Resource Estimation for Quantum Variational Simulations of the Hubbard Model
Open accessAbstract
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 paper, 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. We perform resource estimation for both silicon spin qubits and superconducting qubits for a 50-qubit simulation, which cannot be solved exactly via classical means, and find similar results. The number of two-qubit gates required is on the order of 20 000. Hence, to suppress the mean circuit-error count to a level such that we can obtain meaningful results with the aid of error mitigation, we need to achieve a two-qubit gate error rate of approximately ${10}^{\ensuremath{-}4}$. When searching for the ground state, we need a few days for one gradient-descent iteration, which is impractical. This can be reduced to around 10 min if we distribute our task among hundreds of quantum-processing units. 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 optimization of our simulation scheme, improvements in the gate fidelity, improvements in the optimization 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 parallelization, which can be done on one single silicon multicore processor or across multiple superconducting processors.
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For specific problems such as chemistry and condensed matter systems, it is possible to use the structure of the problem to reduce the number of measurements.
“For specific problems such as chemistry and condensed matter systems, it is possible to use the structure of the problem to reduce the number of measurements (Cade et al. , 2020; Cai, 2020; Gokhale and Chong, 2019; Huggins et al. , 2019).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Cai, 2020
In a Fermi-Hubbard model studied using VQE, the number of measurements is reduced by considering multiple orderings of the qubit operators when applying the Jordan-Wigner transformation.
“In particular, in (Cai, 2020), where a Fermi-Hubbard model is studied using VQE, the number of measurements is reduced by considering multiple orderings of the qubit operators when applying the Jordan-Wigner transformation.”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Cai, 2020
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- Authors
- Cai, Z.
- Affiliations
- University of Oxford (GB)
- Corresponding author
- Cai, Zhenyu
- ORCID
- Cai, Zhenyu
- Venue
- Physical Review Applied
- Publisher
- American Physical Society (APS)
- Published
- 2020-07-21
- Volume
- 14
- Issue
- 1
- ISSN
- 2331-7019 (ISSN-L)
- OpenAlex
- W3044574471
- Cited by
- 78
- References
- 60
- Citations by year
- 2026: 1 · 2025: 10 · 2024: 9 · 2023: 16 · 2022: 13 · 2021: 21 · 2020: 8
- FWCI
- 5.70
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Physical Review Applied (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Quantum Motion Technologies Ltd and the QCS Hub (EP/T001062/1)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Keywords
- variational quantum eigensolver, Fermi-Hubbard model, resource estimation, NISQ devices, error mitigation, silicon spin qubits, superconducting qubits, quantum circuit depth, ground state energy, quantum hardware scalability
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