Harnessing Tensor Networks for Error Mitigation in Quantum Computing

The complexity of the noise-mitigating tensor network is directly linked to its bond dimension-the key parameter that quantifies the computational complexity of the classical post-processing. Interestingly, as the noise in the quantum device decreases, the bond dimension required for effective error mitigation also decreases. By truncating the least significant terms in the tensor network, we can focus on mitigating the most critical noise components while keeping the computational complexity manageable.

This approach is vital because, as quantum computing continues to evolve, noise remains the primary hurdle to overcome. Error mitigation methods like TEM will have a significant impact on the development and practical application of quantum technologies in the near term.

In April 2024, Algorithmiq organised a strategic workshop, Quantum Now, bringing together major actors in quantum computing: IBM, AWS, Google, Q-Ctrl, Phasecraft, Caltech, EPFL, ICFO, Nvidia, and many others. The scope was to discuss in detail the resources needed to achieve quantum advantage and value with near-term quantum computers. The outcomes of this meeting are now summarised in a perspective paper which will be soon announced to the public, containing the combined input of all these key players.

In this paper we debunk commonly believed myths on near-term quantum computing and we identify the use cases and applications that are possible with current hardware, using best-in-class error mitigation methods. We show that applications in the fields of quantum chaos, many-body physics, Hubbard dynamics, and small molecule chemistry simulations, requiring circuit volumes ranging from 100×100 to 100×10000, may be implemented using the most powerful error mitigation methods and for error rates typical of current devices. We also argue that existing near-term algorithms can be capable of providing practical quantum advantage at this scale.