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The influence of basis sets and ansatze building to quantum computing in chemistry.

Caio M Porto1, Rene Alfonso Nome2, Nelson H Morgon3

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Summary

Quantum computing, using the variational quantum eigensolver (VQE) and unitary coupled cluster (UCC) ansatz, shows promise for chemistry but is limited by circuit depth and gate count on current hardware. Error mitigation helps but does not fully resolve issues for small molecules and basis sets.

Keywords:
QiskitQuantum computingUCCSDVQE

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Area of Science:

  • Quantum Computing
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Quantum computing is rapidly advancing, showing significant potential for computational and theoretical chemistry.
  • The variational quantum eigensolver (VQE) is a key algorithm for solving electronic structure problems on noisy intermediate-scale quantum (NISQ) hardware.
  • Unitary coupled cluster (UCC) is a widely used ansatz for VQE calculations, generating quantum circuits from chosen basis sets.

Purpose of the Study:

  • Investigate the relationship between circuit depth, gate count, basis sets, and molecular size in VQE calculations.
  • Assess the tractability of VQE calculations on current quantum devices.
  • Evaluate the effectiveness of error mitigation techniques.

Main Methods:

  • Utilized Qiskit for quantum computations and PySCF for electronic structure calculations.
  • Employed the Unitary Coupled Cluster with Singles and Doubles (UCCSD) method for ansatz generation across various basis sets (STO-3G to aug-cc-pVTZ).
  • Mapped operators and Hamiltonians using the Jordan-Wigner scheme and employed the Simultaneous Perturbation Stochastic Approximation (SPSA) optimizer on IBM's Nairobi and Osaka quantum computers.

Main Results:

  • VQE calculations are currently feasible only for small molecules and limited basis sets due to circuit depth and gate count constraints.
  • The H2 molecule with cc-pVTZ and aug-cc-pVTZ basis sets resulted in circuit depths of 10^3 to 10^4 gates.
  • The CH4 molecule with the 3-21G basis set required a circuit depth of 10^3 gates, and the H2 molecule with STO-3G required over 500 shots to reduce error.

Conclusions:

  • Current quantum hardware limitations restrict the application of VQE to small molecular systems and basis sets.
  • While error mitigation can reduce inaccuracies in VQE calculations, it does not eliminate them entirely.
  • Further advancements in quantum hardware and algorithms are necessary for tackling larger and more complex chemical problems.