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Register a new userCorrelating the Antisymmetrized Geminal Power Wave Function
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Strong pairing correlations are responsible for superconductivity and off-diagonal long range order in the two-particle density matrix. The antisymmetrized geminal power wave function was championed many years ago as the simplest model that can provide a reasonable qualitative description for these correlations without breaking number symmetry. The fact remains, however, that the antisymmetrized geminal power is not generally quantitatively accurate in all correlation regimes. In this work, we discuss how we might use this wave function as a reference state for a more sophisticated correlation technique such as configuration interaction, coupled cluster theory, or the random phase approximation.
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The antisymmetrized geminal power (AGP) wavefunction has a long history and is known by different names in various chemical and physical problems. There has been recent interest in using AGP as a starting point for strongly correlated electrons. Here, we show that in a seniority-conserving regime, different AGP based correlator representations based on generators of the algebra, killing operators, and geminal replacement operators are all equivalent. We implement one representation that uses number operators as correlators and has linearly independent curvilinear metrics to distinguish the regions of Hilbert space. This correlation method called J-CI, provides excellent accuracy in energies when applied to the pairing Hamiltonian.
We present a wave function representation for the canonical ensemble thermal density matrix by projecting the thermofield double state against the desired number of particles. The resulting canonical thermal state obeys an imaginary time-evolution equation. Starting with the mean-field approximation, where the canonical thermal state becomes an antisymmetrized geminal power wave function, we explore two different schemes to add correlation: by number-projecting a correlated grand-canonical thermal state, and by adding correlation to the number-projected mean-field state. As benchmark examples, we use number-projected configuration interaction and an AGP-based perturbation theory to study the Hydrogen molecule in a minimal basis and the six-site Hubbard model.
We developed a new variational method for tensor-optimized antisymmetrized molecular dynamics (TOAMD) for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion are introduced and used in the power series form of the wave function, which is different from the Jastrow method. Here, nucleon pairs are correlated in multi-steps with different forms, while they are correlated only once including all pairs in the Jastrow correlation method. Each correlation function in every term is independently optimized in the variation of total energy in TOAMD. For $s$-shell nuclei using the nucleon-nucleon interaction, the energies in TOAMD are better than those in the variational Monte Carlo method with the Jastrow correlation function. This means that the power series expansion using the correlation functions in TOAMD describes the nuclei better than the Jastrow correlation method.
For variational algorithms on the near term quantum computing hardware, it is highly desirable to use very accurate ansatze with low implementation cost. Recent studies have shown that the antisymmetrized geminal power (AGP) wavefunction can be an excellent starting point for ansatze describing systems with strong pairing correlations, as those occurring in superconductors. In this work, we show how AGP can be efficiently implemented on a quantum computer with circuit depth, number of CNOTs, and number of measurements being linear in system size. Using AGP as the initial reference, we propose and implement a unitary correlator on AGP and benchmark it on the ground state of the pairing Hamiltonian. The results show highly accurate ground state energies in all correlation regimes of this model Hamiltonian.
The determination of the ground state of quantum many-body systems via digital quantum computers rests upon the initialization of a sufficiently educated guess. This requirement becomes more stringent the greater the system. Preparing physically-motivated ans{a}tze on quantum hardware is therefore important to achieve quantum advantage in the simulation of correlated electrons. In this spirit, we introduce the Gutzwiller Wave Function (GWF) within the context of the digital quantum simulation of the Fermi-Hubbard model. We present a quantum routine to initialize the GWF that comprises two parts. In the first, the noninteracting state associated with the $U = 0$ limit of the model is prepared. In the second, the non-unitary Gutzwiller projection that selectively removes states with doubly-occupied sites from the wave function is performed by adding to every lattice site an ancilla qubit, the measurement of which in the $|0rangle$ state confirms the projection was made. Due to its non-deterministic nature, we estimate the success rate of the algorithm in generating the GWF as a function of the lattice size and the interaction strength $U/t$. The scaling of the quantum circuit metrics and its integration in general quantum simulation algorithms are also discussed.
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