Band theory on a quantum computer

K.G. Nichols, E. V. Vernon

Yi Fan, Jie Liu, Zhenyu Li +1 more

Band structure is a cornerstone to understand the electronic properties of materials. Accurate band structure calculations using a high-level quantum chemistry theory can be computationally very expensive. It is promising to speed up such calculations with a quantum computer. In this study, we present a quantum algorithm for band structure calculations based on the equation-of-motion (EOM) theory. First, we introduce a new variational quantum eigensolver algorithm named ADAPT-C for ground-state quantum simulation of solids, where the wave function is built adaptively from a complete set of anti-Hermitian operators. Then, on top of the ADAPT-C ground state, quasiparticle energies and the band structure can be calculated using the EOM theory in a quantum-subspace-expansion style, where the projected excitation operators guarantee that the killer condition is satisfied. As a proof of principle, such an EOM-ADAPT-C protocol is used to calculate the band structures of silicon and diamond using a quantum computer simulator.

Kyle Sherbert, Frank Cerasoli, Marco Buongiorno Nardelli

of tight-binding orbitals per unit-cell, similarly to its classical counterparts. Our simulations offer a new insight into the "quantum" mindset and demonstrate how the algorithms under active development today can be optimized in special cases, such as band structure calculations.

Alicia J. Kollár, Mattias Fitzpatrick, Peter Sarnak +1 more

Nicholas M. Harrison

John Charlton Polkinghorne

‘Further developments’ outlines some of the insights provided during the long developmental period after the mid-1920s in which the implications of quantum theory were explored and exploited. Firstly, the concepts of tunnelling, bose statistics, and fermi statistics are described, followed by a discussion on band structure and delayed choice experiments. Richard Feynman's way of reformulating quantum theory is discussed along with more about dechoerence. Paul Dirac's contributions in the form of relativistic quantum theory and quantum theory are then explained. Finally, quantum computing — the possibility of exploiting the superposition principle as a means for gaining greatly enhanced computing power — is reviewed.