Limitations of Noisy Quantum Devices in Computational and Entangling Power
Quantum computing promises significant enhancement in computational capabilities, yet it is hindered by noise and limited qubit counts, restricting us to Noisy Intermediate-Scale Quantum (NISQ) devices. While progress is being made to achieve quantum advantage with NISQ through approaches like variational algorithms and error mitigation, understanding their fundamental limitations remains a critical challenge. In my talk, I will explore the computational boundaries and entanglement capacities of NISQ devices without error correction. Our research indicates that once circuit depths surpass $\omega(\log(n))$, NISQ devices fail to outperform classical counterparts as determined by polynomial-time algorithms, ruling out the use of prominent quantum algorithms and simulations in this context. Additionally, we identify a logarithmic upper limit on entanglement within one-dimensional qubit arrays, highlighting the entanglement scalability constraints of current quantum systems. This talk is primarily based on the work [arXiv:2306.02836].