Localized Quantum Chemistry on Quantum Computers

Abstract

Quantum chemistry calculations of large, strongly correlated systems are typically limited by the computation cost that scales exponentially with the size of the system. Quantum algorithms, designed specifically for quantum computers, can alleviate this, but the resources required are still too large for today’s quantum devices. Here we present a quantum algorithm that combines a localization of multireference wave functions of chemical systems with quantum phase estimation (QPE) and variational unitary coupled cluster singles and doubles (UCCSD) to compute their ground state energy. Our algorithm, termed “local active space unitary coupled cluster” (LAS-UCC), scales linearly with system size for certain geometries, providing a polynomial reduction in the total number of gates compared with QPE, while providing accuracy above that of the variational quantum eigensolver using the UCCSD ansatz and also above that of the classical local active space self-consistent field. The accuracy of LAS-UCC is demonstrated by dissociating (H2)2 into two H2 molecules and by breaking the two double bonds in trans-butadiene and resources estimates are provided for linear chains of up to 20 H2 molecules.

Perspective on the Current State-of-the-Art of Quantum Computing for Drug Discovery Applications

“…Finally, it should be mentioned that a number of embedding methods have already been proposed for use with quantum computers in an attempt to reduce the heavy resource requirements. Local approaches to active space construction have been recently proposed and applied to quantum computing . The quantum variants of dynamical mean field theory and density matrix embedding theory (DMET) were published some years ago, and costing studies are also available for DMET .…”

“…Local approaches to active space construction have been recently proposed 127 and applied to quantum computing. 128 The quantum variants of dynamical mean field theory 129 and density matrix embedding theory (DMET) 130 were published some years ago, and costing studies are also available for DMET. 131 Energy-weighted DMET 132 and Gutzwiller variational embedding 133 approaches have been tested on current quantum processors.…”

Statistical errors in reduced density matrices sampled from quantum circuit simulation and the impact on multireference perturbation theory

“…Simulation of the Hamiltonian for strongly entangled quantum systems is widely regarded as a promising application 10–18 in both noisy intermediate-scale quantum (NISQ) devices 19–24 and fault-tolerant quantum computers (FTQC), 25–28 which has the potential to enable calculations for large CAS wavefunctions that are difficult to achieve with classical computers. By associating an electronic configuration in the active space with an eigenstate of qubits, it is possible to map a CAS wavefunction onto a superposition state of qubits; the required number of qubits is equal to the number of spin–orbitals in the active space.…”