Quantum-classical hybrid algorithm using an error-mitigating N -representability condition to compute the Mott metal-insulator transition

Abstract

Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence, connectivity and gate errors required for their experimental realization. Here we propose a class of quantumclassical hybrid algorithms that compute the energy from a two-electron reduced density matrix (2-RDM). The 2-RDM is constrained by N-representability conditions, conditions for representing an N-electron wave function, that mitigates noise from the quantum circuit. We compute the strongly correlated dissociation of doublet H3 into three hydrogen atoms. The hybrid quantum-classical computer matches the energies from full configuration interaction to 0.1 kcal/mol, one-tenth of "chemical accuracy," even in the strongly correlated limit of dissociation. Furthermore, the spatial locality of the computed one-electron RDM reveals that the quantum computer accurately predicts the Mott metal-insulator transition.

Quantum simulations of materials on near-term quantum computers

“…Quantum computers hold promise to enable efficient quantum mechanical simulations of weakly and strongly-correlated molecules and materials alike [8][9][10][11][12][13][14][15][16][17] ; in particular when using quantum computers, one is able to simulate systems of interacting electrons exponentially faster than using classical computers. Thanks to decades of successful experimental efforts, we are now entering the noisy intermediate-scale quantum (NISQ) era 18 , with quantum computers expected to have on the order of 100 quantum bits (qubits); unfortunately this limited number of qubits still prevents straightforward quantum simulations of realistic molecules and materials, whose description requires hundreds of atoms and thousands to millions of degrees of freedom to represent the electronic wavefunctions.…”

Efficient two-electron ansatz for benchmarking quantum chemistry on a quantum computer

“…The method of symmetry verification for error mitigation is useful in that its different forms are low cost and can easily correct flagrant faults in the output, such as particle count (or more generally, parity) and the projected spin symmetries. Other forms of error mitigation related to the RDMs can be implemented as constraints on the tomography from N representability, or in a form of postcorrection of the twoelectron RDM, where the measured 2RDM is purified through semidefinite programming, which can be applied to arbitrary N-electron systems [40]. Additionally, the mapping we use can have difficulties when errors begin to change the ordering of occupations for larger and larger systems.…”

“…Again, we are able to obtain chemically accurate energies across the dissociation curve, although there is difficulty in sampling the uncorrelated Hartree-Fock state which is a vertex of the polytope. The error mitigation techniques we use also extend the capabilities of noise-limited quantum computers, which otherwise do not span the ideal N representability of the state [40].…”

“…The error correction is similar to previous work where we look for a transformation A to map the experimental polytope S to the correct polytope S [40]. The structure of the N-representability conditions is such that the ordering inequalities applied to each of the half sets ({n i } and {n i }) describe a hyperplane.…”

Simulating the electronic structure of spin defects on quantum computers

“…Whether one can achieve quantum advantage in solving useful chemistry and physics problems on quantum computers is still under debate. However, efforts to develop algorithms to simulate molecules and solids on quantum computers have been flourishing in the last decade, and several interesting results on ground and excited states of small molecular systems (containing up to a dozen atoms) have appeared in the literature [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”