The Variational Quantum Eigensolver algorithm can be generalized to study a non-normalized wavefunction by applying a non-unitary quantum operator that is computed in the classical computer during the optimization procedure. Effectively, this procedure simply requires measuring more Pauli-matrix strings during the optimization. The non-unitary variational operator contains variational parameters, so we are able to tune these parameters to obtain a lower energy.<br/>We implement a non-unitary operator in a way that is inspired by the Jastrow factor in Quantum Monte Carlo. This Jastrow operator has one variational parameter for each qubit and one for each pair of qubits, and with these parameters it can model additional correlations between the qubits.<br/>We show that with this linearized Jastrow operator the extended non-unitary VQE converges to the ground state energy of water with fewer entangling blocks, i.e. fewer CNOT gates. Hence this method allows to reduce the circuit depth to compute the ground state energy of a molecule using the VQE, at the cost of measuring more Pauli-matrix strings. This tradeoff can be valuable especially with the current NISQ devices. The number of additional measurements grows only quartically with the number of qubits.<br/>This method works with any qubit mapping type, and scales well with the number of qubits, so it is applicable to any molecule. The recovered correlation energy increases faster with increasing the number of entangling blocks in the wavefunction than it does for the regular VQE.

Quantum Monte Carlo-inspired wavefunctions for improved convergence in the VQE algorithm

Macromolecular Chemistry: The Second Century

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ACS Spring 2020 National Meeting & Expo

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.