We develop a resource-efficient step-merged quantum imaginary time evolution approach (smQITE) to solve for the ground state of a Hamiltonian on quantum computers. This heuristic method features a fixed shallow quantum circuit depth along the state evolution path. We use this algorithm to determine the binding energy curves of a set of molecules, including H2, H4, H6, LiH, HF, H2O, and BeH2, and find highly accurate results. The required quantum resources of smQITE calculations can be further reduced by adopting the circuit form of the variational quantum eigensolver (VQE) technique, such as the unitary coupled cluster ansatz. We demonstrate that smQITE achieves a similar computational accuracy as VQE at the same fixed-circuit ansatz, without requiring a generally complicated high-dimensional nonconvex optimization. Finally, smQITE calculations are carried out on Rigetti quantum processing units, demonstrating that the approach is readily applicable on current noisy intermediate-scale quantum devices.
A necessary condition for superconductivity (SC) driven by electron correlations is that electron-electron (e-e) interactions enhance superconducting pair-pair correlations, relative to the noninteracting limit. We report high-precision numerical calculations of the ground state within the frustrated two-dimensional (2D) Hubbard Hamiltonian for a wide range of carrier concentration ρ (0 < ρ < 1) per site. We find that long range superconducting pair correlations are enhanced only for ρ 0.5. At all other fillings e-e interactions mostly suppress pair correlations. The enhancement of pair correlations is driven by the strong tendency to local singlet bond formation and spin gap (SG) in ρ = 0.5, in lattices with quantum fluctuation [1][2][3] . We also report determinantal quantum Monte Carlo (DQMC) calculations that are in strong agreement with our ground state results. Our work provides a key ingredient to the mechanism of SC in the 2D organic charge-transfer solids (CTS), and many other unconventional superconductors with frustrated crystal lattices and ρ 0.5, while explaining the absence of SC in structurally related materials with substantially different ρ.The possibility that e-e interactions can be the driving force behind SC in correlated-electron systems has been intensely investigated since the discovery of SC in the high T c cuprates. The minimal requirements for a complete theory are, (i) the superconducting pair correlations are enhanced by e-e interactions, and (ii) pair correlations are long range. For moderate to large e-e interactions, pair correlations are perhaps best calculated numerically, which however can be done only for finite clusters. The simplest model incorporating e-e interactions is usually assumed to be the Hubbard model, which in quite general form can be written asAll terms in Eq. 1 have their standard meaning. The first sum is the kinetic energy of noninteracting electrons within a 2D tight-binding model with hopping matrix elements t ij ; U and V ij are onsite and nearest neighbor (n.n.) Coulomb interactions respectively. Existing numerical calculations within Eq. 1 on 2D lattices have failed to find enhancement of pair-pair correlations relative to the noninteracting model without making severe approximations 4 . It has sometimes been surmised that correlated-electron SC might evolve upon doping a spin-gapped semiconductor, as would occur in toy models such as a 2D lattice consisting of weakly coupled even-leg ladders 5,6 . Finding realistic 2D models with SG and enhanced pair correlations however remains challenging. In the present work we demonstrate from explicit numerical calculations on frustrated 2D lattices enhanced pair correlations evolving from a spin-gapped state at a carrier density ρ 0.5, far from the region most heavily investigated until now (0.7 < ρ < 1.0). We further point out the strong relevance of the resulting theoretical picture to real materials, in particular the 2D CTS superconductors, which were discovered earlier than the cuprates 7 but are still not un...
An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near‐term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan distance is constrained by the quality of the ansatz, the AVQITE method iteratively expands the ansatz along the dynamical path to keep the McLachlan distance below a chosen threshold. This ensures the state is able to follow the quantum imaginary time evolution path in the system Hilbert space rather than in a restricted variational manifold set by a predefined fixed ansatz. AVQITE is used to prepare ground states of H4, H2O, and BeH2 molecules, where it yields compact variational ansätze and ground state energies within chemical accuracy. Polynomial scaling of circuit depth with system size is shown through a set of AVQITE calculations of quantum spin models. Finally, quantum Lanczos calculations are demonstrated alongside AVQITE without additional quantum resource costs.
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