Contribution from Asier Piñeiro Orioli, Quantum Scientist at QPerfect
Recently at QPerfect we were discussing over coffee the stream of amazing results on quantum error correction from companies such as QuEra/Harvard [1], Quantinuum [2], Google AI [3]. These groups are trying out different quantum error correction (QEC) codes, slowly but surely increasing the performance of their logical qubits and even starting to assemble them together into small logical circuits!
The race to implement practical quantum error correction with ever-improving hardware is opening tons of exciting questions. For example, how well will QEC work on realistic noise sources of the hardware? Can we implement fully error-corrected logical circuits while keeping overheads to a manageable minimum?
We believe that simulations, and more specifically tensor network simulators like MIMIQ can help answer these questions.
What is QEC? And can it be simulated?
Quantum error correction codes are essentially specialized quantum algorithms that make many noisy qubits behave as a smaller number of more robust qubits. It’s the only theoretically known way to systematically reduce noise in a scalable way in quantum computers.
What are the limits of Clifford simulators?
Realistic noise in experiments is definitely not described by Clifford operators. You can have many kinds of noise such as spontaneous emission or thermal noise, and trickier cases like correlated noise, coherent noise, leakage, non-Markovian noise. None of these are captured by Pauli or Clifford models, even powerful tools like Stim [4]. We need large-scale universal simulators like MIMIQ that can handle both large circuits of 100s of qubits and any kind of noise. Tensor-network methods are well placed for this — see, for instance, Darmawan & Poulin (PRL 2017) [5].
Conclusion
The possibility to simulate realistic noise and fault-tolerant algorithms with non-Clifford gates at scale holds great potential for accelerating progress in practical QEC. We recently partnered with QuEra to study the use of MPS simulators for simulating quantum error correction. So far, the results are encouraging — stay tuned!
References
- Bluvstein et al., “Logical quantum processor based on reconfigurable atom arrays”, Nature (2024).
- Yamamoto et al., “Demonstrating Bayesian quantum phase estimation with quantum error detection”, arXiv:2404.08616 (Quantinuum).
- Google Quantum AI, “Quantum error correction below the surface code threshold”, arXiv:2408.13687.
- Gidney, “Stim: a fast stabilizer circuit simulator”, arXiv:2103.02202.
- Darmawan & Poulin, “Tensor-Network Simulations of the Surface Code under Realistic Noise”, Phys. Rev. Lett. 119, 040502 (2017).