s research team successfully conducted various quantum experiments using their Micius satellite, including the distribution of entangled photons over long distances. These experiments played a vital role in establishing secure quantum communication.

4. QuTech’s Quantum Internet Demonstrator: QuTech, a collaboration between Delft University of Technology and TNO, showcased a Quantum Internet Demonstrator. This project aims to realize a network of quantum nodes connected through an advanced fiber-optic network.

5. Microsoft’s Azure Quantum Expansion: Microsoft expanded its Azure Quantum service, allowing more users to access quantum computing resources. They also added integration with Python-based quantum programming language libraries, enhancing ease of development.

6. Google’s Quantum Supremacy Demonstration: Although it occurred at the end of 2019, Google’s demonstration of quantum supremacy with its Sycamore processor had ripple effects in 2021. It solidified the belief that quantum computers can surpass classical computers in solving certain tasks.

7. Rigetti’s Amazon Bracket Integration: Rigetti Computing integrated its quantum computers into Amazon Web Services (AWS) through Amazon Bracket. This integration allowed AWS users to develop, test, and run quantum algorithms on Rigetti’s hardware.

8. Honeywell’s Quantum Volume Milestone: Honeywell reached a quantum volume of 512, marking significant progress. Their trapped-ion quantum processors have shown remarkable potential for simulating quantum systems and optimization problems.

9. Toshiba’s Major Breakthrough in Quantum Error Correction: Toshiba achieved a breakthrough in quantum error correction, successfully operating a logical qubit, protected by error-correcting codes, for over a day. This advancement is crucial for building practical, fault-tolerant quantum computers.

10. D-Wave’s Pegasus Quantum System: D-Wave released its next-generation quantum annealer, the Advantage™ Pegasus. This system features over 5,000 qubits and promises to solve more complex optimization problems efficiently.

These advancements represent some of the significant achievements in the field of quantum computing in 2021. However, it is important to note that the field is rapidly evolving, and new advancements may have occurred since the time of this response.

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