Correlated Reference-Assisted Variational Quantum Eigensolver

Abstract

We propose an active-space approximation to reduce the quantum resources required for variational quantum eigensolver (VQE). Starting from the double exponential unitary coupled-cluster ansatz and employing the downfolding technique, we arrive at an effective Hamiltonian for active space composed of the bare Hamiltonian and a correlated potential caused by the internal-external interaction. The correlated potential is obtained from the one-body second-order Møller–Plesset perturbation theory (OBMP2), which is derived using the canonical transformation and cumulant approximation. Considering different systems with singlet and doublet ground states, we examine the accuracy in predicting both energy and density matrix (by evaluating dipole moment). We show that our approach can dramatically outperform the active-space VQE with an uncorrelated Hartree–Fock reference.

Variational Quantum Eigensolver Boosted by Adiabatic Connection

“…The orbital rotation (unitary change of MO basis) can be expressed as an exponential of an antihermitian operator, κ: 65 = U( ) e (23) where…”

“…Since the structure of the UCC single excitations is identical to the orbital rotation operator (23), it can be absorbed into the classical orbital-optimization routine, which was briefly described above, and only the double excitations remain in the UCC cluster operator (7). 61 This method is denoted as OO-UCCD.…”

“…The existing approaches can be classified into two categories. The first is based on the dimensionality reduction of the many-body Hamiltonians used in quantum algorithms, which includes, for example, the theory of transcorrelated Hamiltonians or downfolding methods. − Recently, the quantum flow algorithm, which is based on the equivalence theorem, was presented and combined with the downfolding methods . The huge advantage of this approach is that it transforms the original large CAS problem into coupled smaller CAS problems, which are solved self-consistently.…”

Reaching High Accuracy for Energetic Properties at Second-Order Perturbation Cost by Merging Self-Consistency and Spin-Opposite Scaling

“…In general, developing new methods based on low-cost perturbation theory that can deal with challenging systems is still highly desirable. Recently, we have developed a new self-consistent perturbation theory named one-body MP2 (OBMP2). − The key idea of OBMP2 is the use of canonical transformation − followed by the cumulant approximation − to derive an effective one-body Hamiltonian. The resulting OBMP2 Hamiltonian is a sum of the standard Fock operator and a one-body correlation MP2 potential.…”

Physical Chemistry of Quantum Information Science

“…We investigate the topic of quantum algorithms tailored for quantum chemistry, molecular dynamics, and statistical mechanics. This includes a quest to enhance the accuracy of classical computations for difficult chemistry problems involving strongly correlated systems in the works by A. Tammaro et al., A. Khamoshi et al, and N. T. Le and L. N. Tran., and calculations of excited states in articles by Y. Kim and A. I. Krylov and by T. Yoshikura et al Outstanding problems of quantum state preparation were discussed by I. Magoulas and F. A. Evangelista, S. G. Mehendale et al, S. E. Ghasempouri et al, J. H. Zhang et al., and L. M. Sager-Smith et al, for near-term quantum algorithms. An equally important topic of quantum measurement is touched upon by Z. P. Bansingh et al and T. Kurita et al In addition, Hamiltonian learning from quantum dynamics is presented by R. Gupta et al, and an interesting and accessible approach to visualization of quantum algorithms is described by I. Ganti and S. S. Iyengar …”