Vibrational ADAPT-VQE: Critical points lead to problematic convergence.

Quantum chemistry is one of the most promising applications for which quantum computing is expected to have a significant impact. Despite considerable research in the field of electronic structure, calculating the vibrational properties of molecules on quantum computers remains a relatively unexplored field. In this work, we develop a vibrational Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (vADAPT-VQE) formalism based on an infinite product representation (IPR) of anti-Hermitian excitation operators of the Full Vibrational Configuration Interaction (FVCI) wavefunction, which allows for preparing eigenstates of vibrational Hamiltonians on quantum computers. In order to establish the vADAPT-VQE algorithm using the IPR, we study the exactness of disentangled Unitary Vibrational Coupled Cluster (dUVCC) theory and show that dUVCC can formally represent the FVCI wavefunction in an infinite expansion. To investigate the performance of the vADAPT-VQE algorithm, we numerically study whether the vADAPT-VQE algorithm generates a sequence of operators that may represent the FVCI wavefunction. Our numerical results indicate frequent appearance of critical points in the wavefunction preparation using vADAPT-VQE. These results imply that one may encounter diminishing usefulness when preparing vibrational wavefunctions on quantum computers using vADAPT-VQE and that additional studies are required to find methods that can circumvent this behavior.

Optimizing the number of measurements for vibrational structure on quantum computers: coordinates and measurement schemes.

One of the primary challenges prohibiting demonstrations of practical quantum advantages for near-term devices amounts to excessive measurement overheads for estimating relevant physical quantities such as ground state energies. However, with major differences between the electronic and vibrational structures of molecules, the question of how the resource requirements of computing anharmonic, vibrational states can be reduced remains relatively unexplored compared to its electronic counterpart. Importantly, bosonic commutation relations, distinguishable Hilbert spaces and vibrational coordinates allow manipulations of the vibrational system that can be exploited to minimize resource requirements. In this work, we investigate the impact of different coordinate systems and measurement schemes on the number of measurements needed to estimate anharmonic, vibrational states for a variety of three-mode (six-mode) molecules. We demonstrate an average of 3-fold (1.5-fold), with up to 7-fold (2.5-fold), reduction in the number of measurements required by employing appropriate coordinate transformations, based on an automized construction of qubit Hamiltonians from a conventional vibrational structure program.

Quantum Maxwell's demon assisted by non-Markovian effects.

Maxwell's demon is the quintessential example of information control, which is necessary for designing quantum devices. In thermodynamics, the demon is an intelligent being who utilizes the entropic nature of information to sort excitations between reservoirs, thus lowering the total entropy. So far, implementations of Maxwell's demon have largely been limited to Markovian baths. In our work, we study the degree to which such a demon may be assisted by non-Markovian effects using a superconducting circuit platform. The setup is two baths connected by a demon-controlled qutrit interface, allowing the transfer of excitations only if the overall entropy of the two baths is lowered. The largest entropy reduction is achieved in a non-Markovian regime and, importantly, due to non-Markovian effects, the demon performance can be optimized through proper timing. Our results demonstrate that non-Markovian effects can be exploited to boost the information transfer rate in quantum Maxwell demons.