Quantum Chemistry

Molecular simulation

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Introduction


The goal is to efficiently simulate a molecule, by computing its ground state energy :
  • First done during the Qhack, a Hackathon hosted by Xanadu, for the BeH2 molecule.

  • This project finished 2nd in the quantum chemistry challenge and 3rd in the hybrid algorithm challenge (out of 3000 participants).

  • Then used during the Quantum Algorithm Quantum Challenge, hosted by Qunasys, for a molecule-like Hamiltonian, with realistic hardware simulation.

Challenges

The main difficulty of simulating molecules is the size of the configuration space, growing exponentially with the number of electrons. This requires to consider many approximations, tampering with the accuracy of the result. Quantum algorithms already exist for this purpose, but often require a high number of physical qubits.

One common algorithm used to find the ground state energy is the variational quantum eigensolver (VQE). However, it is often hard to improve its accuracy without increasing too much the depth or the number of parameters.

Solution

We implemented an algorithm that, starting from the result of the VQE, further improves the energy prediction. Expectations values are computed on the quantum computer to create a subspace. Then, a classical diagonalization is done to find the energy. We iterate on the subspace basis to find the most relevant parts of the configurations space, and so the best energy estimation.

Business Value

This hybrid approach conserves the advantage of using a quantum computer. It allows to improve the energy estimation of a VQE, without adding parameters or increasing the depth. Finally, the last part being done on classical computer makes the result stable.

Graphics Sigma Chemistry Start with the VQE, with a relative error of 2⋅10 −5.
In 10 steps, with a subspace of dimension 42, the relative error drop to 9⋅10−7.
This is approximately 20 times more accurate, using a third of the full Hilbert space.
In 15 steps, the error is 10−7, 200 times more accurate using half of the Hilbert space.

Conclusion

Although VQE is the one of the most NISQ and prefered method of computing ground states, it is often hard to increase its accuracy without increasing too much the depth or the number of parameters. By making several carefully choosen expectation values, the algorithm was able to ehance the result of the VQE, without the aforementionned limitations.

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    Sigma Reply is the Reply group company offering answers in the field of Quantum Computing. We support the business to adapt to this new revolution and deliver cutting-edge solutions to a wide range of problems faced by the industry, i.e. combinatorial optimisation, encryption and security, machine learning, simulation processes, chemistry and strategic consulting for Quantum adoption and implementation.