(Physics.aps) A specialized algorithm is needed to realize the quantum advantage of quantum computers. Perhaps the most promising application for such algorithms is the simulation of quantum systems like molecules or materials, though an ongoing challenge is to design algorithms that can be run in a practical amount of time.
An approach proposed by Earl Campbell of the University of Sheffield in the UK could speed up the simulation of certain molecules [1]. His algorithm uses a random—as opposed to deterministic—sequence of operations. It may outperform other approaches when a molecule’s energy is determined by many small contributions, and Campbell considers propane, carbon-dioxide, and ethane as test cases.
The kind of simulation Campbell considers is one where you know the allowed orbitals on a molecule and want to figure out the way electrons occupy them. This occupancy involves superpositions of electron configurations that can vary with time. Mathematically, this time evolution is obtained from an exponential of the molecule’s Hamiltonian, which is given by a sum of terms, each corresponding to a different contribution to the molecule’s energy.

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