Relatore: Leonardo Guidoni (Università de L’Aquila)
Quantum Computers can be used to perform Quantum Chemistry calculations by energy evaluation of variational wavefunction on the molecular Hamiltonian. One of the mostly used approach is the Variational Quantum Eigensolver algorithm which can be used to investigate the ground states of small molecular systems. We propose a generalization of the VQE algorithm to study a non-normalized wavefunction by applying a nonunitary quantum operator that is computed in the classical computer during the optimization procedure. In practice, 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.
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.
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 Noisy Intermediate-Scale Quantum computer. The number of additional measurements grows only quartically with the number of qubits.
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.