Reducing qubit requirements while maintaining numerical precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach

Abstract

We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wavefunctions. Our approach directly determines system-specific representations of qubit Hamiltonians while fully omitting globally defined basis sets. In this work, we use directly determined pair-natural orbitals on the level of second-order perturbation theory. This results in compact qubit Hamiltonians with high numerical accuracy. We demonstrate initial applications with compact Hamiltonians on up to 20 qubits where conventional representation would for the same systems require 40-100 or more qubits.

A Feasible Approach for Automatically Differentiable Unitary Coupled-Cluster on Quantum Computers

“…Our strategies to compile gradients can be done entirely in the fermionic representation making it independent of the used qubit mapping. The developed techniques combined with tequilas automatic differentiation framework provide a testbed for quantum chemistry on quantum computers where new ideas, like low-depth approaches based on pair-natural orbitals [48] or Krylov subspaces [67,68], can be prototyped and demonstrated in a blackboard fashion. Our implementation provides an easy to use, automatically differentiable framework for unitary-coupled cluster, that leverages state of the art high performance simulators [52,53] and is ready for emerging quantum computers.…”

“…Our implementation is available within the free to use and open-source tequila [29] package. The improved gradient evaluation schemes are automatically applied to already implemented methods like UpCCGSD [47] that was employed in previously developed basis-set-free methods [48] and as an application for the meta-VQE [49] approach. Apart from already existing implementations, the developed schemes can be employed for the development of new unitary coupledcluster approaches in a blackboard style fashion.…”

“…Combined with the qubit-compressed, low-depth approaches of Ref. [48] successful demonstration on emerging quantum computers can however be anticipated. For the results of this work we interfaced qulacs [52] as simulation backend, the BFGS implementation of scipy [57], molecular integrals from psi4 [58] and qubit encodings from openfermion [54].…”

Mutual information-assisted adaptive variational quantum eigensolver

“…Hamiltonian by a surrogated basis-set-free approach called MRA-PNO-MP2 [28] according to reference [39] using Tequila [40] with MADNESS [41] as backend. The active orbitals that define the qubit Hamiltonian are two occupied Hartree-Fock orbitals and four optimized pair-natural orbitals on MP2 level.…”

“…After tapering one stationary qubit by the BK transformation, the qubit Hamiltonian of the system contains 11 qubits. Adaptive ansatz construction on Hamiltonian generated in this way have been studied in a previous work [39] and here we apply our method with both the QCC pool and the qubit fermionic-excitation pool on it. The latter was first proposed in the qubit-ADAPT-VQE method [22] and here we define it as the pool containing all the entanglers {e −i Pi t } whose Pauli words { Pi } appear in the transformed set of fermionic operators {a † q a † p a r a s − a † s a † r a p a q } ∪ {a † q a p − a † p a q } with q, p, r, s going over the indices of all the spin-orbitals.…”