Quantum Error Correction
Quantum Error Correction (QEC) is a critical component for building practical and reliable quantum computers. Qubits, regardless of modality, are highly susceptible to noise and environmental disturbances that can alter their states. By constructing logical qubits from collections of physical qubits and using error correction codes, QEC detects and corrects errors, enabling longer and more accurate quantum computations.
QuEra and its collaborators at Harvard, MIT, and other institutions are leaders in the research and implementation of efficient and effective quantum error correction. Some research highlights include:
Rodriguez, P.S., Robinson, J., Jepsen, P.N. et al. (2024). Experimental Demonstration of Logical Magic State Distillation. arXiv preprint, arXiv:2412.15165.
This experimental work, performed on our Gemini-class quantum computer, realizes one of the most important building blocks of large-scale quantum computation—-logical magic state distillation (MSD). Stabilizer states and Clifford operations are often easy to implement on an error-corrected quantum computer. However, such states can also be efficiently simulated classically, and do not suffice for universal quantum computation. This is where magic states come in: "Magic", which describes how far away a quantum state is from a stabilizer state, is a key resource for performing universal quantum computation and achieving quantum advantage. Unfortunately, high-quality magic states are one of the most complex things to prepare for large-scale quantum computers. Magic state distillation prepares high-fidelity magic resource states by refining multiple lower-fidelity ones. This has been a well-studied protocol, but until now, logical-level MSD had not been demonstrated. In this work, we realized logical-level MSD on a neutral-atom quantum computer using 2D color codes. For both distance 3 and 5 codes, we demonstrated that the output magic state fidelity surpassed the input. Beyond demonstrating distillation gain, we also probed the quadratic error suppression of the MSD process, varying the fidelity of input states and verifying the output improvements experimentally. Neutral atom platforms offer unique advantages, such as dynamic reconfigurability and parallel control: we encoded ten distance-3 or five distance-5 logical qubits simultaneously, and leveraged these features for transversal operations. These experiments demonstrate a key building block of universal fault-tolerant quantum computation, and represent an important step towards large-scale logical quantum processors.
Zhou, H., Zhao, C., Cain, M., Bluvstein, D., Duckering, C., Hu, H.Y., Wang, S.T., Kubica, A., & Lukin, M.D. (2024). Algorithmic fault tolerance for fast quantum computing. arXiv preprint, arXiv:2406.17653
In this work led by our QEC team, in collaboration with Harvard and Yale researchers, we propose a novel framework for transversal algorithmic fault tolerance in quantum computing, focusing on reducing the overall space-time volume required for computations. Conventional QEC methods require repeated syndrome extraction for each logical operation, leading to a logical clock speed significantly slower (often 30x in relevant regimes) than the physical clock speed. In this work, we propose and prove a new fault tolerance strategy, transversal algorithmic fault tolerance, which achieves a 10-100x reduction in the time overhead of QEC by considering the complete algorithmic context in decoding. We further show that this yields competitive performance in numerical simulations of the method. This work thus sheds new light on the theory of quantum fault tolerance, and has the potential to reduce the space-time cost of practical fault-tolerant quantum computation by orders of magnitude.
Cain, M., Zhao, C., Zhou, H., Meister, N., Ataides, J.P.B., Jaffe, A., Bluvstein, D., & Lukin, M.D. (2024). Correlated decoding of logical algorithms with transversal gates. Physical Review Letters.
In this collaboration led by Harvard University, we explore the use of correlated decoding strategies for logical quantum algorithms implemented with transversal gates. We show that the performance of logical algorithms can be substantially improved by decoding the qubits jointly to account for physical error propagation during transversal entangling gates. These results demonstrate that correlated decoding provides a major advantage in early fault-tolerant computation, and indicate it has considerable potential to reduce the space-time cost in large-scale logical algorithms.
Bluvstein, D., Evered, S.J., Geim, A.A., et al. (2024). Logical quantum processor based on reconfigurable atom arrays. Nature, 626, 58–65.
This paper, led by our collaborators at Harvard and experimentally carried out in the first atom array experiment system at Harvard, presents the groundbreaking demonstration of a logical quantum processor using reconfigurable atom arrays. We introduce a scalable architecture where neutral atoms serve as physical qubits, and logical qubits are controlled by parallel operations. Key innovations include dynamic qubit reconfiguration and direct, efficient control of logical qubits rather than individual physical qubits. We demonstrate improvement of surface code two-qubit logic gates by scaling the code distance from d=3 to d=7, fault-tolerantly prepare logical GHZ states, and realize computationally complex sampling circuits with up to 48 logical qubits, 228 logical two-qubit gates and 48 logical CCZ gates. This architecture represents a significant step toward fault-tolerant quantum computation, realizing some of the most complex error-corrected quantum algorithms to date. The work also showcases the flexible adaptability of atom arrays for different quantum error correcting codes and quantum algorithms.