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Register a new userConstruction of linearly independent non-orthogonal AGP states
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We show how to construct a linearly independent set of antisymmetrized geminal power (AGP) states, which allows us to rewrite our recently introduced geminal replacement models as linear combinations of non-orthogonal AGPs. This greatly simplifies the evaluation of matrix elements and permits us to introduce an AGP-based selective configuration interaction method, which can reach arbitrary excitation levels relative to a reference AGP, balancing accuracy and cost as we see fit.
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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.
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.
Spin-momentum locking is a unique feature of spin-orbit coupled materials and a key to their promise of applications in spintronics and quantum computation. Much of the existing work has been focused on an orthogonal locking between the directions of spin and momentum vectors in the context of both topological and non-topological materials. Mechanisms responsible for non-orthogonal spin-momentum locking (NOSML) have drawn little attention, although an NOSML effect has been reported on the topological surface of $alpha$-$Sn$. Here, we demonstrate how spin-orbit scattering from non-magnetic impurities can produce the NOSML state. The parameter describing spin-orbit coupling strength in our analysis of the NOMSL could be extracted directly from the spin-resolved angle-resolved photoemission (S-ARPES) spectra. Our formalism is applicable to all spin-orbit coupled systems and not limited only to topological states. An understanding of NOSML effects bears on spin-orbit dependent phenomena more generally, including issues of spin-to-charge conversion and the interpretation of quasiparticle interference (QPI) patterns and scanning-tunneling spectra (STS) in materials.
We propose an exact model of anyon ground states including higher Landau levels, and use it to obtain fractionally quantized Hall states at filling fractions $ u=p/(p(m-1)+1)$ with $m$ odd, from integer Hall states at $ u=p$ through adiabatic localization of magnetic flux. For appropriately chosen two-body potential interactions, the energy gap remains intact during the process. The construction hence establishes the existence of incompressible states at these fillings.
Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal. We develop a general description of such a quantum walk and show how to map it into a standard one with orthogonal states, thereby making available all the tools developed for the latter. This enables a variety of experiments, which can be implemented with smaller step sizes and more steps. Tuning the non-orthogonality allows for an easy preparation of extended states such as momentum eigenstates, which travel at a well-defined speed with low dispersion. We introduce a method to adjust their velocity by momentum shifts, which allows to investigate intriguing effects such as the analog of Bloch oscillations.
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