• DOI:10.1103/physrevapplied.14.014059
• Corpus ID: 203836049

Resource Estimation for Quantum Variational Simulations of the Hubbard Model

@article{Cai2019ResourceEF,
  title={Resource Estimation for Quantum Variational Simulations of the Hubbard Model},
  author={Zhenyu Cai},
  journal={arXiv: Quantum Physics},
  year={2019}
}

• Zhenyu Cai
• Published 7 October 2019
• Physics
• arXiv: Quantum Physics

As the advances in quantum hardware bring us into the noisy intermediate-scale quantum (NISQ) era, one possible task we can perform without quantum error correction using NISQ machines is the variational quantum eigensolver (VQE) due to its shallow depth. A specific problem that we can tackle is the strongly interacting Fermi-Hubbard model, which is classically intractable and has practical implications in areas like superconductivity. In this Article, we will perform resource estimation on Hubbard VQE using silicon spin qubits as our example platform, though many of our arguments can be extended to other hardware platforms like superconducting qubits, trapped-ion qubits, etc. We outline the details about the gate sequence, the measurement scheme and the relevant error mitigation techniques for the implementation of the Hubbard VQE on a NISQ platform. For a 50-qubit simulation of the Fermi-Hubbard model, which cannot be solved exactly via classical means, we need $\sim 40000$ gates, which means that we need a gate infidelity of $10^{-4}$ to obtain meaningful results with the aid of error mitigations. When searching for the ground state presuming a $\mu s$ gate time, the time required for one time step in gradient descent is $\sim 6 \text{ days}$, which can be reduced to less than $10$ minutes if we distribute our task among 1000 quantum processors. Hence, implementing a 50-qubit Hubbard model VQE on a NISQ machine can be on the brink of being feasible in near term, but further optimisation of our simulation scheme, improvements in the gate fidelity, improvements in the optimisation scheme and advances in the error mitigation techniques are needed to overcome the remaining obstacles. The scalability of the hardware platform is also essential to overcome the runtime issue via parallelisation.