Quantum Computation of Electronic Transitions Using a Variational Quantum Eigensolver

Abstract

We develop an extension of the variational quantum eigensolver (VQE) algorithm -multistate, contracted VQE (MC-VQE) -that allows for the efficient computation of the transition energies between the ground state and several low-lying excited states of a molecule, as well as the oscillator strengths associated with these transitions. We numerically simulate MC-VQE by computing the absorption spectrum of an ab initio exciton model of an 18-chromophore light-harvesting complex from purple photosynthetic bacteria.The accurate modeling of the many-body interactions in the ground and excited-state solutions of the electronic Schrödinger equation is a prerequisite for the quantitative prediction of molecular physical phenomena such as light harvesting. Using classical computers, this problem scales formally as the factorial of the number of involved electrons [1], via the solution of the full configuration interaction (FCI) equations, though many polynomialscaling approximations such as density functional theory [2][3][4][5] (DFT), coupled cluster theory [6-9] (CC), density matrix renormalization group [10,11] (DMRG), adaptive and/or stochastic configuration interation methods [12][13][14][15][16][17][18] (CIPSI and variants), and semistochastic coupled cluster methods [19,20], have been developed to combat this problem. Recently, there has been a surge of interest in using quantum computers to naturally solve the many-body electronic structure problem through methods such as the iterative phase estimation algorithm [21][22][23][24][25][26] (IPEA) or the variational quantum eigensolver [27][28][29][30][31][32] (VQE), However, the quartic-scaling complexity in number of molecular orbitals of the second-quantized electronic Hamiltonian, coupled with the overhead of encoding the fermionic antisymmetry of the electrons through the Jordan-Wigner [33, 34] (JW), 36] (KB), or superfast Bravyi-Kitaev [37, 38] (SFKB) transformations, implies that rather long circuit depths will be required to directly model the electronic structure problem. We also point out a recent approach [39][40][41] that might formally reduce this complexity to quadratic or linear via a tensor hypercontraction representation [42][43][44] of the potential. In the present work, we explore a domain-and problem-specific means to reduce the complexity of the representation of the electronic structure problem in quantum computing: an ab initio exciton model [45][46][47][48][49]. For large-scale photoactive complexes consisting of a number of nonbonded chromophore units, the ab initio exciton model compresses the details of the electronic structure on each chromophore into a handful of monomer electronic states. The determination of the full configuration interaction wavefunctions describing the mixing of monomer electronic states in the full complex remains a formidable task -here we show that this might be a natural computational task for a nearterm quantum computer.Another area that deserves exploration is the development of efficient quantum algorithms for the ...

Increasing the Representation Accuracy of Quantum Simulations of Chemistry without Extra Quantum Resources

“…These methods exhibit a natural adaptation to device parameters as well as intrinsic robustness to systematic errors that make them attractive candidates. Since their inception, they have been extended to treat excited states [25][26][27] and different problem areas [28,29], and have been demonstrated on numerous experimental architectures [22,26,[30][31][32][33].…”

A non-orthogonal variational quantum eigensolver

“…The θ (i) values that parametrize each basis function φ i (θ (i) ) can then be optimized by a classical outer loop to lower the energy further, solving a new generalized eigenvalue problem at each step. Our approach shares similarities with recent work in NISQ-era variational algorithms that involve solving generalized eigenvalue problems [16,22,23], as well as a technique from classical quantum chemistry known as non-orthogonal configuration interaction [24][25][26] (NOCI). However, our approach also differs from this work in some key respects.…”

“…Most importantly, we make no assumptions about the form of the component wavefunctions |φ i , other than that they have efficient quantum circuit implementations. In the context of quantum algorithms, prior work has assumed that these wavefunctions are generated by excitations from a fixed reference state [16], by imaginary time evolution [22], or by the simultaneous rotation of a set of orthogonal reference wavefunctions [23].…”

Angewandtes Quantencomputing

“…Nach diesem Prinzip arbeiten die derzeit vielversprechendsten Algorithmen -z. B. VQE (Variational Quantum Eigensolver) [12], verschiedene QNN-Varianten (Quan-Abb. 1 Schematische Darstellung des Prinzips der hybriden quantenklassischen Algorithmen.…”