State preparation of AGP on a quantum computer without number projection

The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen-Cooper-Schrieffer (PBCS) wavefunction. It is also an elementary symmetric polynomial (ESP) state. We generalize previous research on deterministically implementing the Dicke state to a state preparation algorithm for an ESP state, or equivalently AGP, on a quantum computer. Our method is deterministic and has polynomial cost, and it does not rely on number symmetry breaking and restoration. We also show that our circuit is equivalent to a disentangled unitary paired coupled cluster operator and a layer of unitary Jastrow operator acting on a single Slater determinant. The method presented herein highlights the ability of disentangled unitary coupled cluster to capture non-trivial entanglement properties that are hardly accessible with traditional Hartree-Fock based electronic structure methods.Comment: 11 pages, 6 figure

AGP-based unitary coupled cluster theory for quantum computers

Electronic structure methods typically benefit from symmetry breaking and restoration, specially in the strong correlation regime. The same goes for Ans\"atze on a quantum computer. We develop a unitary coupled cluster method on the antisymmetrized geminal power (AGP) -- a state formally equivalent to the number-projected Bardeen--Cooper--Schrieffer wavefunction. We demonstrate our method for the single-band Fermi--Hubbard Hamiltonian in one and two dimensions. We also explore post-selection as a state preparation step to obtain correlated AGP and prove that it scales no worse than $\mathcal{O}(\sqrt{M})$ in the number of measurements, thereby making it a less expensive alternative to gauge integration to restore particle number symmetry

Correlated pair ansatz with a binary tree structure

We develop an efficient algorithm to implement the recently introduced binary tree state (BTS) ansatz on a classical computer. BTS allows a simple approximation to permanents arising from the computationally intractable antisymmetric product of interacting geminals and respects size-consistency. We show how to compute BTS overlap and reduced density matrices efficiently. We also explore two routes for developing correlated BTS approaches: Jastrow coupled cluster on BTS and linear combinations of BT states. The resulting methods show great promise in benchmark applications to the reduced Bardeen-Cooper-Schrieffer Hamiltonian and the one-dimensional XXZ Heisenberg Hamiltonian.Comment: 12 pages, 10 figure

Even-odd layer-dependent magnetotransport of high-mobility Q-valley electrons in transition metal disulfides

In few-layer transition metal dichalcogenides (TMDCs), the conduction bands along the ΓK directions shift downward energetically in the presence of interlayer interactions, forming six Q valleys related by threefold rotational symmetry and time reversal symmetry. In even layers, the extra inversion symmetry requires all states to be Kramers degenerate; whereas in odd layers, the intrinsic inversion asymmetry dictates the Q valleys to be spin-valley coupled. Here we report the transport characterization of prominent Shubnikov-de Hass (SdH) oscillations and the observation of the onset of quantum Hall plateaus for the Q-valley electrons in few-layer TMDCs. Universally in the SdH oscillations, we observe a valley Zeeman effect in all odd-layer TMDC devices and a spin Zeeman effect in all even-layer TMDC devices, which provide a crucial information for understanding the unique properties of multi-valley band structures of few-layer TMDCs